diff --git a/.gitignore b/.gitignore new file mode 100644 index 00000000..c13ccf89 --- /dev/null +++ b/.gitignore @@ -0,0 +1,30 @@ +# Logs +logs +*.log + +# Runtime data +pids +*.pid +*.seed + +# Directory for instrumented libs generated by jscoverage/JSCover +lib-cov + +# Coverage directory used by tools like istanbul +coverage + +# Grunt intermediate storage (http://gruntjs.com/creating-plugins#storing-task-files) +.grunt + +# Compiled binary addons (http://nodejs.org/api/addons.html) +build/Release + +# Dependency directory +# Deployed apps should consider commenting this line out: +# see https://npmjs.org/doc/faq.html#Should-I-check-my-node_modules-folder-into-git +node_modules + +_book/ +book.pdf +book.epub +book.mobi diff --git a/README.html b/README.html new file mode 100644 index 00000000..31ed3782 --- /dev/null +++ b/README.html @@ -0,0 +1,226 @@ + + + + +机器学习课程简介 + + +

斯坦福大学2014机器学习教程中文笔记

课程目录：目录

课程地址：https://www.coursera.org/course/ml

Machine Learning(机器学习)是研究计算机怎样模拟或实现人类的学习行为，以获取新的知识或技能，重新组织已有的知识结构使之不断改善自身的性能。它是人工智能的核心，是使计算机具有智能的根本途径，其应用遍及人工智能的各个领域，它主要使用归纳、综合而不是演译。在过去的十年中，机器学习帮助我们自动驾驶汽车，有效的语音识别，有效的网络搜索，并极大地提高了人类基因组的认识。机器学习是当今非常普遍，你可能会使用这一天几十倍而不自知。很多研究者也认为这是最好的人工智能的取得方式。在本课中，您将学习最有效的机器学习技术，并获得实践，让它们为自己的工作。更重要的是，你会不仅得到理论基础的学习，而且获得那些需要快速和强大的应用技术解决问题的实用技术。最后，你会学到一些硅谷利用机器学习和人工智能的最佳实践创新。

本课程提供了一个广泛的介绍机器学习、数据挖掘、统计模式识别的课程。主题包括：（一）监督学习（参数/非参数算法，支持向量机，核函数，神经网络）。（二）无监督学习（聚类，降维，推荐系统，深入学习推荐）。（三）在机器学习的最佳实践（偏差/方差理论；在机器学习和人工智能创新过程）。本课程还将使用大量的案例研究，您还将学习如何运用学习算法构建智能机器人（感知，控制），文本的理解（Web搜索，反垃圾邮件），计算机视觉，医疗信息，音频，数据挖掘，和其他领域。

本课程需要10周共18节课，相对以前的机器学习视频，这个视频更加清晰，而且每课都有ppt课件，推荐学习。

本人2014年下半年开始翻译本课程字幕，并写了课程的中文笔记。笔记被下载了几万次，应该帮助了不少人，也有很多人一直在帮助我，现在我把笔记的word原稿和markdown原稿分享给大家。

markdown的笔记和课程中英文字幕我将放在github和码云，希望大家能继续完善。为方便数学公式的在线显示，在线观看的是html文件，公式已经被转为图片，公式源码在markdown文件。

最后想对各位朋友说： +赠人玫瑰，手有余香！ +在人工智能的道路上，你不是一个人在战斗！

黄海广

2017-11-3 夜

我的知乎

文件夹说明：

docx：笔记的word版本

media：笔记的图片

ppt：课程的原版课件

srt：课程的中英文字幕（mp4文件需要在百度云下载）

code：课程的python代码（有一部分是国外大牛写的）

机器学习视频下载链接：http://pan.baidu.com/s/1dFCQvxZ 密码：dce8

包含mp4视频和字幕

笔记在线阅读

笔记pdf版本下载

机器学习qq群：554839127

+ + + + \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 00000000..7095c290 --- /dev/null +++ b/README.md @@ -0,0 +1,50 @@ +**斯坦福大学2014机器学习教程中文笔记** + +课程目录：[目录](index.html) + +课程地址： + +Machine Learning(机器学习)是研究计算机怎样模拟或实现人类的学习行为，以获取新的知识或技能，重新组织已有的知识结构使之不断改善自身的性能。它是人工智能的核心，是使计算机具有智能的根本途径，其应用遍及人工智能的各个领域，它主要使用归纳、综合而不是演译。在过去的十年中，机器学习帮助我们自动驾驶汽车，有效的语音识别，有效的网络搜索，并极大地提高了人类基因组的认识。机器学习是当今非常普遍，你可能会使用这一天几十倍而不自知。很多研究者也认为这是最好的人工智能的取得方式。在本课中，您将学习最有效的机器学习技术，并获得实践，让它们为自己的工作。更重要的是，你会不仅得到理论基础的学习，而且获得那些需要快速和强大的应用技术解决问题的实用技术。最后，你会学到一些硅谷利用机器学习和人工智能的最佳实践创新。 + +本课程提供了一个广泛的介绍机器学习、数据挖掘、统计模式识别的课程。主题包括：（一）监督学习（参数/非参数算法，支持向量机，核函数，神经网络）。（二）无监督学习（聚类，降维，推荐系统，深入学习推荐）。（三）在机器学习的最佳实践（偏差/方差理论；在机器学习和人工智能创新过程）。本课程还将使用大量的案例研究，您还将学习如何运用学习算法构建智能机器人（感知，控制），文本的理解（Web搜索，反垃圾邮件），计算机视觉，医疗信息，音频，数据挖掘，和其他领域。 + +本课程需要10周共18节课，相对以前的机器学习视频，这个视频更加清晰，而且每课都有ppt课件，推荐学习。 + +本人2014年下半年开始翻译本课程字幕，并写了课程的中文笔记。笔记被下载了几万次，应该帮助了不少人，也有很多人一直在帮助我，现在我把笔记的word原稿和markdown原稿分享给大家。 + +markdown的笔记和课程中英文字幕我将放在github和码云，希望大家能继续完善。为方便数学公式的在线显示，在线观看的是html文件，公式已经被转为图片，公式源码在markdown文件。 + +**最后想对各位朋友说：** +**赠人玫瑰，手有余香！** +**在人工智能的道路上，你不是一个人在战斗！** + +黄海广 + +2017-11-3 夜 + +[我的知乎](https://www.zhihu.com/people/fengdu78/activities) + +----------------------- + +文件夹说明： + +docx：笔记的word版本 + +media：笔记的图片 + +ppt：课程的原版课件 + +srt：课程的中英文字幕（mp4文件需要在百度云下载） + +code：课程的python代码（有一部分是国外大牛写的） + +机器学习视频下载链接：http://pan.baidu.com/s/1dFCQvxZ 密码：dce8 + +包含mp4视频和字幕 + +[笔记在线阅读](http://www.ai-start.com/ml2014) + +[笔记pdf版本下载](http://fengdu78.gitee.io/coursera-ml-andrewng-notes/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E4%B8%AA%E4%BA%BA%E7%AC%94%E8%AE%B0%E5%AE%8C%E6%95%B4%E7%89%88v5.pdf) + +机器学习qq群：554839127 + diff --git a/SUMMARY.md b/SUMMARY.md new file mode 100644 index 00000000..7cd2c786 --- /dev/null +++ b/SUMMARY.md @@ -0,0 +1,297 @@ +# 斯坦福大学2014机器学习教程中文笔记目录 + +* [第一周](week1.md) + +一、 引言(Introduction) + +1.1 欢迎 + +1.2 机器学习是什么？ + +1.3 监督学习 + +1.4 无监督学习 + +二、单变量线性回归(Linear Regression with One Variable) + +2.1 模型表示 + +2.2 代价函数 + +2.3 代价函数的直观理解I + +2.4 代价函数的直观理解II + +2.5 梯度下降 + +2.6 梯度下降的直观理解 + +2.7 梯度下降的线性回归 + +2.8 接下来的内容 + +三、线性代数回顾(Linear Algebra Review) + +3.1 矩阵和向量 + +3.2 加法和标量乘法 + +3.3 矩阵向量乘法 + +3.4 矩阵乘法 + +3.5 矩阵乘法的性质 + +3.6 逆、转置 + +* [第二周](week2.md) + +四、多变量线性回归(Linear Regression with Multiple Variables) + +4.1 多维特征 + +4.2 多变量梯度下降 + +4.3 梯度下降法实践1-特征缩放 + +4.4 梯度下降法实践2-学习率 + +4.5 特征和多项式回归 + +4.6 正规方程 + +4.7 正规方程及不可逆性（选修） + +五、Octave教程(Octave Tutorial) + +5.1 基本操作 + +5.2 移动数据 + +5.3 计算数据 + +5.4 绘图数据 + +5.5 控制语句：for，while，if语句 + +5.6 向量化 88 + +5.7 工作和提交的编程练习 + +* [第三周](week3.md) + +六、逻辑回归(Logistic Regression) + +6.1 分类问题 + +6.2 假说表示 + +6.3 判定边界 + +6.4 代价函数 + +6.5 简化的成本函数和梯度下降 + +6.6 高级优化 + +6.7 多类别分类：一对多 + +七、正则化(Regularization) + +7.1 过拟合的问题 + +7.2 代价函数 + +7.3 正则化线性回归 + +7.4 正则化的逻辑回归模型 + +* [第四周](week4.md) + +第八、神经网络：表述(Neural Networks: Representation) + +8.1 非线性假设 + +8.2 神经元和大脑 + +8.3 模型表示1 + +8.4 模型表示2 + +8.5 样本和直观理解1 + +8.6 样本和直观理解II + +8.7 多类分类 + +* [第五周](week5.md) + +九、神经网络的学习(Neural Networks: Learning) + +9.1 代价函数 + +9.2 反向传播算法 + +9.3 反向传播算法的直观理解 + +9.4 实现注意：展开参数 + +9.5 梯度检验 + +9.6 随机初始化 + +9.7 综合起来 + +9.8 自主驾驶 + +* [第六周](week6.md) + +十、应用机器学习的建议(Advice for Applying Machine Learning) + +10.1 决定下一步做什么 + +10.2 评估一个假设 + +10.3 模型选择和交叉验证集 + +10.4 诊断偏差和方差 + +10.5 正则化和偏差/方差 + +10.6 学习曲线 + +10.7 决定下一步做什么 + +十一、机器学习系统的设计(Machine Learning System Design) + +11.1 首先要做什么 + +11.2 误差分析 + +11.3 类偏斜的误差度量 + +11.4 查准率和查全率之间的权衡 + +11.5 机器学习的数据 + +[第7周](week7.md) + +十二、支持向量机(Support Vector Machines) + +12.1 优化目标 + +12.2 大边界的直观理解 + +12.3 数学背后的大边界分类（选修） + +12.4 核函数1 + +12.5 核函数2 + +12.6 使用支持向量机 + +* [第八周](week8.md) + +十三、聚类(Clustering) + +13.1 无监督学习：简介 + +13.2 K-均值算法 + +13.3 优化目标 + +13.4 随机初始化 + +13.5 选择聚类数 + +十四、降维(Dimensionality Reduction) + +14.1 动机一：数据压缩 + +14.2 动机二：数据可视化 + +14.3 主成分分析问题 + +14.4 主成分分析算法 + +14.5 选择主成分的数量 + +14.6 重建的压缩表示 + +14.7 主成分分析法的应用建议 + +* [第九周](week9.md) + +十五、异常检测(Anomaly Detection) + +15.1 问题的动机 + +15.2 高斯分布 + +15.3 算法 + +15.4 开发和评价一个异常检测系统 + +15.5 异常检测与监督学习对比 + +15.6 选择特征 + +15.7 多元高斯分布（选修） + +15.8 使用多元高斯分布进行异常检测（选修） + +十六、推荐系统(Recommender Systems) + +16.1 问题形式化 + +16.2 基于内容的推荐系统 + +16.3 协同过滤 + +16.4 协同过滤算法 + +16.5 向量化：低秩矩阵分解 + +16.6 推行工作上的细节：均值归一化 + +* [第十周](week10.md) + +十七、大规模机器学习(Large Scale Machine Learning) + +17.1 大型数据集的学习 + +17.2 随机梯度下降法 + +17.3 小批量梯度下降 + +17.4 随机梯度下降收敛 + +17.5 在线学习 + +17.6 映射化简和数据并行 + +十八、应用实例：图片文字识别(Application Example: Photo OCR) + +18.1 问题描述和流程图 + +18.2 滑动窗口 + +18.3 获取大量数据和人工数据 + +18.4 上限分析：哪部分管道的接下去做 + +十九、总结(Conclusion) + +19.1 总结和致谢 + +--------------- + +**机器学习视频下载链接：http://pan.baidu.com/s/1dFCQvxZ 密码：dce8** + +**包含mp4视频和字幕** + +**[笔记在线阅读](index.html)** + +**[笔记pdf版本下载](机器学习个人笔记完整版v4.7.pdf)** + +**机器学习qq群：554839127** \ No newline at end of file diff --git a/code/ex1-linear regression/1.linear_regreesion_v1.ipynb b/code/ex1-linear regression/1.linear_regreesion_v1.ipynb new file mode 100644 index 00000000..a793d0e7 --- /dev/null +++ b/code/ex1-linear regression/1.linear_regreesion_v1.ipynb @@ -0,0 +1,1645 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# linear regreesion（线性回归）\n", + "注意：python版本为3.6，\n", + "安装TensorFlow的方法：pip install tensorflow" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import seaborn as sns\n", + "sns.set(context=\"notebook\", style=\"whitegrid\", palette=\"dark\")\n", + "import matplotlib.pyplot as plt\n", + "import tensorflow as tf\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "df = pd.read_csv('ex1data1.txt', names=['population', 'profit'])#读取数据并赋予列名" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n", + "
" + ], + "text/plain": [ + " population profit\n", + "0 6.1101 17.5920\n", + "1 5.5277 9.1302\n", + "2 8.5186 13.6620\n", + "3 7.0032 11.8540\n", + "4 5.8598 6.8233" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.head()#看前五行" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "RangeIndex: 97 entries, 0 to 96\n", + "Data columns (total 2 columns):\n", + "population 97 non-null float64\n", + "profit 97 non-null float64\n", + "dtypes: float64(2)\n", + "memory usage: 1.6 KB\n" + ] + } + ], + "source": [ + "df.info()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***\n", + "# 看下原始数据" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.lmplot('population', 'profit', df, size=6, fit_reg=False)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def get_X(df):#读取特征\n", + "# \"\"\"\n", + "# use concat to add intersect feature to avoid side effect\n", + "# not efficient for big dataset though\n", + "# \"\"\"\n", + " ones = pd.DataFrame({'ones': np.ones(len(df))})#ones是m行1列的dataframe\n", + " data = pd.concat([ones, df], axis=1) # 合并数据，根据列合并\n", + " return data.iloc[:, :-1].as_matrix() # 这个操作返回 ndarray,不是矩阵\n", + "\n", + "\n", + "def get_y(df):#读取标签\n", + "# '''assume the last column is the target'''\n", + " return np.array(df.iloc[:, -1])#df.iloc[:, -1]是指df的最后一列\n", + "\n", + "\n", + "def normalize_feature(df):\n", + "# \"\"\"Applies function along input axis(default 0) of DataFrame.\"\"\"\n", + " return df.apply(lambda column: (column - column.mean()) / column.std())#特征缩放" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "多变量的假设 h 表示为：\\\\[{{h}_{\\theta }}\\left( x \\right)={{\\theta }_{0}}+{{\\theta }_{1}}{{x}_{1}}+{{\\theta }_{2}}{{x}_{2}}+...+{{\\theta }_{n}}{{x}_{n}}\\\\] \n", + "这个公式中有n+1个参数和n个变量，为了使得公式能够简化一些，引入${{x}_{0}}=1$，则公式转化为： \n", + "此时模型中的参数是一个n+1维的向量，任何一个训练实例也都是n+1维的向量，特征矩阵X的维度是 m*(n+1)。 因此公式可以简化为：${{h}_{\\theta }}\\left( x \\right)={{\\theta }^{T}}X$，其中上标T代表矩阵转置。\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def linear_regression(X_data, y_data, alpha, epoch, optimizer=tf.train.GradientDescentOptimizer):# 这个函数是旧金山的一个大神Lucas Shen写的\n", + " # placeholder for graph input\n", + " X = tf.placeholder(tf.float32, shape=X_data.shape)\n", + " y = tf.placeholder(tf.float32, shape=y_data.shape)\n", + "\n", + " # construct the graph\n", + " with tf.variable_scope('linear-regression'):\n", + " W = tf.get_variable(\"weights\",\n", + " (X_data.shape[1], 1),\n", + " initializer=tf.constant_initializer()) # n*1\n", + "\n", + " y_pred = tf.matmul(X, W) # m*n @ n*1 -> m*1\n", + "\n", + " loss = 1 / (2 * len(X_data)) * tf.matmul((y_pred - y), (y_pred - y), transpose_a=True) # (m*1).T @ m*1 = 1*1\n", + "\n", + " opt = optimizer(learning_rate=alpha)\n", + " opt_operation = opt.minimize(loss)\n", + "\n", + " # run the session\n", + " with tf.Session() as sess:\n", + " sess.run(tf.global_variables_initializer())\n", + " loss_data = []\n", + "\n", + " for i in range(epoch):\n", + " _, loss_val, W_val = sess.run([opt_operation, loss, W], feed_dict={X: X_data, y: y_data})\n", + " loss_data.append(loss_val[0, 0]) # because every loss_val is 1*1 ndarray\n", + "\n", + " if len(loss_data) > 1 and np.abs(loss_data[-1] - loss_data[-2]) < 10 ** -9: # early break when it's converged\n", + " # print('Converged at epoch {}'.format(i))\n", + " break\n", + "\n", + " # clear the graph\n", + " tf.reset_default_graph()\n", + " return {'loss': loss_data, 'parameters': W_val} # just want to return in row vector format" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " population profit\n", + "0 6.1101 17.5920\n", + "1 5.5277 9.1302\n", + "2 8.5186 13.6620\n", + "3 7.0032 11.8540\n", + "4 5.8598 6.8233" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv('ex1data1.txt', names=['population', 'profit'])#读取数据，并赋予列名\n", + "\n", + "data.head()#看下数据前5行" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 计算代价函数\n", + "$$J\\left( \\theta \\right)=\\frac{1}{2m}\\sum\\limits_{i=1}^{m}{{{\\left( {{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}} \\right)}^{2}}}$$\n", + "其中：\\\\[{{h}_{\\theta }}\\left( x \\right)={{\\theta }^{T}}X={{\\theta }_{0}}{{x}_{0}}+{{\\theta }_{1}}{{x}_{1}}+{{\\theta }_{2}}{{x}_{2}}+...+{{\\theta }_{n}}{{x}_{n}}\\\\] " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(97, 2) \n", + "(97,) \n" + ] + } + ], + "source": [ + "X = get_X(data)\n", + "print(X.shape, type(X))\n", + "\n", + "y = get_y(data)\n", + "print(y.shape, type(y))\n", + "#看下数据维度" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "theta = np.zeros(X.shape[1])#X.shape[1]=2,代表特征数n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def lr_cost(theta, X, y):\n", + "# \"\"\"\n", + "# X: R(m*n), m 样本数, n 特征数\n", + "# y: R(m)\n", + "# theta : R(n), 线性回归的参数\n", + "# \"\"\"\n", + " m = X.shape[0]#m为样本数\n", + "\n", + " inner = X @ theta - y # R(m*1)，X @ theta等价于X.dot(theta)\n", + "\n", + " # 1*m @ m*1 = 1*1 in matrix multiplication\n", + " # but you know numpy didn't do transpose in 1d array, so here is just a\n", + " # vector inner product to itselves\n", + " square_sum = inner.T @ inner\n", + " cost = square_sum / (2 * m)\n", + "\n", + " return cost" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "32.072733877455676" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lr_cost(theta, X, y)#返回theta的值" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# batch gradient decent（批量梯度下降）\n", + "$${{\\theta }_{j}}:={{\\theta }_{j}}-\\alpha \\frac{\\partial }{\\partial {{\\theta }_{j}}}J\\left( \\theta \\right)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gradient(theta, X, y):\n", + " m = X.shape[0]\n", + "\n", + " inner = X.T @ (X @ theta - y) # (m,n).T @ (m, 1) -> (n, 1)，X @ theta等价于X.dot(theta)\n", + "\n", + " return inner / m" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def batch_gradient_decent(theta, X, y, epoch, alpha=0.01):\n", + "# 拟合线性回归，返回参数和代价\n", + "# epoch: 批处理的轮数\n", + "# \"\"\"\n", + " cost_data = [lr_cost(theta, X, y)]\n", + " _theta = theta.copy() # 拷贝一份，不和原来的theta混淆\n", + "\n", + " for _ in range(epoch):\n", + " _theta = _theta - alpha * gradient(_theta, X, y)\n", + " cost_data.append(lr_cost(_theta, X, y))\n", + "\n", + " return _theta, cost_data\n", + "#批量梯度下降函数" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "epoch = 500\n", + "final_theta, cost_data = batch_gradient_decent(theta, X, y, epoch)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-2.28286727, 1.03099898])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final_theta\n", + "#最终的theta" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[32.072733877455676,\n", + " 6.7371904648700109,\n", + " 5.9315935686049563,\n", + " 5.9011547070813881,\n", + " 5.8952285864442207,\n", + " 5.8900949431173304,\n", + " 5.8850041584436461,\n", + " 5.8799324804914175,\n", + " 5.8748790947625729,\n", + " 5.8698439118063854,\n", + " 5.8648268653129305,\n", + " 5.8598278899321805,\n", + " 5.8548469205722897,\n", + " 5.849883892376587,\n", + " 5.8449387407220339,\n", + " 5.8400114012183613,\n", + " 5.8351018097072282,\n", + " 5.8302099022613882,\n", + " 5.825335615183862,\n", + " 5.8204788850070992,\n", + " 5.8156396484921542,\n", + " 5.8108178426278689,\n", + " 5.8060134046300451,\n", + " 5.8012262719406298,\n", + " 5.7964563822268991,\n", + " 5.7917036733806526,\n", + " 5.7869680835173956,\n", + " 5.7822495509755392,\n", + " 5.7775480143155962,\n", + " 5.7728634123193823,\n", + " 5.7681956839892123,\n", + " 5.7635447685471197,\n", + " 5.7589106054340471,\n", + " 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4.7525661851005694,\n", + " 4.7515735085024247,\n", + " 4.7505844074680983,\n", + " 4.7495988691186195,\n", + " 4.7486168806214,\n", + " 4.7476384291900784,\n", + " 4.7466635020843446,\n", + " 4.745692086609786,\n", + " 4.7447241701177063,\n", + " 4.7437597400049727,\n", + " 4.7427987837138508,\n", + " 4.7418412887318322,\n", + " 4.7408872425914828,\n", + " 4.7399366328702737,\n", + " 4.7389894471904226,\n", + " 4.7380456732187284,\n", + " 4.7371052986664157,\n", + " 4.7361683112889716,\n", + " 4.7352346988859892,\n", + " 4.7343044493010051,\n", + " 4.7333775504213413,\n", + " 4.7324539901779517,\n", + " 4.7315337565452618,\n", + " 4.7306168375410103,\n", + " 4.7297032212260985,\n", + " 4.7287928957044265,\n", + " 4.7278858491227513,\n", + " 4.7269820696705187,\n", + " 4.7260815455797172,\n", + " 4.7251842651247218,\n", + " 4.7242902166221432,\n", + " 4.7233993884306775,\n", + " 4.7225117689509464,\n", + " 4.7216273466253593,\n", + " 4.7207461099379495,\n", + " 4.7198680474142325,\n", + " 4.7189931476210534,\n", + " 4.7181213991664395,\n", + " 4.7172527906994519,\n", + " 4.7163873109100365,\n", + " 4.7155249485288744,\n", + " 4.7146656923272445,\n", + " 4.7138095311168664]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cost_data\n", + "# 看下代价数据" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4.7138095311168664" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 计算最终的代价\n", + "lr_cost(final_theta, X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# visualize cost data（代价数据可视化）" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Nnz5dt9xyi0499VRt375dw4YN0/Lly1VSUqLXX39dP/nJT5RKpXTqqafqrrvu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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ax = sns.tsplot(cost_data, time=np.arange(epoch+1))\n", + "ax.set_xlabel('epoch')\n", + "ax.set_ylabel('cost')\n", + "plt.show()\n", + "#可以看到从第二轮代价数据变换很大，接下来平稳了" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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rha4t+DNOJC9uHb6sGERibtysQP373xJt8/b2wp3sORL3yHr8GSeSJ7cOX1YM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\n448/7ta/rzXPFXD876tLh+/mzZuxYME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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "b = final_theta[0] # intercept，Y轴上的截距\n", + "m = final_theta[1] # slope，斜率\n", + "\n", + "plt.scatter(data.population, data.profit, label=\"Training data\")\n", + "plt.plot(data.population, data.population*m + b, label=\"Prediction\")\n", + "plt.legend(loc=2)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3- 选修章节" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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squarebedroomsprice
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" + ], + "text/plain": [ + " square bedrooms price\n", + "0 2104 3 399900\n", + "1 1600 3 329900\n", + "2 2400 3 369000\n", + "3 1416 2 232000\n", + "4 3000 4 539900" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "raw_data = pd.read_csv('ex1data2.txt', names=['square', 'bedrooms', 'price'])\n", + "raw_data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# 标准化数据\n", + "最简单的方法是令：\n", + "\n", + " \n", + "\n", + "其中 是平均值，sn 是标准差。\n" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def normalize_feature(df):\n", + "# \"\"\"Applies function along input axis(default 0) of DataFrame.\"\"\"\n", + " return df.apply(lambda column: (column - column.mean()) / column.std())" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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squarebedroomsprice
00.130010-0.2236750.475747
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" + ], + "text/plain": [ + " square bedrooms price\n", + "0 0.130010 -0.223675 0.475747\n", + "1 -0.504190 -0.223675 -0.084074\n", + "2 0.502476 -0.223675 0.228626\n", + "3 -0.735723 -1.537767 -0.867025\n", + "4 1.257476 1.090417 1.595389" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = normalize_feature(raw_data)\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2. multi-var batch gradient decent（多变量批量梯度下降）" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(47, 3) \n", + "(47,) \n" + ] + } + ], + "source": [ + "X = get_X(data)\n", + "print(X.shape, type(X))\n", + "\n", + "y = get_y(data)\n", + "print(y.shape, type(y))#看下数据的维度和类型" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "alpha = 0.01#学习率\n", + "theta = np.zeros(X.shape[1])#X.shape[1]：特征数n\n", + "epoch = 500#轮数" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "final_theta, cost_data = batch_gradient_decent(theta, X, y, epoch, alpha=alpha)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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2AiD12+0+fy8RERGzmHakoHfv3qxatYohQ4ZgGAZTp05l8eLF5OXlkZSURP/+/Rk2bBh2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\nUCgQERGRMv8PrJcV17eQ2PMAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.tsplot(time=np.arange(len(cost_data)), data = cost_data)\n", + "plt.xlabel('epoch', fontsize=18)\n", + "plt.ylabel('cost', fontsize=18)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ -1.20848957e-16, 8.30383883e-01, 8.23982853e-04])" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final_theta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3. learning rate（学习率）" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.00000000e-05 3.00000000e-05 2.15443469e-04 6.46330407e-04\n", + " 4.64158883e-03 1.39247665e-02 1.00000000e-01 3.00000000e-01]\n" + ] + } + ], + "source": [ + "base = np.logspace(-1, -5, num=4)\n", + "candidate = np.sort(np.concatenate((base, base*3)))\n", + "print(candidate)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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NSqXi/fffd1hWt25d2+MuXbrQpUuXItsIIYQQQgghhBBC3AlU5d0BIYQQQgghhBBCCCEh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ZFy53dDGldXVx577DHy8vKA4ndKP/roIz766KPf/PqioiK6d+9e8lWKnb2T5mzZdNIA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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "epoch=50\n", + "\n", + "fig, ax = plt.subplots(figsize=(16, 9))\n", + "\n", + "for alpha in candidate:\n", + " _, cost_data = batch_gradient_decent(theta, X, y, epoch, alpha=alpha)\n", + " ax.plot(np.arange(epoch+1), cost_data, label=alpha)\n", + "\n", + "ax.set_xlabel('epoch', fontsize=18)\n", + "ax.set_ylabel('cost', fontsize=18)\n", + "ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n", + "ax.set_title('learning rate', fontsize=18)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4. normal equation（正规方程）\n", + "正规方程是通过求解下面的方程来找出使得代价函数最小的参数的：$\\frac{\\partial }{\\partial {{\\theta }_{j}}}J\\left( {{\\theta }_{j}} \\right)=0$ 。\n", + " 假设我们的训练集特征矩阵为 X（包含了${{x}_{0}}=1$）并且我们的训练集结果为向量 y，则利用正规方程解出向量 $\\theta ={{\\left( {{X}^{T}}X \\right)}^{-1}}{{X}^{T}}y$ 。\n", + "上标T代表矩阵转置，上标-1 代表矩阵的逆。设矩阵$A={{X}^{T}}X$，则：${{\\left( {{X}^{T}}X \\right)}^{-1}}={{A}^{-1}}$\n", + "\n", + "梯度下降与正规方程的比较：\n", + "\n", + "梯度下降：需要选择学习率α，需要多次迭代，当特征数量n大时也能较好适用，适用于各种类型的模型\t\n", + "\n", + "正规方程：不需要选择学习率α，一次计算得出，需要计算${{\\left( {{X}^{T}}X \\right)}^{-1}}$，如果特征数量n较大则运算代价大，因为矩阵逆的计算时间复杂度为O(n3)，通常来说当n小于10000 时还是可以接受的，只适用于线性模型，不适合逻辑回归模型等其他模型\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# 正规方程\n", + "def normalEqn(X, y):\n", + " theta = np.linalg.inv(X.T@X)@X.T@y#X.T@X等价于X.T.dot(X)\n", + " return theta" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ -1.14491749e-16, 8.84765988e-01, -5.31788197e-02])" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final_theta2=normalEqn(X, y)#感觉和批量梯度下降的theta的值有点差距\n", + "final_theta2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# run the tensorflow graph over several optimizer" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(47, 3) \n", + "(47, 1) \n" + ] + } + ], + "source": [ + "X_data = get_X(data)\n", + "print(X_data.shape, type(X_data))\n", + "\n", + "y_data = get_y(data).reshape(len(X_data), 1) # special treatment for tensorflow input data\n", + "print(y_data.shape, type(y_data))" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "epoch = 2000\n", + "alpha = 0.01" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "optimizer_dict={'GD': tf.train.GradientDescentOptimizer,\n", + " 'Adagrad': tf.train.AdagradOptimizer,\n", + " 'Adam': tf.train.AdamOptimizer,\n", + " 'Ftrl': tf.train.FtrlOptimizer,\n", + " 'RMS': tf.train.RMSPropOptimizer\n", + " }\n", + "results = []\n", + "for name in optimizer_dict:\n", + " res = linear_regression(X_data, y_data, alpha, epoch, optimizer=optimizer_dict[name])\n", + " res['name'] = name\n", + " results.append(res)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 画图" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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r6xIBAAAAALAMQYbNuP0JCpfEggzvUXZkSJKvtylP0Ktlr31Ul+UB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\nW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"language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/code/ex1-linear regression/ML-Exercise1.ipynb b/code/ex1-linear regression/ML-Exercise1.ipynb new file mode 100644 index 00000000..5298a8a4 --- /dev/null +++ b/code/ex1-linear regression/ML-Exercise1.ipynb @@ -0,0 +1,1187 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 机器学习练习 1 - 线性回归" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "这个是另一位大牛写的，作业内容在根目录： [作业文件](ex1.pdf)\n", + "\n", + "代码修改并注释：黄海广，haiguang2000@qq.com" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 单变量线性回归" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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PopulationProfit
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PopulationProfit
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mean8.1598005.839135
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50%6.5894004.562300
75%8.5781007.046700
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\n", + "
" + ], + "text/plain": [ + " Population Profit\n", + "count 97.000000 97.000000\n", + "mean 8.159800 5.839135\n", + "std 3.869884 5.510262\n", + "min 5.026900 -2.680700\n", + "25% 5.707700 1.986900\n", + "50% 6.589400 4.562300\n", + "75% 8.578100 7.046700\n", + "max 22.203000 24.147000" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.describe()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "看下数据长什么样子" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+cet2QXm//oDPTk+ORF9BG7zRBEaJEE3fRv3j1p2Csj/g0D5vNIFRIUTTt3H4uHWnoOwP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\nFwBAkpRSHqi1ntr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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "data.plot(kind='scatter', x='Population', y='Profit', figsize=(12,8))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在让我们使用梯度下降来实现线性回归，以最小化成本函数。 以下代码示例中实现的方程在“练习”文件夹中的“ex1.pdf”中有详细说明。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "首先，我们将创建一个以参数θ为特征函数的代价函数\n", + "$$J\\left( \\theta \\right)=\\frac{1}{2m}\\sum\\limits_{i=1}^{m}{{{\\left( {{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}} \\right)}^{2}}}$$\n", + "其中：\\\\[{{h}_{\\theta }}\\left( x \\right)={{\\theta }^{T}}X={{\\theta }_{0}}{{x}_{0}}+{{\\theta }_{1}}{{x}_{1}}+{{\\theta }_{2}}{{x}_{2}}+...+{{\\theta }_{n}}{{x}_{n}}\\\\] " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def computeCost(X, y, theta):\n", + " inner = np.power(((X * theta.T) - y), 2)\n", + " return np.sum(inner) / (2 * len(X))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们在训练集中添加一列，以便我们可以使用向量化的解决方案来计算代价和梯度。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "data.insert(0, 'Ones', 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在我们来做一些变量初始化。" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# set X (training data) and y (target variable)\n", + "cols = data.shape[1]\n", + "X = data.iloc[:,0:cols-1]#X是所有行，去掉最后一列\n", + "y = data.iloc[:,cols-1:cols]#X是所有行，最后一列" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "观察下 X (训练集) and y (目标变量)是否正确." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Profit\n", + "0 17.5920\n", + "1 9.1302\n", + "2 13.6620\n", + "3 11.8540\n", + "4 6.8233" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "代价函数是应该是numpy矩阵，所以我们需要转换X和Y，然后才能使用它们。 我们还需要初始化theta。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "X = np.matrix(X.values)\n", + "y = np.matrix(y.values)\n", + "theta = np.matrix(np.array([0,0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "theta 是一个(1,2)矩阵" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[0, 0]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "看下维度" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((97, 2), (1, 2), (97, 1))" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X.shape, theta.shape, y.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "计算代价函数 (theta初始值为0)." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "32.072733877455676" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "computeCost(X, y, theta)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# batch gradient decent（批量梯度下降）\n", + "$${{\\theta }_{j}}:={{\\theta }_{j}}-\\alpha \\frac{\\partial }{\\partial {{\\theta }_{j}}}J\\left( \\theta \\right)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gradientDescent(X, y, theta, alpha, iters):\n", + " temp = np.matrix(np.zeros(theta.shape))\n", + " parameters = int(theta.ravel().shape[1])\n", + " cost = np.zeros(iters)\n", + " \n", + " for i in range(iters):\n", + " error = (X * theta.T) - y\n", + " \n", + " for j in range(parameters):\n", + " term = np.multiply(error, X[:,j])\n", + " temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term))\n", + " \n", + " theta = temp\n", + " cost[i] = computeCost(X, y, theta)\n", + " \n", + " return theta, cost" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "初始化一些附加变量 - 学习速率α和要执行的迭代次数。" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "alpha = 0.01\n", + "iters = 1000" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在让我们运行梯度下降算法来将我们的参数θ适合于训练集。" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[-3.24140214, 1.1272942 ]])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g, cost = gradientDescent(X, y, theta, alpha, iters)\n", + "g" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "最后，我们可以使用我们拟合的参数计算训练模型的代价函数（误差）。" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4.5159555030789118" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "computeCost(X, y, g)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在我们来绘制线性模型以及数据，直观地看出它的拟合。" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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LL7/QoEEDdu3aVer1zzzzTGbOnAnA6tWr2bBhAwkJCTX9tEREREQimkK0nzVp0oRp06bR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\nkiRJGRmiJUmSpIwM0ZIkSVJGhmhJkiQpI0O0JLVYROyMiNU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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(data.Population.min(), data.Population.max(), 100)\n", + "f = g[0, 0] + (g[0, 1] * x)\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,8))\n", + "ax.plot(x, f, 'r', label='Prediction')\n", + "ax.scatter(data.Population, data.Profit, label='Traning Data')\n", + "ax.legend(loc=2)\n", + "ax.set_xlabel('Population')\n", + "ax.set_ylabel('Profit')\n", + "ax.set_title('Predicted Profit vs. Population Size')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "由于梯度方程式函数也在每个训练迭代中输出一个代价的向量，所以我们也可以绘制。 请注意，代价总是降低 - 这是凸优化问题的一个例子。" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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KA3VRBmpJkiRVYaAuykAtSZKkKgzURRmoJUmSVIWBuigDtSRJkqowUBdloJYkSVIVBuqi\nBgzIgfq998quRJIkSQ3EQF3U0KH5cdKkcuuQJElSQzFQF9UcqF95pdw6JEmS1FAM1EWttlp+NFBL\nkiSpBQN1Uauumm9MNFBLkiSpBQN1UX365LaPO+90tg9JkiT9m4G6PU4+Ge67Dy6+uOxKJEmS1CAM\n1O1x3HGwzTbwzW/C66+XXY0kSZIagIG6PZqa4He/g/ffz+Ha1g9JkqQez0DdXuuvD6eeCjfcAL//\nfdnVSJIkqWQG6sXx9a/DzjvDN74BL75YdjWSJEkqkYF6cTQ1wR/+kJ8fdRTMnVtqOZIkSSqPgXpx\nDRsGv/oV3H03nHVW2dVIkiSpJAbqWhx9NOy7L3z/+/DUU2VXI0mSpBIYqGsRARdcAP37w5FHwuzZ\nZVckSZKkTmagrtVKK8E558DDD+fZPyRJktSjGKg7wmc/C4ceCj/5CYwfX3Y1kiRJ6kQG6o5y9tkw\nZAgcfjh88EHZ1UiSJKmTGKg7yqBBcNFF+ebEb3+77GokSZLUSQzUHWnkSPjOd+Dcc+Evfym7GkmS\nJHUCA3VH++//hs02g2OOgddeK7saSZIk1ZmBuqP17Qt//jNMnw5f+IKrKEqSJHVzBup6WH99+OUv\n4bbb4Mwzy65GkiRJdWSgrpcvfhH23z+vovjoo2VXI0mSpDoxUNdL8yqKgwbBYYfBhx+WXZEkSZLq\nwEBdT4MHwx//CE8+Cd/9btnVSJIkqQ4M1PW2xx7wzW/Cb37jVHqSJEndkIG6M5x6KmyxRZ714+WX\ny65GkiRJHchA3Rn69oXLLoNZs+DQQ/OjJEmSugUDdWcZPhzOPx/+9jf40Y/KrkaSJEkdxEDdmQ49\nFI49NreA3HZb2dVIkiSpAxioO9uZZ8KGG8LnPufS5JIkSd2Agbqz9esHV1wB770HRxwBc+aUXZEk\nSZJqYKAuwwYbwNlnw513ws9/XnY1kiRJqoGBuixHHQWHHw4//jHcc0/Z1UiSJGkxGajLEgHnnANr\nrZWXJn/jjbIrkiRJ0mIwUJdp6aXhyivh7bfzDCCzZ5ddkSRJktrJQF22TTfNI9V33QWnnFJ2NZIk\nSWonA3Uj+MIX4Ljj8vzU119fdjWSJElqBwN1o/j1r2GLLeDII+H558uuRpIkSQUZqBvFkkvC6NH5\n+Wc+AzNmlFuPJEmSCjFQN5I114SLL4YJE+CrXy27GkmSJBVgoG40++4LP/gBXHAB/P73ZVcjSZKk\nRTBQN6L/+i8YORK+/GV45JGyq5EkSdJCGKgbUa9ecOmlsMIK8KlPwdSpZVckSZKkNhioG9XgwXDV\nVfDqq3DIIS76IkmS1KAKBeqI+FORfepgW2+dF325/XY46aSyq5EkSVIVvQuet2HLFxHRC9iy48vR\nAo46CsaPh9NPh803h8MOK7siSZIktbDQEeqIOCki3gM2iYhple094E3guk6pUPDLX8JOO8Gxx+Yp\n9SRJktQwFhqoU0qnppSWBk5LKS1T2ZZOKS2fUrIHobMssQRceSUsvzwceCC89VbZFUmSJKmi6E2J\nN0REf4CIOCIifhkRa9SxLrU2ZAhccw28/jocdJA3KUqSJDWIooH6HOCDiNgU+DbwHHBR3apSdSNG\nwPnnw113wXe/W3Y1kiRJonignp1SSsABwNkppd8AS9evLLXpyCPh61+HM86AP/yh7GokSZJ6vKKB\n+r2IOAn4HHBjRDQBS9SvLC3UaafllRSPPx7uv7/saiRJknq0ooH6YGAmcHRK6XVgNeC0ulWlhWu+\nSXHNNfNNii+8UHZFkiRJPVahQF0J0ZcAy0bEKGBGSske6jIttxxcf32+OXG//WDatLIrkiRJ6pGK\nrpR4EDAG+CxwEPBQRHymnoWpgHXWgdGj4amn4NBDYc6csiuSJEnqcYq2fPwA2Cql9PmU0pHA1sB/\n1q8sFTZyJJx9Ntx0E3zve2VXI0mS1OMUXXq8KaX0ZovXUykexlVvJ5wAEyfmFRXXXz+vqChJkqRO\nUTRQ3xIRtwKXVl4fDNxUn5K0WP73f+Hpp+FLX4K114Zddim7IkmSpB5hoaPMEbF2RGyfUvoucB6w\nSWV7EDi/E+pTUb17w+WXw/Dh8OlPw7PPll2RJElSj7Coto0zgGkAKaWrU0rfSil9C7imckyNZNll\n88wfEbDvvjB1atkVSZIkdXuLCtQrppQeb72zsm9YXSpSbdZaC669Fl56CQ44AGbMKLsiSZKkbm1R\ngXrgQo4t1ZGFqAPtsANcdBE88AB8/vMwd27ZFUmSJHVbiwrUYyPiuNY7I+JYYFx9SlKHOOigvET5\nFVfA979fdjWSJEnd1qJm+fgGcE1EHM68AD0C6AMcWM/C1AG+/e28LPlpp8GwYfDlL5ddkSRJUrez\n0ECdUnoD2C4idgU2quy+MaV0Z90rU+0i4Mwz4ZVX4KtfhaFD8zLlkiRJ6jCF5qFOKd0F3FXnWlQP\nvXvDpZfmeakPOQTuuQdGjCi7KkmSpG7D1Q57gv794YYbYMiQPJ3eCy+UXZEkSVK3YaDuKVZcEW6+\nGWbNgr33hrfeKrsiSZKkbsFA3ZOstx5cd12eo3rUKJg+veyKJEmSujwDdU+z4455ifKHH85LlH/0\nUdkVSZIkdWkG6p5o//3h//4Pbr0VjjrKhV8kSZJqUGiWj8UVES8C7wFzgNkppRGtju8CXAc03yV3\ndUrpJ/WsSRVHHw1vvgknnQSDB8OvfpWn2ZMkSVK71DVQV+yaUlrYHXD3pZRGdUIdau0//iOH6l/9\nKt+0eNJJZVckSZLU5XRGoFajioDTT4cpU+Dkk/NI9bHHll2VJElSl1LvHuoE3B4R4yLi+DbO2S4i\nHouImyNiwzrXo9aamuB3v8tT6X3xi3DNNWVXJEmS1KXUO1DvkFLaDNgbODEidmp1fDywekppE+As\n4NpqHxIRx0fE2IgYO2XKlPpW3BMtsQRceSVsvTUceijc6crykiRJRdU1UKeUJlce3wSuAbZudXxa\nSun9yvObgCUiYoUqn3N+SmlESmnE4MGD61lyz9W8muLw4XkWkAcfLLsiSZKkLqFugToi+kfE0s3P\ngT2Af7Q6Z6WIPLVERGxdqWdqvWrSIiy/PPz1r7DyyrkFZMKEsiuSJElqePUcoV4RuD8iHgXGADem\nlG6JiBMi4oTKOZ8B/lE559fAISmlVMeatCgrrQR33AHLLgt77AETJ5ZdkSRJUkOLrpZfR4wYkcaO\nHVt2Gd3fM8/ATjvlmUDuuw/WWqvsiiRJkjpVRIxrvY5KNa6UqOqGD8/tHx99BCNHwiuvlF2RJElS\nQzJQq20bbZSXJ3/nHdh9d3jjjbIrkiRJajgGai3cllvCTTfBpEnwiU/A22+XXZEkSVJDMVBr0bbf\nHq67Dp5+Ot+o+M47ZVckSZLUMAzUKmb33fMqio8/nkP1v/5VdkWSJEkNwUCt4vbZB666Ch591FAt\nSZJUYaBW+4waBVdfDY88AnvuCe++W3ZFkiRJpTJQq/1Gjcoj1RMm5JFqQ7UkSerBDNRaPPvtB1de\nmUP1nnvCtGllVyRJklQKA7UW3wEHwBVXwLhxhmpJktRjGahVm09+MofqsWPtqZYkST2SgVq1O/DA\neSPVI0fC1KllVyRJktRpDNTqGAcemOep/sc/YNddXaZckiT1GAZqdZx994Ubb4TnnoOdd4bJk8uu\nSJIkqe4M1OpYI0fCrbfCq6/CTjvBiy+WXZEkSVJdGajV8XbYAe64A955J4fqZ54puyJJkqS6MVCr\nPrbaCu66Cz78MIfqJ58suyJJkqS6MFCrfjbdFO65ByJyT/X48WVXJEmS1OEM1KqvDTaAe++F/v1h\nl13g7rvLrkiSJKlDGahVf2uvDQ88AEOHwl57wbXXll2RJElShzFQq3Osuircdx9sthl8+tPw+9+X\nXZEkSVKHMFCr8wwaBLffDrvvDkcfDaedVnZFkiRJNTNQq3MNGADXXw8HHwzf+x78x39ASmVXJUmS\ntNh6l12AeqA+feCSS2C55eB//gemToVzz4Xe/uUoSZK6HhOMytGrF/z2tzB4MPz0pzBlClx6KfTr\nV3ZlkiRJ7WLLh8oTAT/5CZx1Vm4D2W23HKwlSZK6EAO1yveVr8BVV8Gjj8J228Fzz5VdkSRJUmEG\najWGAw+EO+6At9+GbbeFMWPKrkiSJKkQA7Uax3bbwd/+lmcC2WWX3AYiSZLU4AzUaizrrgsPPpiX\nLP/kJ+G888quSJIkaaEM1Go8K64Id9+dlyk/4QQ4+WSYO7fsqiRJkqoyUKsxDRgA110Hxx0Hp56a\nF4L54IOyq5IkSVqAgVqNq3fv3PJx+ul5FpCdd4bXXiu7KkmSpPkYqNXYIuDb34Zrr4WJE2HrreGR\nR8quSpIk6d8M1Ooa9t8f7r8/P99hB/jLX8qtR5IkqcJAra5js83y/NTNM4CcfjqkVHZVkiSphzNQ\nq2tZeeU8A8inPw3f/W6+afGjj8quSpIk9WAGanU9/frB5ZfDD38IF14Ie+wBU6aUXZUkSeqhDNTq\nmpqa4Kc/hYsvhoceghEjYPz4squSJEk9kIFaXdvhh+ebFVOC7beHSy4puyJJktTDGKjV9W25JYwd\nm6fUO+II+M53YPbssquSJEk9hIFa3cOQIXD77XDiifC//wt77w1Tp5ZdlSRJ6gEM1Oo+llgCzj4b\nLrgA7r0XttoKHnus7KokSVI3Z6BW93PMMXDPPTBjBmy7LVxxRdkVSZKkbsxAre5pm21g3DjYdFM4\n+GD4xjecr1qSJNWFgVrdV/MiMF//Opx5JuyyC0yaVHZVkiSpmzFQq3vr0wfOOCMvBPP447D55vnm\nRUmSpA5ioFbPcNB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00.130010-0.2236750.475747
1-0.504190-0.223675-0.084074
20.502476-0.2236750.228626
3-0.735723-1.537767-0.867025
41.2574761.0904171.595389
\n", + "
" + ], + "text/plain": [ + " Size Bedrooms Price\n", + "0 0.130010 -0.223675 0.475747\n", + "1 -0.504190 -0.223675 -0.084074\n", + "2 0.502476 -0.223675 0.228626\n", + "3 -0.735723 -1.537767 -0.867025\n", + "4 1.257476 1.090417 1.595389" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data2 = (data2 - data2.mean()) / data2.std()\n", + "data2.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在我们重复第1部分的预处理步骤，并对新数据集运行线性回归程序。" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.13070336960771892" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# add ones column\n", + "data2.insert(0, 'Ones', 1)\n", + "\n", + "# set X (training data) and y (target variable)\n", + "cols = data2.shape[1]\n", + "X2 = data2.iloc[:,0:cols-1]\n", + "y2 = data2.iloc[:,cols-1:cols]\n", + "\n", + "# convert to matrices and initialize theta\n", + "X2 = np.matrix(X2.values)\n", + "y2 = np.matrix(y2.values)\n", + "theta2 = np.matrix(np.array([0,0,0]))\n", + "\n", + "# perform linear regression on the data set\n", + "g2, cost2 = gradientDescent(X2, y2, theta2, alpha, iters)\n", + "\n", + "# get the cost (error) of the model\n", + "computeCost(X2, y2, g2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们也可以快速查看这一个的训练进程。" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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rXwn33gv33FN1JZIkSRrAoN3K+vtp/+xn1dYhSZKk5zFot7J994WpU+Hqq6uu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\nSmDQliRJkkrw/wOcUIPzigueowAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(12,8))\n", + "ax.plot(np.arange(iters), cost2, 'r')\n", + "ax.set_xlabel('Iterations')\n", + "ax.set_ylabel('Cost')\n", + "ax.set_title('Error vs. Training Epoch')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们也可以使用scikit-learn的线性回归函数，而不是从头开始实现这些算法。 我们将scikit-learn的线性回归算法应用于第1部分的数据，并看看它的表现。" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn import linear_model\n", + "model = linear_model.LinearRegression()\n", + "model.fit(X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "scikit-learn model的预测表现" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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dJ9Pj/LbDDjts/bqmpkabN28uew0AAACVgG2/fTZr1iw9+uijeu655yRJb7/9tp555hlN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\nCTYSAQAAlY6ZaB9kmvXNtGpHLos6etQ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.array(X[:, 1].A1)\n", + "f = model.predict(X).flatten()\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,8))\n", + "ax.plot(x, f, 'r', label='Prediction')\n", + "ax.scatter(data.Population, data.Profit, label='Traning Data')\n", + "ax.legend(loc=2)\n", + "ax.set_xlabel('Population')\n", + "ax.set_ylabel('Profit')\n", + "ax.set_title('Predicted Profit vs. Population Size')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4. normal equation（正规方程）\n", + "正规方程是通过求解下面的方程来找出使得代价函数最小的参数的：$\\frac{\\partial }{\\partial {{\\theta }_{j}}}J\\left( {{\\theta }_{j}} \\right)=0$ 。\n", + " 假设我们的训练集特征矩阵为 X（包含了${{x}_{0}}=1$）并且我们的训练集结果为向量 y，则利用正规方程解出向量 $\\theta ={{\\left( {{X}^{T}}X \\right)}^{-1}}{{X}^{T}}y$ 。\n", + "上标T代表矩阵转置，上标-1 代表矩阵的逆。设矩阵$A={{X}^{T}}X$，则：${{\\left( {{X}^{T}}X \\right)}^{-1}}={{A}^{-1}}$\n", + "\n", + "梯度下降与正规方程的比较：\n", + "\n", + "梯度下降：需要选择学习率α，需要多次迭代，当特征数量n大时也能较好适用，适用于各种类型的模型\t\n", + "\n", + "正规方程：不需要选择学习率α，一次计算得出，需要计算${{\\left( {{X}^{T}}X \\right)}^{-1}}$，如果特征数量n较大则运算代价大，因为矩阵逆的计算时间复杂度为$O(n3)$，通常来说当$n$小于10000 时还是可以接受的，只适用于线性模型，不适合逻辑回归模型等其他模型" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# 正规方程\n", + "def normalEqn(X, y):\n", + " theta = np.linalg.inv(X.T@X)@X.T@y#X.T@X等价于X.T.dot(X)\n", + " return theta" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[-3.89578088],\n", + " [ 1.19303364]])" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "final_theta2=normalEqn(X, y)#感觉和批量梯度下降的theta的值有点差距\n", + "final_theta2" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "#梯度下降得到的结果是matrix([[-3.24140214, 1.1272942 ]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在练习2中，我们将看看分类问题的逻辑回归。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/code/ex1-linear regression/ex1.pdf b/code/ex1-linear regression/ex1.pdf new file mode 100644 index 00000000..dda3e963 Binary files /dev/null and b/code/ex1-linear regression/ex1.pdf differ diff --git a/code/ex1-linear regression/ex1data1.txt b/code/ex1-linear regression/ex1data1.txt new file mode 100644 index 00000000..0f88ccb6 --- /dev/null +++ b/code/ex1-linear regression/ex1data1.txt @@ -0,0 +1,97 @@ +6.1101,17.592 +5.5277,9.1302 +8.5186,13.662 +7.0032,11.854 +5.8598,6.8233 +8.3829,11.886 +7.4764,4.3483 +8.5781,12 +6.4862,6.5987 +5.0546,3.8166 +5.7107,3.2522 +14.164,15.505 +5.734,3.1551 +8.4084,7.2258 +5.6407,0.71618 +5.3794,3.5129 +6.3654,5.3048 +5.1301,0.56077 +6.4296,3.6518 +7.0708,5.3893 +6.1891,3.1386 +20.27,21.767 +5.4901,4.263 +6.3261,5.1875 +5.5649,3.0825 +18.945,22.638 +12.828,13.501 +10.957,7.0467 +13.176,14.692 +22.203,24.147 +5.2524,-1.22 +6.5894,5.9966 +9.2482,12.134 +5.8918,1.8495 +8.2111,6.5426 +7.9334,4.5623 +8.0959,4.1164 +5.6063,3.3928 +12.836,10.117 +6.3534,5.4974 +5.4069,0.55657 +6.8825,3.9115 +11.708,5.3854 +5.7737,2.4406 +7.8247,6.7318 +7.0931,1.0463 +5.0702,5.1337 +5.8014,1.844 +11.7,8.0043 +5.5416,1.0179 +7.5402,6.7504 +5.3077,1.8396 +7.4239,4.2885 +7.6031,4.9981 +6.3328,1.4233 +6.3589,-1.4211 +6.2742,2.4756 +5.6397,4.6042 +9.3102,3.9624 +9.4536,5.4141 +8.8254,5.1694 +5.1793,-0.74279 +21.279,17.929 +14.908,12.054 +18.959,17.054 +7.2182,4.8852 +8.2951,5.7442 +10.236,7.7754 +5.4994,1.0173 +20.341,20.992 +10.136,6.6799 +7.3345,4.0259 +6.0062,1.2784 +7.2259,3.3411 +5.0269,-2.6807 +6.5479,0.29678 +7.5386,3.8845 +5.0365,5.7014 +10.274,6.7526 +5.1077,2.0576 +5.7292,0.47953 +5.1884,0.20421 +6.3557,0.67861 +9.7687,7.5435 +6.5159,5.3436 +8.5172,4.2415 +9.1802,6.7981 +6.002,0.92695 +5.5204,0.152 +5.0594,2.8214 +5.7077,1.8451 +7.6366,4.2959 +5.8707,7.2029 +5.3054,1.9869 +8.2934,0.14454 +13.394,9.0551 +5.4369,0.61705 diff --git a/code/ex1-linear regression/ex1data2.txt b/code/ex1-linear regression/ex1data2.txt new file mode 100644 index 00000000..79e9a807 --- /dev/null +++ b/code/ex1-linear regression/ex1data2.txt @@ -0,0 +1,47 @@ +2104,3,399900 +1600,3,329900 +2400,3,369000 +1416,2,232000 +3000,4,539900 +1985,4,299900 +1534,3,314900 +1427,3,198999 +1380,3,212000 +1494,3,242500 +1940,4,239999 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"source": [ + "# 备注\n", + "运行环境：python 3.6 \n", + "现在我知道我应该考虑列向量，而Tensorflow对数据的形状非常挑剔。 但是在numpy中，正常的一维ndarray已经被表示为列向量。 如果我重新塑造$\\mathbb{R}^n$ 为 $\\mathbb{R}^{n\\times1}$，它不再是列向量了，而是是1列的矩阵,那使用scipy会有麻烦。\n", + "*所以我们应该把TensorFlow的数据视为特殊情况。 我们继续使用numpy的惯例。" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "plt.style.use('fivethirtyeight')\n", + "import matplotlib.pyplot as plt\n", + "# import tensorflow as tf\n", + "from sklearn.metrics import classification_report#这个包是评价报告" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 准备数据" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " exam1 exam2 admitted\n", + "count 100.000000 100.000000 100.000000\n", + "mean 65.644274 66.221998 0.600000\n", + "std 19.458222 18.582783 0.492366\n", + "min 30.058822 30.603263 0.000000\n", + "25% 50.919511 48.179205 0.000000\n", + "50% 67.032988 67.682381 1.000000\n", + "75% 80.212529 79.360605 1.000000\n", + "max 99.827858 98.869436 1.000000" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.describe()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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9XAMsfg/CGU4E8osQyivUuiwiIlNRNUyzs7Px/PPPDzpeVVWlZhlpw9rWiMymuuhji9+D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\nQfQ0sSgdcfF+7TFM1cIgTaj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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.set(context=\"notebook\", style=\"darkgrid\", palette=sns.color_palette(\"RdBu\", 2))\n", + "\n", + "sns.lmplot('exam1', 'exam2', hue='admitted', data=data, \n", + " size=6, \n", + " fit_reg=False, \n", + " scatter_kws={\"s\": 50}\n", + " )\n", + "plt.show()#看下数据的样子" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def get_X(df):#读取特征\n", + "# \"\"\"\n", + "# use concat to add intersect feature to avoid side effect\n", + "# not efficient for big dataset though\n", + "# \"\"\"\n", + " ones = pd.DataFrame({'ones': np.ones(len(df))})#ones是m行1列的dataframe\n", + " data = pd.concat([ones, df], axis=1) # 合并数据，根据列合并\n", + " return data.iloc[:, :-1].as_matrix() # 这个操作返回 ndarray,不是矩阵\n", + "\n", + "\n", + "def get_y(df):#读取标签\n", + "# '''assume the last column is the target'''\n", + " return np.array(df.iloc[:, -1])#df.iloc[:, -1]是指df的最后一列\n", + "\n", + "\n", + "def normalize_feature(df):\n", + "# \"\"\"Applies function along input axis(default 0) of DataFrame.\"\"\"\n", + " return df.apply(lambda column: (column - column.mean()) / column.std())#特征缩放" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(100, 3)\n", + "(100,)\n" + ] + } + ], + "source": [ + "X = get_X(data)\n", + "print(X.shape)\n", + "\n", + "y = get_y(data)\n", + "print(y.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# sigmoid 函数\n", + "g 代表一个常用的逻辑函数（logistic function）为S形函数（Sigmoid function），公式为： \\\\[g\\left( z \\right)=\\frac{1}{1+{{e}^{-z}}}\\\\] \n", + "合起来，我们得到逻辑回归模型的假设函数： \n", + "\t\\\\[{{h}_{\\theta }}\\left( x \\right)=\\frac{1}{1+{{e}^{-{{\\theta }^{T}}X}}}\\\\] \n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sigmoid(z):\n", + " return 1 / (1 + np.exp(-z))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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EP+PK2bZRbiBdbnqO12kAdCKKC4C4Z1dvlhUNN25tsSyv4wDoRBQXAHGPYSIg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\n1dTUxG67rivHcZrc/vWvf61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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "ax.plot(np.arange(-10, 10, step=0.01),\n", + " sigmoid(np.arange(-10, 10, step=0.01)))\n", + "ax.set_ylim((-0.1,1.1))\n", + "ax.set_xlabel('z', fontsize=18)\n", + "ax.set_ylabel('g(z)', fontsize=18)\n", + "ax.set_title('sigmoid function', fontsize=18)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# cost function(代价函数)\n", + "> * $max(\\ell(\\theta)) = min(-\\ell(\\theta))$ \n", + "> * choose $-\\ell(\\theta)$ as the cost function\n", + "\n", + "$$\\begin{align}\n", + " & J\\left( \\theta \\right)=-\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[{{y}^{(i)}}\\log \\left( {{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)+\\left( 1-{{y}^{(i)}} \\right)\\log \\left( 1-{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)]} \\\\ \n", + " & =\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[-{{y}^{(i)}}\\log \\left( {{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)-\\left( 1-{{y}^{(i)}} \\right)\\log \\left( 1-{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)]} \\\\ \n", + "\\end{align}$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0., 0., 0.])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta = theta=np.zeros(3) # X(m*n) so theta is n*1\n", + "theta" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def cost(theta, X, y):\n", + " ''' cost fn is -l(theta) for you to minimize'''\n", + " return np.mean(-y * np.log(sigmoid(X @ theta)) - (1 - y) * np.log(1 - sigmoid(X @ theta)))\n", + "\n", + "# X @ theta与X.dot(theta)等价" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.69314718055994529" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cost(theta, X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# gradient descent(梯度下降)\n", + "* 这是批量梯度下降（batch gradient descent） \n", + "* 转化为向量化计算： $\\frac{1}{m} X^T( Sigmoid(X\\theta) - y )$\n", + "$$\\frac{\\partial J\\left( \\theta \\right)}{\\partial {{\\theta }_{j}}}=\\frac{1}{m}\\sum\\limits_{i=1}^{m}{({{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}})x_{_{j}}^{(i)}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gradient(theta, X, y):\n", + "# '''just 1 batch gradient'''\n", + " return (1 / len(X)) * X.T @ (sigmoid(X @ theta) - y)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ -0.1 , -12.00921659, -11.26284221])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "gradient(theta, X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# 拟合参数\n", + "> * 这里我使用 [`scipy.optimize.minimize`](http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize) 去寻找参数 \n" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import scipy.optimize as opt" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "res = opt.minimize(fun=cost, x0=theta, args=(X, y), method='Newton-CG', jac=gradient)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " fun: 0.20349770172083584\n", + " jac: array([ 1.98942032e-06, 1.34698328e-04, 1.47259166e-04])\n", + " message: 'Optimization terminated successfully.'\n", + " nfev: 73\n", + " nhev: 0\n", + " nit: 30\n", + " njev: 270\n", + " status: 0\n", + " success: True\n", + " x: array([-25.16227358, 0.20623923, 0.20147921])\n" + ] + } + ], + "source": [ + "print(res)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 用训练集预测和验证" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def predict(x, theta):\n", + " prob = sigmoid(x @ theta)\n", + " return (prob >= 0.5).astype(int)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " precision recall f1-score support\n", + "\n", + " 0 0.87 0.85 0.86 40\n", + " 1 0.90 0.92 0.91 60\n", + "\n", + "avg / total 0.89 0.89 0.89 100\n", + "\n" + ] + } + ], + "source": [ + "final_theta = res.x\n", + "y_pred = predict(X, final_theta)\n", + "\n", + "print(classification_report(y, y_pred))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 寻找决策边界\n", + "http://stats.stackexchange.com/questions/93569/why-is-logistic-regression-a-linear-classifier\n", + "> $X \\times \\theta = 0$ (this is the line)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-25.16227358 0.20623923 0.20147921]\n" + ] + } + ], + "source": [ + "print(res.x) # this is final theta" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 124.88769463 -1.0236254 -1. ]\n" + ] + } + ], + "source": [ + "coef = -(res.x / res.x[2]) # find the equation\n", + "print(coef)\n", + "\n", + "x = np.arange(130, step=0.1)\n", + "y = coef[0] + coef[1]*x" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " exam1 exam2 admitted\n", + "count 100.000000 100.000000 100.000000\n", + "mean 65.644274 66.221998 0.600000\n", + "std 19.458222 18.582783 0.492366\n", + "min 30.058822 30.603263 0.000000\n", + "25% 50.919511 48.179205 0.000000\n", + "50% 67.032988 67.682381 1.000000\n", + "75% 80.212529 79.360605 1.000000\n", + "max 99.827858 98.869436 1.000000" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.describe() # find the range of x and y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "> you know the intercept would be around 125 for both x and y" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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4rTa9C2HNpLlY1IiDgwNTp06lffv2HDx4kPXr13NzI4g5Fp8QQghbIpWsqDFH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\n/CWH6EbZVckWFhbiwoULUKlUAGD+BJnFixcjOTk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" + ], + "text/plain": [ + " test1 test2 accepted\n", + "0 0.051267 0.69956 1\n", + "1 -0.092742 0.68494 1\n", + "2 -0.213710 0.69225 1\n", + "3 -0.375000 0.50219 1\n", + "4 -0.513250 0.46564 1" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_csv('ex2data2.txt', names=['test1', 'test2', 'accepted'])\n", + "df.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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tsH79eraptGfPnrC2tsa2bdvk+kOLioowdepUrFmzBhYWFujduzdsbGywf/9+udrbzz//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\nBg4ciK1bt6KmpgYbNmxAVVUVcnNzoVJ1/OXLzs5GTk6OPZd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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.set(context=\"notebook\", style=\"ticks\", font_scale=1.5)\n", + "\n", + "sns.lmplot('test1', 'test2', hue='accepted', data=df, \n", + " size=6, \n", + " fit_reg=False, \n", + " scatter_kws={\"s\": 50}\n", + " )\n", + "\n", + "plt.title('Regularized Logistic Regression')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# feature mapping（特征映射）\n", + "\n", + "polynomial expansion\n", + "\n", + "```\n", + "for i in 0..i\n", + " for p in 0..i:\n", + " output x^(i-p) * y^p\n", + "```\n", + "" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def feature_mapping(x, y, power, as_ndarray=False):\n", + "# \"\"\"return mapped features as ndarray or dataframe\"\"\"\n", + " # data = {}\n", + " # # inclusive\n", + " # for i in np.arange(power + 1):\n", + " # for p in np.arange(i + 1):\n", + " # data[\"f{}{}\".format(i - p, p)] = np.power(x, i - p) * np.power(y, p)\n", + "\n", + " data = {\"f{}{}\".format(i - p, p): np.power(x, i - p) * np.power(y, p)\n", + " for i in np.arange(power + 1)\n", + " for p in np.arange(i + 1)\n", + " }\n", + "\n", + " if as_ndarray:\n", + " return pd.DataFrame(data).as_matrix()\n", + " else:\n", + " return pd.DataFrame(data)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "x1 = np.array(df.test1)\n", + "x2 = np.array(df.test2)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(118, 28)\n" + ] + }, + { + "data": { + "text/html": [ + "
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[ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(118, 28)\n", + "(118,)\n" + ] + } + ], + "source": [ + "theta = np.zeros(data.shape[1])\n", + "X = feature_mapping(x1, x2, power=6, as_ndarray=True)\n", + "print(X.shape)\n", + "\n", + "y = get_y(df)\n", + "print(y.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def regularized_cost(theta, X, y, l=1):\n", + "# '''you don't penalize theta_0'''\n", + " theta_j1_to_n = theta[1:]\n", + " regularized_term = (l / (2 * len(X))) * np.power(theta_j1_to_n, 2).sum()\n", + "\n", + " return cost(theta, X, y) + regularized_term\n", + "#正则化代价函数" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6931471805599454" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "regularized_cost(theta, X, y, l=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "this is the same as the not regularized cost because we init theta as zeros...\n", + "因为我们设置theta为0，所以这个正则化代价函数与代价函数的值相同" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# regularized gradient(正则化梯度)\n", + "$$\\frac{\\partial J\\left( \\theta \\right)}{\\partial {{\\theta }_{j}}}=\\left( \\frac{1}{m}\\sum\\limits_{i=1}^{m}{\\left( {{h}_{\\theta }}\\left( {{x}^{\\left( i \\right)}} \\right)-{{y}^{\\left( i \\right)}} \\right)} \\right)+\\frac{\\lambda }{m}{{\\theta }_{j}}\\text{ }\\text{ for j}\\ge \\text{1}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def regularized_gradient(theta, X, y, l=1):\n", + "# '''still, leave theta_0 alone'''\n", + " theta_j1_to_n = theta[1:]\n", + " regularized_theta = (l / len(X)) * theta_j1_to_n\n", + "\n", + " # by doing this, no offset is on theta_0\n", + " regularized_term = np.concatenate([np.array([0]), regularized_theta])\n", + "\n", + " return gradient(theta, X, y) + regularized_term" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 8.47457627e-03, 7.77711864e-05, 3.76648474e-02,\n", + " 2.34764889e-02, 3.93028171e-02, 3.10079849e-02,\n", + " 3.87936363e-02, 1.87880932e-02, 1.15013308e-02,\n", + " 8.19244468e-03, 3.09593720e-03, 4.47629067e-03,\n", + " 1.37646175e-03, 5.03446395e-02, 7.32393391e-03,\n", + " 1.28600503e-02, 5.83822078e-03, 7.26504316e-03,\n", + " 1.83559872e-02, 2.23923907e-03, 3.38643902e-03,\n", + " 4.08503006e-04, 3.93486234e-02, 4.32983232e-03,\n", + " 6.31570797e-03, 1.99707467e-02, 1.09740238e-03,\n", + " 3.10312442e-02])" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "regularized_gradient(theta, X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 拟合参数" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import scipy.optimize as opt" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "init cost = 0.6931471805599454\n" + ] + }, + { + "data": { + "text/plain": [ + " fun: 0.5290027297127737\n", + " jac: array([ 1.05541650e-07, 6.13738958e-08, -7.04772465e-08,\n", + " -1.36777274e-08, -2.84652117e-08, -3.41659162e-08,\n", + " -5.15630062e-08, -1.74645557e-08, 7.50726574e-09,\n", + " 1.18564041e-08, 1.78853446e-08, 1.12436692e-08,\n", + " 8.73092759e-09, 5.56139873e-08, 4.12686771e-09,\n", + " -2.49410770e-08, -6.34978298e-09, -1.34271390e-08,\n", + " -2.13487848e-09, 4.54710087e-10, -4.37439525e-09,\n", + " -1.26745782e-09, -3.40985521e-09, 7.34158338e-09,\n", + " -7.74561697e-09, -9.84723852e-11, 9.65250750e-10,\n", + " -1.18501368e-08])\n", + " message: 'Optimization terminated successfully.'\n", + " nfev: 7\n", + " nhev: 0\n", + " nit: 6\n", + " njev: 66\n", + " status: 0\n", + " success: True\n", + " x: array([ 1.27273981, 1.18108974, -1.43166669, -0.17513036, -1.19281478,\n", + " -0.45635758, -0.9246528 , 0.62527237, -0.9174247 , -0.35723884,\n", + " -0.27470605, -0.29537769, -0.14388711, -2.0199599 , -0.36553508,\n", + " -0.61555685, -0.27778507, -0.32738029, 0.12400668, -0.05098942,\n", + " -0.04473108, 0.01556645, -1.45815829, -0.20600596, -0.29243192,\n", + " -0.24218804, 0.02777165, -1.04320421])" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print('init cost = {}'.format(regularized_cost(theta, X, y)))\n", + "\n", + "res = opt.minimize(fun=regularized_cost, x0=theta, args=(X, y), method='Newton-CG', jac=regularized_gradient)\n", + "res" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 预测" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " precision recall f1-score support\n", + "\n", + " 0 0.90 0.75 0.82 60\n", + " 1 0.78 0.91 0.84 58\n", + "\n", + "avg / total 0.84 0.83 0.83 118\n", + "\n" + ] + } + ], + "source": [ + "final_theta = res.x\n", + "y_pred = predict(X, final_theta)\n", + "\n", + "print(classification_report(y, y_pred))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 使用不同的 $\\lambda$ （这个是常数）\n", + "# 画出决策边界\n", + "* 我们找到所有满足 $X\\times \\theta = 0$ 的x\n", + "* instead of solving polynomial equation, just create a coridate x,y grid that is dense enough, and find all those $X\\times \\theta$ that is close enough to 0, then plot them" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def draw_boundary(power, l):\n", + "# \"\"\"\n", + "# power: polynomial power for mapped feature\n", + "# l: lambda constant\n", + "# \"\"\"\n", + " density = 1000\n", + " threshhold = 2 * 10**-3\n", + "\n", + " final_theta = feature_mapped_logistic_regression(power, l)\n", + " x, y = find_decision_boundary(density, power, final_theta, threshhold)\n", + "\n", + " df = pd.read_csv('ex2data2.txt', names=['test1', 'test2', 'accepted'])\n", + " sns.lmplot('test1', 'test2', hue='accepted', data=df, size=6, fit_reg=False, scatter_kws={\"s\": 100})\n", + "\n", + " plt.scatter(x, y, c='R', s=10)\n", + " plt.title('Decision boundary')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def feature_mapped_logistic_regression(power, l):\n", + "# \"\"\"for drawing purpose only.. not a well generealize logistic regression\n", + "# power: int\n", + "# raise x1, x2 to polynomial power\n", + "# l: int\n", + "# lambda constant for regularization term\n", + "# \"\"\"\n", + " df = pd.read_csv('ex2data2.txt', names=['test1', 'test2', 'accepted'])\n", + " x1 = np.array(df.test1)\n", + " x2 = np.array(df.test2)\n", + " y = get_y(df)\n", + "\n", + " X = feature_mapping(x1, x2, power, as_ndarray=True)\n", + " theta = np.zeros(X.shape[1])\n", + "\n", + " res = opt.minimize(fun=regularized_cost,\n", + " x0=theta,\n", + " args=(X, y, l),\n", + " method='TNC',\n", + " jac=regularized_gradient)\n", + " final_theta = res.x\n", + "\n", + " return final_theta" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def find_decision_boundary(density, power, theta, threshhold):\n", + " t1 = np.linspace(-1, 1.5, density)\n", + " t2 = np.linspace(-1, 1.5, density)\n", + "\n", + " cordinates = [(x, y) for x in t1 for y in t2]\n", + " x_cord, y_cord = zip(*cordinates)\n", + " mapped_cord = feature_mapping(x_cord, y_cord, power) # this is a dataframe\n", + "\n", + " inner_product = mapped_cord.as_matrix() @ theta\n", + "\n", + " decision = mapped_cord[np.abs(inner_product) < threshhold]\n", + "\n", + " return decision.f10, decision.f01\n", + "#寻找决策边界函数" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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c5Z1ylr/KmpPZ/FtdxS7kcsY3f/GiyYssrkzkFDhF8AXetbr77bff8N577+HC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SEhIAqKaWAaBFixY6z9WiRQts3LgRS5cuRXp6OhQKBZKSkrBp0yZ4ebne+h2b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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "draw_boundary(power=6, l=0) # no regularization, over fitting，#lambda=0,没有正则化，过拟合了" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Lk23Yilly7W63Bq7cus4oUSP4DylZwi6E0BbQGHxzX/IRtmOWfEnw4sqtSy0d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\nMxJbEgJH6tLUldKOR8yaGDvW+kpyQH30xNFENbp45MiRKC8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "draw_boundary(power=6, l=100) # underfitting，#lambda=100,欠拟合" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/code/ex2-logistic regression/ML-Exercise2.ipynb b/code/ex2-logistic regression/ML-Exercise2.ipynb new file mode 100644 index 00000000..3197f9c1 --- /dev/null +++ b/code/ex2-logistic regression/ML-Exercise2.ipynb @@ -0,0 +1,1193 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 机器学习练习 2 - 逻辑回归" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "这个笔记包含了以Python为编程语言的Coursera上机器学习的第二次编程练习。请参考 [作业文件](ex2.pdf) 详细描述和方程。\n", + "在这一次练习中，我们将要实现逻辑回归并且应用到一个分类任务。我们还将通过将正则化加入训练算法，来提高算法的鲁棒性，并用更复杂的情形来测试它。\n", + "\n", + "代码修改并注释：黄海广，haiguang2000@qq.com" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 逻辑回归" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在训练的初始阶段，我们将要构建一个逻辑回归模型来预测，某个学生是否被大学录取。设想你是大学相关部分的管理者，想通过申请学生两次测试的评分，来决定他们是否被录取。现在你拥有之前申请学生的可以用于训练逻辑回归的训练样本集。对于每一个训练样本，你有他们两次测试的评分和最后是被录取的结果。为了完成这个预测任务，我们准备构建一个可以基于两次测试评分来评估录取可能性的分类模型。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们从检查数据开始。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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Exam 1Exam 2Admitted
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\n", + "
" + ], + "text/plain": [ + " Exam 1 Exam 2 Admitted\n", + "0 34.623660 78.024693 0\n", + "1 30.286711 43.894998 0\n", + "2 35.847409 72.902198 0\n", + "3 60.182599 86.308552 1\n", + "4 79.032736 75.344376 1" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "path = 'ex2data1.txt'\n", + "data = pd.read_csv(path, header=None, names=['Exam 1', 'Exam 2', 'Admitted'])\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们创建两个分数的散点图，并使用颜色编码来可视化，如果样本是正的（被接纳）或负的（未被接纳）。" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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P+GFRX+vltXc+F2bZNW/ePD322GME7BRxdz322GOaN29ewx+DspA0GR6WVq6cuhq4sv3O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\nwGFJ1Vx/VNK7JHVXHDvZ3Q+W335I0sl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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positive = data[data['Admitted'].isin([1])]\n", + "negative = data[data['Admitted'].isin([0])]\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,8))\n", + "ax.scatter(positive['Exam 1'], positive['Exam 2'], s=50, c='b', marker='o', label='Admitted')\n", + "ax.scatter(negative['Exam 1'], negative['Exam 2'], s=50, c='r', marker='x', label='Not Admitted')\n", + "ax.legend()\n", + "ax.set_xlabel('Exam 1 Score')\n", + "ax.set_ylabel('Exam 2 Score')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "看起来在两类间，有一个清晰的决策边界。现在我们需要实现逻辑回归，那样就可以训练一个模型来预测结果。方程实现在下面的代码示例在\"exercises\" 文件夹的 \"ex2.pdf\" 中。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# sigmoid 函数\n", + "g 代表一个常用的逻辑函数（logistic function）为S形函数（Sigmoid function），公式为： \\\\[g\\left( z \\right)=\\frac{1}{1+{{e}^{-z}}}\\\\] \n", + "合起来，我们得到逻辑回归模型的假设函数： \n", + "\t\\\\[{{h}_{\\theta }}\\left( x \\right)=\\frac{1}{1+{{e}^{-{{\\theta }^{T}}X}}}\\\\] " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sigmoid(z):\n", + " return 1 / (1 + np.exp(-z))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们做一个快速的检查，来确保它可以工作。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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FxoyBPn1yp5EkrcRiLEm95eqri63aHKOQpJpkMZak3pASXHwx7LQTvOtdudNI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\nD/iWfPodA7wwAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nums = np.arange(-10, 10, step=1)\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,8))\n", + "ax.plot(nums, sigmoid(nums), 'r')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "棒极了！现在，我们需要编写代价函数来评估结果。\n", + "代价函数：\n", + "$J\\left( \\theta \\right)=\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[-{{y}^{(i)}}\\log \\left( {{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)-\\left( 1-{{y}^{(i)}} \\right)\\log \\left( 1-{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)]}$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def cost(theta, X, y):\n", + " theta = np.matrix(theta)\n", + " X = np.matrix(X)\n", + " y = np.matrix(y)\n", + " first = np.multiply(-y, np.log(sigmoid(X * theta.T)))\n", + " second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))\n", + " return np.sum(first - second) / (len(X))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在，我们要做一些设置，和我们在练习1在线性回归的练习很相似。" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# add a ones column - this makes the matrix multiplication work out easier\n", + "data.insert(0, 'Ones', 1)\n", + "\n", + "# set X (training data) and y (target variable)\n", + "cols = data.shape[1]\n", + "X = data.iloc[:,0:cols-1]\n", + "y = data.iloc[:,cols-1:cols]\n", + "\n", + "# convert to numpy arrays and initalize the parameter array theta\n", + "X = np.array(X.values)\n", + "y = np.array(y.values)\n", + "theta = np.zeros(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们来检查矩阵的维度来确保一切良好。" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0., 0., 0.])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((100, 3), (3,), (100, 1))" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X.shape, theta.shape, y.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们计算初始化参数的代价函数(theta为0)。" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.69314718055994529" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cost(theta, X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "看起来不错，接下来，我们需要一个函数来计算我们的训练数据、标签和一些参数thata的梯度。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# gradient descent(梯度下降)\n", + "* 这是批量梯度下降（batch gradient descent） \n", + "* 转化为向量化计算： $\\frac{1}{m} X^T( Sigmoid(X\\theta) - y )$\n", + "$$\\frac{\\partial J\\left( \\theta \\right)}{\\partial {{\\theta }_{j}}}=\\frac{1}{m}\\sum\\limits_{i=1}^{m}{({{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}})x_{_{j}}^{(i)}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gradient(theta, X, y):\n", + " theta = np.matrix(theta)\n", + " X = np.matrix(X)\n", + " y = np.matrix(y)\n", + " \n", + " parameters = int(theta.ravel().shape[1])\n", + " grad = np.zeros(parameters)\n", + " \n", + " error = sigmoid(X * theta.T) - y\n", + " \n", + " for i in range(parameters):\n", + " term = np.multiply(error, X[:,i])\n", + " grad[i] = np.sum(term) / len(X)\n", + " \n", + " return grad" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "注意，我们实际上没有在这个函数中执行梯度下降，我们仅仅在计算一个梯度步长。在练习中，一个称为“fminunc”的Octave函数是用来优化函数来计算成本和梯度参数。由于我们使用Python，我们可以用SciPy的“optimize”命名空间来做同样的事情。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们看看用我们的数据和初始参数为0的梯度下降法的结果。" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ -0.1 , -12.00921659, -11.26284221])" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "gradient(theta, X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在可以用SciPy's truncated newton（TNC）实现寻找最优参数。" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([-25.1613186 , 0.20623159, 0.20147149]), 36, 0)" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import scipy.optimize as opt\n", + "result = opt.fmin_tnc(func=cost, x0=theta, fprime=gradient, args=(X, y))\n", + "result" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们看看在这个结论下代价函数计算结果是什么个样子~" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.20349770158947464" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cost(result[0], X, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "接下来，我们需要编写一个函数，用我们所学的参数theta来为数据集X输出预测。然后，我们可以使用这个函数来给我们的分类器的训练精度打分。\n", + "逻辑回归模型的假设函数： \n", + "\t\\\\[{{h}_{\\theta }}\\left( x \\right)=\\frac{1}{1+{{e}^{-{{\\theta }^{T}}X}}}\\\\] \n", + "当${{h}_{\\theta }}$大于等于0.5时，预测 y=1\n", + "\n", + "当${{h}_{\\theta }}$小于0.5时，预测 y=0 。" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def predict(theta, X):\n", + " probability = sigmoid(X * theta.T)\n", + " return [1 if x >= 0.5 else 0 for x in probability]" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "accuracy = 89%\n" + ] + } + ], + "source": [ + "theta_min = np.matrix(result[0])\n", + "predictions = predict(theta_min, X)\n", + "correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y)]\n", + "accuracy = (sum(map(int, correct)) % len(correct))\n", + "print ('accuracy = {0}%'.format(accuracy))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们的逻辑回归分类器预测正确，如果一个学生被录取或没有录取，达到89%的精确度。不坏！记住，这是训练集的准确性。我们没有保持住了设置或使用交叉验证得到的真实逼近，所以这个数字有可能高于其真实值（这个话题将在以后说明）。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 正则化逻辑回归" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在训练的第二部分，我们将要通过加入正则项提升逻辑回归算法。如果你对正则化有点眼生，或者喜欢这一节的方程的背景，请参考在\"exercises\"文件夹中的\"ex2.pdf\"。简而言之，正则化是成本函数中的一个术语，它使算法更倾向于“更简单”的模型（在这种情况下，模型将更小的系数）。这个理论助于减少过拟合，提高模型的泛化能力。这样，我们开始吧。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "设想你是工厂的生产主管，你有一些芯片在两次测试中的测试结果。对于这两次测试，你想决定是否芯片要被接受或抛弃。为了帮助你做出艰难的决定，你拥有过去芯片的测试数据集，从其中你可以构建一个逻辑回归模型。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "和第一部分很像，从数据可视化开始吧！" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Test 1 Test 2 Accepted\n", + "0 0.051267 0.69956 1\n", + "1 -0.092742 0.68494 1\n", + "2 -0.213710 0.69225 1\n", + "3 -0.375000 0.50219 1\n", + "4 -0.513250 0.46564 1" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "path = 'ex2data2.txt'\n", + "data2 = pd.read_csv(path, header=None, names=['Test 1', 'Test 2', 'Accepted'])\n", + "data2.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ApvT0hKopPT2zM+Td3bPbc7N4E8kbGwvVa+J13KPqNRs3UlcdQKmlWmccQL6sWxeqpuza\nFXLEV60KM+IE4ljQwMBsQyNpbl33zZupqw6g1ChtCGQV5ffQrDw8V+J13CPxOu8AUDCUNgTyjlP7\naFYenitRh9E4AnEAIBgHMit+aj8Ksji1j3ry8FyJxhQX//AAACVFMI5yykN1h2gmMQqyurpmgytm\nFBGX9edK7YeDmZn5Hx4AoKTIGUc5jY6G0/fxYCUeMIyMhE6MWeA+t6bgzEz6wRWyKavPlTz9vwFA\nm5AzDiwkD6f1JU7to3lZfq4MDISAOz5LH83mj4xk5/8NAFJAMI5yyvppfYlT+2he1p8rZmHmu/b/\nqtF2IC4PaYVACwjGUV5Zr+4wNjb/A0L8A0QWKmQgG3iuoMjyUC0IaAHBOMory6f1JU7to3k8V1Bk\neUkrBJaJBZwop9oX89qOgFmaIQeAsqNpFHKo2QWcBOMoJ6o7AEC+ZLVaENAA1VSAhXBaHwDyI+tp\nhUALCMZRTlR3AIB8yHq1IKBFh6Y9AAAAgIYaVQuSwvb+ftIKkWsE4wAAILuitMKBgflphf39pBUi\n9wjGAQBAdkXpg81uB3KGnHEAAAAgJQTjAAAAQEoIxgEAAICUEIwDAAAAKSEYBwAgSe6hC3BtfexG\n2wEUGsE4ALRBpSLt3Clt2xYuK5W0R4TMGhuTNm6c27AmamyzcWPYD6A0KG0IAC0aH5fWrw+NAaen\npe5uaetWafduad26tEeHzBkYmO0gKYV62fEOk9TNBkrFvESnw/r6+nxiYiLtYQAokEpF6u2tPxPe\n0yMdOCCtWJH8uJBx8RbvkXiHSQC5Z2Z73L1vsduRpgIgd7KUErJrV5gRr2dmJuwH5om3dI8QiAOl\nRDAOIFfGx8NM9JYt0o4d4bK3N2xPw+RkSE2pZ3pa2rs32fEgJ6KZ8bh4DjmA0iAYB5AblUrIza5U\nZgPg6enZ7VNTyY9p9eqQI15Pd7e0alWy40EOxFNUNm8Op1CiHHICcqB0CMYB5EYWU0IGB6WuBq+k\nXV1hPzDH2NhsIB6lpgwNzQbkVFMBSoVgHEBuZDElpKcnVE3p6ZmdIe/unt3O4k3MMzAgjYzMzRGP\nAvKREaqpACVDMA7goCwtjKwnqykh69aFqinDw9L27eHywIEclDXMcvOZLI+tVWbShg3zF2s22g6g\n0AjGAUjK3sLIerKcErJihbRpk3TppeEyFzPiWW4+k+WxAUAbEYwDyOTCyHpICWmzePOZKOjNSvOZ\nLI8NANqIDpwAmloYuWlTsmNqJEoJ2bUr5IivWhVmxAnElyFe63p4eLYBTRaaz2R5bADQRnTgBKBt\n20JqSiPbt4f0CxSU+9z8n5mZ7AS7WR5b3rmHdJ+BgbnHtNF2AEtCB04ATcvqwkgkIMvNZ7I8tiIg\nLx/IBIJxAJleGIkOynLzmSyPrSjIywcyIdWccTM7W9KwpEMk7XT3P6/Z//uS3li9eqikUyQd4+6P\nmtk+SRVJv5T0RDOnAQDUFy2AXL8+xDzT02FGvKuLhZGF1qj5jBS29/eHUnuMrZjIywcyIbWccTM7\nRNLdkl4h6T5J35Z0obvf0eD2r5V0ibu/tHp9n6Q+d/9xs7+TnHFgYVNTLIwslSznDGd5bEVDXj7Q\nEc3mjKc5M36GpL3u/n1JMrNrJJ0rqW4wLulCSVcnNDaglKJa2SiJqMlMs9uTlOWxFUmjvHxmxoHE\npJkz3ivpR7Hr91W3zWNmR0g6W9I/xza7pBvMbI+ZXdzol5jZxWY2YWYTDz/8cBuGDQBAAWQpL7/I\nHVeBReRlAedrJX3d3R+NbVvn7msknSPp3Wb2knp3dPcr3L3P3fuOOeaYJMYKAED2NcrLjwLyJKup\nUNkFJZZmmsp+SSfErq+sbqvnAtWkqLj7/urlQ2Y2qpD2cmMHxgkAQPEMDEgjI3Pz76OAvL8/2Woq\n8couUhgDlV1QEmku4DxUYQHnyxSC8G9LeoO7f7fmdk+V9ANJJ7j7dHVbt6Qud69Uv/+SpD919y8s\n9DtZwAkAQEbF02YiVHZBjmW+6Y+7PyHpPZK+KOlOSf/o7t81s3eY2TtiN90g6fooEK86VtK4md0q\n6VuS/m2xQBwAAGRYvNRihEAcJZBqzri773b3X3P3/8fd/6y67XJ3vzx2m0+6+wU19/u+u59W/Xpu\ndF+UWB4X/+RxzADQKXRcRUnlZQEnsLA8Lv7J45hTUqlIO3dK27aFy0ol7RFlC8cHuZelyi5A0ty9\nNF/Pf/7zHQU1M+O+ebO7FC7rXc+aPI45BV/7mntPj3t3dzg03d3h+te+lvbIsoHjg0IYGZn/2hd/\nTRwZSXd8wDJImvAm4tPUFnCmgQWcBZfHxT95HHMbVCqh0+fkpLR6dej02dNT/3a9vfVnent6pAMH\nyt0hlOPTWc0+T9EGdFxFATW7gJNgHMWSx7bOeRxzC8bHpfXrw8Ocnpa6u8PD371bWrdu7m137pS2\nbAm3q9XdHT7DlLljKMenc5byPAWAejJfTQUZU4TFhHlc/JPHMbegUgkBTqUyG0BOT89un5qae/vJ\nyfqBZnS/vXvbP7485V4nfXzKYqnPUwBoBcE4grwvJszj4p88jrlFu3aFh1nPzEzYH7d6dZiRrKe7\nW1q1qn1jGx8PKR9btkg7doTL3t6wPauSPD5lstTnKQC0gmAcQbz7WRQI5qn7WZbaOjcrj2Nu0VJn\ncgcH52bwxHV1hf3tkNeZ0KSOT9lwxgFAkg5NewDIiHizheHh2QWFeVlMmKW2zs3K45hbFM3kNspx\nrp3J7ekJObqNcnfbtTixmZnQLOZeJ3V8ymapz9OksbAUKBYWcGKuki0mRLKWW/1jaioEH3v3hkBo\ncLC9gea2bSE1pZHt26VLL23f72u3Th+fsslylRoWlhYcVWUKpdkFnMyMY1ajxYR5mBlHLix3JnfF\nis7OTGd9JnQxnT4+ZZPVMw7xdKpI9Jxdv55SloUQrd+Kn5WOp42OjEgbNqQ9SrQZwTiC2hzxoaG5\n9a8JyNEm69aFoCFLM7mDg9LWrfX3kXtdTll8nuY1nQpLEF+/Jc19L87D+i0sC8E4gkaLCaWwvb+f\nT+Nom6XO5HY6RzarM6FIV9bOOLCwtATyvn4Ly0LOOALy1JBRSebIknuNLKPJU4mwfqsQ6MBZB8E4\nkC9ZXkgHJI3/hyYUYWIpnjYaYWY8l+jACbRR3jozFgXNV4BZUTpVT89ss6fu7tntpQ/EJRrYIZfI\nGQcWUS9NYutWSoklgRxZYK4sLizNlLwvgGT9VikRjAMLoJRYuvJechDohKwtLM2UvC+ALGEzOJCm\nAiyINIl00e4dHeEujY7OP+XfaDvyJR6QR/IQiEthjBs2zB9ro+0oBIJxYAGkSaSLHFl0RN7zirGw\nRg3s+JCFjCJNBVgAaRLpI0cWbZf3vGI0RgM75BClDYEFUEoMKCjKxxXT6Cjt5JEZ1Bmvg2Acy5Fk\n0xkACaKxSvEUoc44CoM648iNrNfwjtIkhoel7dvD5YEDBOJArpFXnK5OLaJlASRyiJxxpCovNbwp\nJQYUCHnF6YsW0ZJOAhCMIz3U8AaQChqrpI9FtMBBBONITTM1vJmNBtB2TTZWqVTC69DkZKisNDgY\nFm6jDfLenAdoIxZwIjXbtkk7djTev327dOmlyY0HwOLKEqCycDshLKJFgbGAE5kX1fCuhxreQPaM\nj4dSn1u2hA/SW7aE6+PjaY+sveIpdFHq3PT07PapqXTHVxgsogUkEYwjRbQ6B/KjTAFqMyl0aFHt\nItqZmdkccgJylAzBOFJDq3MgP8oUoE5O1u+6K4Xte/cmO55CarSINgrIx8bSHiGQGBZwIlW0Ogfy\noUwBapRCV+/xkkLXJk0uogXKgGAcqaOGN7KiLIsTl6NMAergYOh3UA8pdG0SNeFpdjtQYFRTAVAo\nyw2oqZ6xsEolLNas1yG3p6d4fQF4PgBoVbPVVAjGARTGcgOosgWay1W2AHVqihQ6AMvXbDBOmkqZ\nuIdFMfEcvYW2AznSSkdXGlA1p9k1HkVJ9yGFDkASCMbLZGxM2rhx7ur1eHmpkRFy9ZBbrQTUZVqc\n2KrFAtR6s+dbtxZ39hwAWkVpwzIZGJhfxzVe55XV68ixVgJqGlC1R5lqkQNAuxCMl0ltHdeurvl1\nXoGcaiWgpgFVe3SiFnmlIu3cKW3bFi7r5fUDQJ4RjJdNFJDHEYijAFoJqGlA1R7tTvcZHw8La7ds\nkXbsCJe9vWE7ABQFwXjZRKkpcbQeRgG0GlBHixOHh6Xt28PlgQPkOS9FO9N9SHkBUBYs4CyT2hzx\noaHZ6xIz5Mi9Vju6Uj2jNe1slkOFGwBlQTBeJmNj83PEo5SV4eHQgphqKplUlFJxSSCgTk90FqJR\nLfKlpPtQ4Qa5QulgtIBgvEwGBkL5wviLQhSQ9/dTTSWjKBWHPGn17EQkSnmpF5BT4QaZQ+lgtCDV\nDpxmdrakYUmHSNrp7n9es/+3JF0r6QfVTSPu/qfN3LceOnBmHDML89AZEmXFcx+5slAaKBXLSqvZ\nDpypLeA0s0MkXSbpHEnPkXShmT2nzk2/5u5rql9/usT7Ik+imYX4gtLoBW7jxrC/ZDpRKg7IAyrc\nZBslJ2tQOhgtSDNN5QxJe939+5JkZtdIOlfSHR2+L7Iq3pRImj+zUMI0GvJmUWbtSnlBe5E610AU\nkEfvYRKBOJqSZjDeK+lHsev3SfqNOrd7kZl9R9J+Sb/n7t9dwn1lZhdLuliSTjzxxDYMGx1Tu6A0\nekEr8cwCebMoOxbkZku85GQken1av77k6UONSgeX9P0Lzct6nfGbJZ3o7qdK+htJS85TcPcr3L3P\n3fuOOeaYtg8QbUZTojnS7gzJqWgAcaTONVCbMz4zM3uml14eWESawfh+SSfErq+sbjvI3X/m7lPV\n73dLOszMjm7mvsgpmhLNkWbeLN0PAdQida6BRqWDo4C8hGue0Lw001S+LWm1mZ2sEEhfIOkN8RuY\n2TMlPejubmZnKHx4eETSTxa7L3Io4aZEeandnUbeLKeiAdRD6lwDlA5GC9Iubbhe0l8rlCe80t3/\nzMzeIUnufrmZvUfSOyU9Iek/JW1195sa3Xex30dpw4wbHU2sTmu9BUhRY5JSL0Cq2rkzzIQ3esMd\nHiaPFygjSk4CzWu2tGGqTX+qqSe7a7ZdHvv+byX9bbP3Rc4lNLPArO/iOBUNoJ52dlkFENCBE9lh\nVn/mu9H2ZWpmAVLZZ305FQ2gEUpOAu1FMI7SYdZ3cYODoW5wPUlUcQGQbZScBNqHYBylw6zv4jgV\nDaDs8rLIH/mX6gLOpLGAExILkJZiaopT0QDKh0X+aIdcLOAE0sCsb/M4FQ2gbFjkj6QRjKOUWIAE\nAKiHRf5IGsE4SotZXwBALRb5I2ldaQ8AAAAgK6JF/vWwyB+dQDAOAABQNTgY1hDVQ2lXdALBOAAA\nQFW0yL+nZ3aGvLt7djtri9Bu5IwDAADEsMgfSSIYB4CU0FQEyC4W+SMpBOMAkIJ6TUW2bqWpCACU\nDTnjAJCweFORqITa9PTs9qmpdMcHAEgOwTgAJKyZpiIAgHIgGAeAhNFUBAAQIRgHgITRVAQAECEY\nB4CE0VQEABAhGAeAhNFUBEBmuUujo+Gyme1oGcE4AKQgaioyPCxt3x4uDxygrCGAlI2NSRs3Spdc\nMht4u4frGzeG/Wgr6owDSAUNb2gqAiCDBgakzZvDDIEkDQ2FQHx4OGwfGEh3fAVkXqLTDX19fT4x\nMZH2MIDSq9fwpquLhjcAkAnRTHgUkEshEB8akszSG1fOmNked+9b9HYE4wCSVKlIvb3hslZPT0jV\nIGcaAFLmPnel+cwMgfgSNRuMkzMOIFE0vAGAjItmxuPiOeRoK4JxJKJSkXbulLZtC5f1ZkVRDjS8\nAYAMi6eobN4cZkmiHHIC8o5gASc6rl5+8Nat5AeXVdTwpl5ATsMbAEjZ2NhsIB7liA8NhX3Dw1J/\nv7RhQ7pjLBhyxtFR5AejFs8JAMgw9xCQDwzMzRFvtB0NkTOOTCA/GLVoeAMAGWYWZr5rA+5G29Ey\n0lTQUeQHo56o4c2uXeE5sGpVqDNOIA4AKBuC8U4r+eke8oM7owgNc2h4AwAAaSqdV/K2soODc8uU\nxnV1hf1xzcWEAAAgAElEQVRYmvHxkHO9ZYu0Y0e47O0N2wEAQL4QjHdavK1sFJCXqK0s+cHtVamE\nyjSVyuzZhunp2e1TU+mODwAALA1pKp1WWxIoai1boray5Ae3TzMLYkn9AAAgP5qaGTezlWZ2VvX7\n/2Fm3Z0dVsHEA/JIuwJxd2l0dH4R/kbbUxLlB196abgkEF8eFsQCAFAsiwbjZvY2SddJ2lnd9CuS\nru3koAqnk21lS56TXjbRgth6WBALAED+NDMz/l5JL5T0M0ly97slPaOTgyqUTreVLXlOetmwIBYA\ngGJpJhj/ubv/d3TFzA6RVPxE53Zp1FY2CqBbnbmu/XldXfN/HwqDBbEAUGA5ST1Fe5kv8oc1s7+S\n9KCkt0p6l6R3S5p09/d1fnjt1dfX5xMTE8n+0qTqjLvPnTKdmSEQL7CpKRbEAkDhjI6GFNP4hFr8\njPfISOiCiVwwsz3u3rfY7ZqppvIHki6WdJekzZK+KOl/tza8Eonaxza7fTka5aQzM15YNMwBkHVF\naE6WuHjqqRTex0k9LbwFg/FqSson3P3Nkv4+mSFhSWpzxOP/uBIBOQAgcePjoffBzEyo9NTdLW3d\nGtLp1q1Le3QZRjnkUmomTWVc0lnu/otkhtQ5qaSpdBqntAAAGVKphK7Alcr8fT09oe8EaXWLIPW0\nEJpNU2lmAec9kr5mZu8zs/dGX60PEW0xMBAC7vgn5uiT9cgIp7QAAIlqpjkZFtDJcsjIpGaC8R9K\n+pKkIyQdE/tqmZmdbWbfM7O9Zra9zv43mtl3zOw2M7vJzE6L7dtX3X6LmRVsunsJotzz2k/MjbYD\nANBBNCdrQafLISOTFl3A6e5/LElm9uTq9f9sxy+u5qNfJukVku6T9G0zu87d74jd7AeS+t39MTM7\nR9IVkn4jtv8sd/9xO8YDAABaFzUnqxeQ05xsEY3KIUthe38/qacF1EwHzueY2bclTUqaNLNvmtkp\nbfjdZ0ja6+7fr9Yxv0bSufEbuPtN7v5Y9eo3JK1sw+8FAAAdQnOyFpB6WkrNpKlcIekP3X2lu6+U\n9H5J/9CG390r6Uex6/dVtzWySdLnY9dd0g1mtsfMLm7DeAAAQItoTtYCUk9LqZk64z3u/qXoirvf\nUG0ElBgzO0shGI8XRFrn7vvN7BmSvmRmd7n7jXXue7FCnXSdeOKJiYwXAIAyW7cuVE2hORmwuGaC\n8X1m9j5Jn65ef5OkfW343fslnRC7vrK6bQ4zO1XSTknnuPsj0XZ331+9fMjMRhXSXuYF4+5+hcLs\nvvr6+lj5AABAAmhOBjSnmTSVtykEzbsl/ZtC0Py2Nvzub0tabWYnm9mTJF0g6br4DczsREkjki5y\n97tj27vNrCf6XtIrJd3ehjEBAAAAiWmmmsojkt7V7l/s7k+Y2XskfVHSIZKudPfvmtk7qvsvl/S/\nJB0l6e8s5Ek9US2efqyk0eq2QyV91t2/0O4xAstFG2gAANCMZjpwfkHSBe7+k+r1p0v6P+7+6gTG\n11aF7MCJpiUVINdrA93VRRtoAADKpNkOnM3kjB8bBeKSVK35fXxLowMSVi9A3rq1/QFypRJ+T7wN\ndFRrd/162kADAIC5mskZnzGzg/W9q3ncQG7EA+QoMJ6ent0+NdW+30UbaAAAsBTNBOP/S9LXzewT\nZvZJhYolf9jRUQFtlGSATBtoAACwFM0s4Pw3MztD0pkKjXb+wN0f6vjIgDZJMkCmDTQAAFiKhjPj\nZnaCmT1Fktz9QUmPSnqJpAvM7LCExge0LAqQ62l3gEwbaAAAsBQLpal8TtJTJMnMTpM0KukhheY6\nl3V+aEB7JBkg0wYaAAAsxUJpKke4+33V79+kUAf8L8ysS9KtnR8a0B5RINyo3GC7A2TaQAMAgGYt\nFIxb7PuXSnq/JLn7jJnRVh65knSATBvoxdEYCQCAhYPx/2tmn5V0v0IXzK9Ikpk9U9IvEhgb0FYE\nyNmRVN13AACybqGc8fdK2i3pAUm/6e7/Xd1+vKQ/7vTAABRTknXfAQDIuoYz4+4+I+n/1Nl+c0dH\nBKDQmqn7zhkMABLpbCiHReuMA0A70RgJQDNIZ0NZNNOBEwDaJsm67wDyiXQ2lAnBOIBE0RgJwGKa\nSWcDimKhDpw9ZvYhM/uEmb2+Zt/fdH5oAIqIxkgAFkM6G8pkoZzxKyXdK+nfJL3NzH5b0pvc/ReS\nXpzE4AAUE42RACwkSmerF5CTzoaiMff6/XvM7BZ3XxO7/gFJL5f0Oklfdve1yQyxffr6+nxiYiLt\nYQAAgAVUKlJvb7is1dMTPszz4R1ZZ2Z73L1vsdstlDN+uJkd3O/ufyLpk5JulHRkyyMEAACog3Q2\nlMlCaSr/Jullkr4UbXD3j5vZA5L+ttMDAwAA5UU6G8qiYZpKEZGmAgAAgCS0I00FAAAAQAcRjAMA\nAAApWTQYN7N5eeX1tgEAAACpcJdGR8NlM9szpJmZ8W81uQ0AAABI3tiYtHGjdMkls4G3e7i+cWPY\nn1ENZ7jN7BmSjpP0ZDN7niSr7nqKpCMSGBsAAACwuIEBafNmaXg4XB8aCoH48HDYPjCQ7vgWsFC6\nyaslvU3SSkmXaTYYr0j64w6PCwAAAFnmHmacBwYks8W3d5JZCMClEIBHQfnmzWF7UuNYhkVLG5rZ\n6939HxMaT0dR2hAAAKBNRkdDCkg84I1SQ4aHpZERacOGZMfkLnXFsrBnZlILxNtZ2vAZZvaU6g+9\n3My+ZWYva3mEAAAAyK94akiUq51makj0++PiOeQZ1UwwfrG7/8zMXqmQQ/47knZ0dlgAAADItCg1\nJArIu7pmA/GkU0NqPwjMzMz/oJBRzQTj0ejXS/qUu9/a5P0AAABQZPFc7UgaOdpjY/M/CMQ/KGS4\nmkozQfWtZrZb0mskfd7MVmg2QAcAAEBZZSU1ZGAg5KjHPwhEAfnISKarqTQTjL9V0gclneHuj0s6\nXNKmTg4KAAAAGZel1BCzsFi0dka+0fYMWbSTprv/0sx+VdIrJP2ZpCeLNBUAAIBya5QaIoXt/f3J\nV1PJoWZKG/6tpMMkvcTdTzGzIyV90d1fkMQA24nShgAAAG2SpTrjGdTO0oYvcve3S/q5JLn7o5Ke\n1OL4kDXuoV5o7YezRtsBAEC55Tg1JEuaCcZ/YWZdqi7aNLOjJM10dFRI3thYKNwfz/GKcsE2bsz0\nKuSiqFSknTulbdvCZaWS9ogAAECnNcwZN7ND3f0JSZdJ+mdJx5jZn0h6vaQ/SWh8SEq8cL8Ucr7S\nLNxfMuPj0vr1Ye3L9LTU3S1t3Srt3i2tW5f26AAAQKc0zBk3s5vdfW31++dKerkkk3SDu9+e3BDb\nh5zxRcRXRUfSKNxfMpWK1Ntbfya8p0c6cEBasaLzY9i1S5qclFavlgYHw+8GAADL02zO+ELB+P/n\n7qe3fWQpIhhvgnvooBWZmSEQ77CdO6UtW8KMeK3u7vDZaFMHi4nWm5Xv6mJWHgCAVjQbjC9U2vAY\nM9vaaKe7f3RZI0N2NSrcz8x4R01O1g/EpbB9797O/e5KJQTi8Vn5aCzr1yczKw8AQJkttIDzEEkr\nJPU0+EKRZKlwf8msXh1mo+vp7pZWrerc7961K/yp65mZCfsB5AOLwNF2VFpLxEIz4/e7+58mNhKk\nK0OF+8uWvzw4GBZr1tPVFfZ3Spqz8gDah0Xg6Iio0lo8NohP3o2M0NSnDRYKxslLKJOBgfBPFS/Q\nHwXk/f2JVVMp4xtKT094fI3ytjuZJhLNyjfKV+/krDyA9iDdDB1DpbVELLSA88hqg5/O/XKzsyUN\nK6TE7HT3P6/Zb9X96yU9Lul/uvvNzdy3HhZwZlsWqoqkaWoqnBHYuzcEwYODyVRRKfMxB4og7UXg\nKDgqrS1byx04EwjED1GoYX6OpOdIutDMnlNzs3Mkra5+XSzp75dwX+RM2fOXV6wIb5iXXhoukwiC\no1n5np7ZvPXu7tntBOJA9pFuho6Kp61GCMTbaqE0lU47Q9Jed/++JJnZNZLOlXRH7DbnSvqUh+n7\nb5jZ08zsOEknNXFf5AxvKOlYty7MgCc9Kw+gPUg3Q0dRaa3j0gzGeyX9KHb9Pkm/0cRtepu8L3KG\nN5T0RLPynVa2xblAEtJcBI6Cq620Fs8ZlwjI22Sh0oaFYGYXm9mEmU08/PDDaQ8HCxgcnNtvKI43\nlPwbHw/56Vu2SDt2hMve3rAdwPKRboaOaVRpLVrUOTaW9ggLIc2Z8f2STohdX1nd1sxtDmvivpIk\nd79C0hVSWMDZ2pDRSWlWFUFnUe0B6CzSzdARGam0VnRpBuPflrTazE5WCKQvkPSGmttcJ+k91Zzw\n35D0U3e/38webuK+yCHeUIqpmcW5VHsAWpNUulli3MPMazwQXGg72s+sfh3xRtuxLKkF4+7+hJm9\nR9IXFcoTXunu3zWzd1T3Xy5pt0JZw70KpQ3futB9U3gY6IDCvaGAxbkAlo6GMyiJNGfG5e67FQLu\n+LbLY9+7pHc3e18A2cTiXABLRsMZlETDpj9FRNMfIB00FwKwLDScQY613PQHANqFag8AloWGMyiB\nVNNUAJQHi3MBLBkNZ1ACzIwDmOUujY6Gy2a2L1G0OPfSS8MlgTiAhmobzszMzOaQX3JJy69HQFYQ\njAOYFVUviL/RRW+IGzfS4AFAcmg4g5IgGEfyOjz7ihbEqxdEATnVCwCkIWo4E09JiQLyqBENUAAE\n40ges6/ZVTvz1NU1f2YKAJIQNZapfd1ptB3IKYJxJI/Z12yjegEAAIkhGC+DrKWFMPuabY2qF5A+\nBADZk7X3eCwZwXgZZDEthNnXbKJ6AQDkSxbf47EkBONlkMW0EGZfs4nqBQCQL1l8j8eSmJco+Onr\n6/OJiYm0h5GOLLUUrn2hGBqaf50Z8nS4h4B7YGDu36DRdgBA+rL0Ho+DzGyPu/ctejuC8RJxD/nZ\nkZmZdP5JR0fDqbP4C0X8hWRkJKyUBwAAzcnKezwOajYYJ02lLLKUFkLtWAAA2idL7/FYMoLxMsja\nojxqxwIA0B5Ze4/Hkh2a9gCQgEaL8qSwvb+ftBAAAPKI9/jcI2e8DFiUBwBAMfEen1ks4KyjtME4\nAAAAEsUCTqDd6HIGAADajGAcaBZdzgAAQJuxgBNoVrzLmTS/WRElGQGg4yoVadcuaXJSWr1aGhyU\nenrSHhWwfOSMA0tBlzMASM34uLR+fajeNz0tdXeHPje7d0vr1qU9OmAuFnDWQTCOtqDLGQAkrlKR\nenvDZa2eHunAAWnFiuTHBTTCAk6gE+hyBgCp2LUrzH3UMzMT9gN5RDAONIsuZ8iBSkXauVPati1c\n1ptFBPJocjKkptQzPS3t3ZvseIB2YQEn0Cy6nCHj6uXTbt1KPi2KYfXq8JyuF5B3d0urViU/JqAd\nyBkHmkWXM2QY+bQoOp7jyBtyxoF2Mwsz37UBd6PtQILIp0XR9fSEszw9PWEmXAqX0XYCceQVaSoA\nUADk06IM1q0LM+C7doXn9KpVoc44gTjyjGAcAJYgqw1HyKfFQrL6vF2OFSukTZuS/Z1FOn7IHnLG\ngRLjDWZpstxwhHxaNJLl520ecPywXDT9qYNgHJjFG8zS5CHY5W+KWnl43mYZxw+tYAEngIYqlRC0\nVSqzaQ3T07Pbp6bSHV8W5WGBZJRPOzwsbd8eLg8cIBAvszw8b7OM44ckEIwDJcQbzNLlZYFklE97\n6aXhklm7csvL8zarCnf83KXR0flN6hptRyIIxoESKtwbTAKiBZL1sEASWcXztjWFO35jY9LGjXO7\nRkfdpTduDPuROIJxLB2frHOv028wRWzJPjgY8q/r6eoK+4Gs4XnbmsIdv4GB0EV6eHg2IL/kktnu\n0gMDaY+wlAjGsXR8ss69Tr7BjI+HBU9btkg7doTL3t6wPc9oOII84nnbmsIdPzNpaGg2IO/qmg3E\nh4ZoXpcSqqlg6Wo/SQ8Nzb/OP3TmdaLyRhkqD0xN0XAE+cPztjWFO37uc2dkZmZ43+4AShvWQTDe\nRvGAPEIgnjvtfoPZuTPMhDdqPDM8nHyzDqAeauyjtHj/TkyzwTgdOLE80amu+D8z/8i50+5OdiwM\nRR7UOyu0dSv12FECC53ZlngfTwk541ie6B86Lp5DjlIqXOUBFA419lFqY2PzU0rjOeSs+UoFwTiW\nrvaT9czM/NXZKKXCVR5A4VBjP7+KWKUpcQMD0sjI3BnwKCAfGaGaSkpIU8HSNfpkLYXt/f3Shg3p\njhGpiCoMNFoYmusFTygEUqnyidSiNjGr//7caDsSkUowbmZHStol6SRJ+yS93t0fq7nNCZI+JelY\nSS7pCncfru77oKTfkfRw9eZ/6O67kxg7NPvJemBg/ifr/n4+WZdc1JK9UJUHUBhRKlWjRcakUmVP\nPLUoEv391q8vRpUmlFtaaSrbJX3Z3VdL+nL1eq0nJP2/7v4cSS+U9G4ze05s/5C7r6l+EYhLyTXj\niT5B1y7yaLQdzSlQMyVasiOrSKXKH1KLUHRpBePnSrqq+v1VkuZNpbr7/e5+c/X7iqQ7JfUmNsI8\nohlPvvH3AzqucE1cSoDUIhRdWjnjx7r7/dXvH1BIRWnIzE6SdLqkb8Y2/66ZvVnShMIM+mN17ioz\nu1jSxZJ04okntjbqrIu3uZXmN+MhfSTb+PsBiSCVKl9ILULRdazpj5ndIOmZdXa9X9JV7v602G0f\nc/enN/g5KyT9X0l/5u4j1W3HSvqxQi75hyQd5+5vW2xMpWj6QzH/TFu00Qh/v5bRzAUoljJ09kUx\nZboDp5l9T9Jvufv9ZnacpH9392fVud1hkv5V0hfd/aMNftZJkv7V3X99sd9bimBcos1tRjXdfp6/\n37I1fYwB5Ar/28ijZoPxtHLGr5P0lur3b5F0be0NzMwkfVzSnbWBeDWAj2yQdHuHxpk/NOPJpKYb\njfD3WzaauQDFFaUWDQ9L27eHywMHCMRRDGkF438u6RVmNinp5dXrMrPjzSyqjPJiSRdJeqmZ3VL9\nWl/dt8PMbjOz70g6S1JN9FJSNOPJrKaqAfD3awkVF4Bio0oTiiqVBZzu/oikl9XZfkDS+ur345Lq\nnpt394s6OsC8ohlPZjVVDYC/X0uouAAAyCM6cBYJzXgyq6lqAPz9WkLFBQBAHqWygDMtpVnAieVz\nDzPU8YB4oe1NohpA53GMAQBZkvUFnEA2dajxDo1GOo9jDADII9JUgLgONt6h0UjncYwBAHlDmgpQ\ni8Y7AACgRZlu+pMWgnE0jcY7AACgBeSMA8tF4x0AAJAQgnEgjsY7AAAgQSzgBOJovAMAABJEMA7E\n0XgHAAAkiGAciDOrP/PdaDsAAEALyBkHAAAAUkIwDgAAAKSEYBwAAABICcE4AAAAkBKCcQD55S6N\njs6v/95oOwDkHa97hUMwDiC/xsakjRvnNmSKGjdt3Bj2A0CR8LpXOJQ2BJBfAwOzHVKlUA8+3kGV\nuvAAiobXvcIxL9HpjL6+Pp+YmEh7GADaKZoRit6YpLkdVAGgaHjdywUz2+PufYvejmAcQO65S12x\nrLuZGd6QABQbr3uZ12wwTs44gHyLZoji4rmUAFA0vO4VCsE4gPyKn6rdvDnMDEW5lA3emCoVaedO\nadu2cFmppDBuAFiuZbzuIdtYwAkgv8bGZt+QolzJoaGwb3hY6u+XNmw4ePPxcWn9+vDeNT0tdXdL\nW7dKu3dL69al9BgaqFSkXbukyUlp9WppcFDq6Ul7VABSt8TXPWQfOeMA8ss9vDENDMzNlayzvVKR\nenvrz4T39EgHDkgrViQ07kXU+9DQ1ZXNDw0AEraE1z2ki5xxIKto2NA+ZmEGqPaNp872XbtCcFvP\nzEzYnwWVSgjEK5UQiEvhMto+NZXu+NJAahEQs4TXPeQDwTjSV7bglIYNqZicnA1ua01PS3v3Jjue\nRvLyoSEp4+PhjMaWLdKOHeGytzdsR0zZXkeBAiEYR/rKFpzGGzZEj5mGDR23enVI96inu1tatSrZ\n8TSSlw8NSeAswRKU7XUUKBCCcaSvbMFptNgmesxdXfMX46DtBgfnluSN6+oK+7MgLx8aksBZgiUo\n2+soUCAs4EQ2lLGbGA0bEpeHhZF5Wmjaadu2hdSURrZvly69NLnxZF4ZX0eBDGMBJ/IlXpopUuQ3\nEBo2pGLduhDMDg+HQG54OFzPSiAuhYB79+5wGc2Qd3fPbi9LIC5xlmDJyvY6ChQEwTiyoUzBKQ0b\nUrVihbRpU5hR3bQpm8FtHj40JCEvqUWZUabXUaBACMaRvrIFp40aNkSPmYVWrSlIVYk8fGjoNM4S\nLEHZXkeBAiFnHOkbHQ2r/ePBafyNZWSkWN3EaNjQWWV7PpXA1FRYrLl3b0hNGRwkEJ+H5z2QOc3m\njBOMI30Ep2in2hnCoaH513k+oWh4HQUyh2C8DoJxoCSoKgEASBnBeB0E40CJUDoSAJAiShsCKC+q\nSgAAcoJgHECxUFUCAJAjh6Y9AABoq0a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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positive = data2[data2['Accepted'].isin([1])]\n", + "negative = data2[data2['Accepted'].isin([0])]\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,8))\n", + "ax.scatter(positive['Test 1'], positive['Test 2'], s=50, c='b', marker='o', label='Accepted')\n", + "ax.scatter(negative['Test 1'], negative['Test 2'], s=50, c='r', marker='x', label='Rejected')\n", + "ax.legend()\n", + "ax.set_xlabel('Test 1 Score')\n", + "ax.set_ylabel('Test 2 Score')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "哇，这个数据看起来可比前一次的复杂得多。特别地，你会注意到其中没有线性决策界限，来良好的分开两类数据。一个方法是用像逻辑回归这样的线性技术来构造从原始特征的多项式中得到的特征。让我们通过创建一组多项式特征入手吧。" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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AcceptedOnesF10F20F21F30F31F32F40F41F42F43
0110.0512670.0026280.0358640.0001350.0018390.0250890.0000070.0000940.0012860.017551
111-0.0927420.008601-0.063523-0.0007980.005891-0.0435090.000074-0.0005460.004035-0.029801
211-0.2137100.045672-0.147941-0.0097610.031616-0.1024120.002086-0.0067570.021886-0.070895
311-0.3750000.140625-0.188321-0.0527340.070620-0.0945730.019775-0.0264830.035465-0.047494
411-0.5132500.263426-0.238990-0.1352030.122661-0.1112830.069393-0.0629560.057116-0.051818
\n", + "
" + ], + "text/plain": [ + " Accepted Ones F10 F20 F21 F30 F31 F32 \\\n", + "0 1 1 0.051267 0.002628 0.035864 0.000135 0.001839 0.025089 \n", + "1 1 1 -0.092742 0.008601 -0.063523 -0.000798 0.005891 -0.043509 \n", + "2 1 1 -0.213710 0.045672 -0.147941 -0.009761 0.031616 -0.102412 \n", + "3 1 1 -0.375000 0.140625 -0.188321 -0.052734 0.070620 -0.094573 \n", + "4 1 1 -0.513250 0.263426 -0.238990 -0.135203 0.122661 -0.111283 \n", + "\n", + " F40 F41 F42 F43 \n", + "0 0.000007 0.000094 0.001286 0.017551 \n", + "1 0.000074 -0.000546 0.004035 -0.029801 \n", + "2 0.002086 -0.006757 0.021886 -0.070895 \n", + "3 0.019775 -0.026483 0.035465 -0.047494 \n", + "4 0.069393 -0.062956 0.057116 -0.051818 " + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "degree = 5\n", + "x1 = data2['Test 1']\n", + "x2 = data2['Test 2']\n", + "\n", + "data2.insert(3, 'Ones', 1)\n", + "\n", + "for i in range(1, degree):\n", + " for j in range(0, i):\n", + " data2['F' + str(i) + str(j)] = np.power(x1, i-j) * np.power(x2, j)\n", + "\n", + "data2.drop('Test 1', axis=1, inplace=True)\n", + "data2.drop('Test 2', axis=1, inplace=True)\n", + "\n", + "data2.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在，我们需要修改第1部分的成本和梯度函数，包括正则化项。首先是成本函数：" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# regularized cost（正则化代价函数）\n", + "$$J\\left( \\theta \\right)=\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[-{{y}^{(i)}}\\log \\left( {{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)-\\left( 1-{{y}^{(i)}} \\right)\\log \\left( 1-{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)]}+\\frac{\\lambda }{2m}\\sum\\limits_{j=1}^{n}{\\theta _{j}^{2}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def cost(theta, X, y, learningRate):\n", + " theta = np.matrix(theta)\n", + " X = np.matrix(X)\n", + " y = np.matrix(y)\n", + " first = np.multiply(-y, np.log(sigmoid(X * theta.T)))\n", + " second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))\n", + " reg = (learningRate / (2 * len(X))) * np.sum(np.power(theta[:,1:theta.shape[1]], 2))\n", + " return np.sum(first - second) / len(X) + reg" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "请注意等式中的\"reg\" 项。还注意到另外的一个“学习率”参数。这是一种超参数，用来控制正则化项。现在我们需要添加正则化梯度函数：" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "如果我们要使用梯度下降法令这个代价函数最小化，因为我们未对${{\\theta }_{0}}$ 进行正则化，所以梯度下降算法将分两种情形：\n", + "\\begin{align}\n", + " & Repeat\\text{ }until\\text{ }convergence\\text{ }\\!\\!\\{\\!\\!\\text{ } \\\\ \n", + " & \\text{ }{{\\theta }_{0}}:={{\\theta }_{0}}-a\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}}]x_{_{0}}^{(i)}} \\\\ \n", + " & \\text{ }{{\\theta }_{j}}:={{\\theta }_{j}}-a\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}}]x_{j}^{(i)}}+\\frac{\\lambda }{m}{{\\theta }_{j}} \\\\ \n", + " & \\text{ }\\!\\!\\}\\!\\!\\text{ } \\\\ \n", + " & Repeat \\\\ \n", + "\\end{align}\n", + "\n", + "对上面的算法中 j=1,2,...,n 时的更新式子进行调整可得： \n", + "${{\\theta }_{j}}:={{\\theta }_{j}}(1-a\\frac{\\lambda }{m})-a\\frac{1}{m}\\sum\\limits_{i=1}^{m}{({{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}})x_{j}^{(i)}}$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gradientReg(theta, X, y, learningRate):\n", + " theta = np.matrix(theta)\n", + " X = np.matrix(X)\n", + " y = np.matrix(y)\n", + " \n", + " parameters = int(theta.ravel().shape[1])\n", + " grad = np.zeros(parameters)\n", + " \n", + " error = sigmoid(X * theta.T) - y\n", + " \n", + " for i in range(parameters):\n", + " term = np.multiply(error, X[:,i])\n", + " \n", + " if (i == 0):\n", + " grad[i] = np.sum(term) / len(X)\n", + " else:\n", + " grad[i] = (np.sum(term) / len(X)) + ((learningRate / len(X)) * theta[:,i])\n", + " \n", + " return grad" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "就像在第一部分中做的一样，初始化变量。" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# set X and y (remember from above that we moved the label to column 0)\n", + "cols = data2.shape[1]\n", + "X2 = data2.iloc[:,1:cols]\n", + "y2 = data2.iloc[:,0:1]\n", + "\n", + "# convert to numpy arrays and initalize the parameter array theta\n", + "X2 = np.array(X2.values)\n", + "y2 = np.array(y2.values)\n", + "theta2 = np.zeros(11)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们初始学习率到一个合理值。，果有必要的话（即如果惩罚太强或不够强）,我们可以之后再折腾这个。" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "learningRate = 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在，让我们尝试调用新的默认为0的theta的正则化函数，以确保计算工作正常。" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6931471805599454" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "costReg(theta2, X2, y2, learningRate)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.00847458, 0.01878809, 0.05034464, 0.01150133, 0.01835599,\n", + " 0.00732393, 0.00819244, 0.03934862, 0.00223924, 0.01286005,\n", + " 0.00309594])" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "gradientReg(theta2, X2, y2, learningRate)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在我们可以使用和第一部分相同的优化函数来计算优化后的结果。" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ 1.22702519e-04, 7.19894617e-05, -3.74156201e-04,\n", + " -1.44256427e-04, 2.93165088e-05, -5.64160786e-05,\n", + " -1.02826485e-04, -2.83150432e-04, 6.47297947e-07,\n", + " -1.99697568e-04, -1.68479583e-05]), 96, 1)" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "result2 = opt.fmin_tnc(func=costReg, x0=theta2, fprime=gradientReg, args=(X2, y2, learningRate))\n", + "result2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "最后，我们可以使用第1部分中的预测函数来查看我们的方案在训练数据上的准确度。" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "accuracy = 77%\n" + ] + } + ], + "source": [ + "theta_min = np.matrix(result2[0])\n", + "predictions = predict(theta_min, X2)\n", + "correct = [1 if ((a == 1 and b == 1) or (a == 0 and b == 0)) else 0 for (a, b) in zip(predictions, y2)]\n", + "accuracy = (sum(map(int, correct)) % len(correct))\n", + "print ('accuracy = {0}%'.format(accuracy))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "虽然我们实现了这些算法，值得注意的是，我们还可以使用高级Python库像scikit-learn来解决这个问题。" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n", + " intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n", + " penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n", + " verbose=0, warm_start=False)" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn import linear_model#调用sklearn的线性回归包\n", + "model = linear_model.LogisticRegression(penalty='l2', C=1.0)\n", + "model.fit(X2, y2.ravel())" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.66101694915254239" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.score(X2, y2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "这个准确度和我们刚刚实现的差了好多，不过请记住这个结果可以使用默认参数下计算的结果。我们可能需要做一些参数的调整来获得和我们之前结果相同的精确度。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "这就是练习2的全部！ 敬请期待下一个练习：多类图像分类。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/code/ex2-logistic regression/ex2.pdf b/code/ex2-logistic regression/ex2.pdf new file mode 100644 index 00000000..39c31da6 Binary files /dev/null and b/code/ex2-logistic regression/ex2.pdf differ diff --git a/code/ex2-logistic regression/ex2data1.txt b/code/ex2-logistic regression/ex2data1.txt new file mode 100644 index 00000000..3a5f9524 --- /dev/null +++ b/code/ex2-logistic regression/ex2data1.txt @@ -0,0 +1,100 @@ +34.62365962451697,78.0246928153624,0 +30.28671076822607,43.89499752400101,0 +35.84740876993872,72.90219802708364,0 +60.18259938620976,86.30855209546826,1 +79.0327360507101,75.3443764369103,1 +45.08327747668339,56.3163717815305,0 +61.10666453684766,96.51142588489624,1 +75.02474556738889,46.55401354116538,1 +76.09878670226257,87.42056971926803,1 +84.43281996120035,43.53339331072109,1 +95.86155507093572,38.22527805795094,0 +75.01365838958247,30.60326323428011,0 +82.30705337399482,76.48196330235604,1 +69.36458875970939,97.71869196188608,1 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+52.34800398794107,60.76950525602592,0 +94.09433112516793,77.15910509073893,1 +90.44855097096364,87.50879176484702,1 +55.48216114069585,35.57070347228866,0 +74.49269241843041,84.84513684930135,1 +89.84580670720979,45.35828361091658,1 +83.48916274498238,48.38028579728175,1 +42.2617008099817,87.10385094025457,1 +99.31500880510394,68.77540947206617,1 +55.34001756003703,64.9319380069486,1 +74.77589300092767,89.52981289513276,1 diff --git a/code/ex2-logistic regression/ex2data2.txt b/code/ex2-logistic regression/ex2data2.txt new file mode 100644 index 00000000..a8889923 --- /dev/null +++ b/code/ex2-logistic regression/ex2data2.txt @@ -0,0 +1,118 @@ +0.051267,0.69956,1 +-0.092742,0.68494,1 +-0.21371,0.69225,1 +-0.375,0.50219,1 +-0.51325,0.46564,1 +-0.52477,0.2098,1 +-0.39804,0.034357,1 +-0.30588,-0.19225,1 +0.016705,-0.40424,1 +0.13191,-0.51389,1 +0.38537,-0.56506,1 +0.52938,-0.5212,1 +0.63882,-0.24342,1 +0.73675,-0.18494,1 +0.54666,0.48757,1 +0.322,0.5826,1 +0.16647,0.53874,1 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+-0.0063364,0.99927,0 +0.63265,-0.030612,0 diff --git a/code/ex3-neural network/1- neural network.ipynb b/code/ex3-neural network/1- neural network.ipynb new file mode 100644 index 00000000..554afa6a --- /dev/null +++ b/code/ex3-neural network/1- neural network.ipynb @@ -0,0 +1,885 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# neural network（神经网络）" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import scipy.io as sio\n", + "import matplotlib\n", + "import scipy.optimize as opt\n", + "from sklearn.metrics import classification_report#这个包是评价报告" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def load_data(path, transpose=True):\n", + " data = sio.loadmat(path)\n", + " y = data.get('y') # (5000,1)\n", + " y = y.reshape(y.shape[0]) # make it back to column vector\n", + "\n", + " X = data.get('X') # (5000,400)\n", + "\n", + " if transpose:\n", + " # for this dataset, you need a transpose to get the orientation right\n", + " X = np.array([im.reshape((20, 20)).T for im in X])\n", + "\n", + " # and I flat the image again to preserve the vector presentation\n", + " X = np.array([im.reshape(400) for im in X])\n", + "\n", + " return X, y" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(5000, 400)\n", + "(5000,)\n" + ] + } + ], + "source": [ + "X, y = load_data('ex3data1.mat')\n", + "\n", + "print(X.shape)\n", + "print(y.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_an_image(image):\n", + "# \"\"\"\n", + "# image : (400,)\n", + "# \"\"\"\n", + " fig, ax = plt.subplots(figsize=(1, 1))\n", + " ax.matshow(image.reshape((20, 20)), cmap=matplotlib.cm.binary)\n", + " plt.xticks(np.array([])) # just get rid of ticks\n", + " plt.yticks(np.array([]))\n", + "#绘图函数" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "this should be 8\n" + ] + } + ], + "source": [ + "pick_one = np.random.randint(0, 5000)\n", + "plot_an_image(X[pick_one, :])\n", + "plt.show()\n", + "print('this should be {}'.format(y[pick_one]))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_100_image(X):\n", + " \"\"\" sample 100 image and show them\n", + " assume the image is square\n", + "\n", + " X : (5000, 400)\n", + " \"\"\"\n", + " size = int(np.sqrt(X.shape[1]))\n", + "\n", + " # sample 100 image, reshape, reorg it\n", + " sample_idx = np.random.choice(np.arange(X.shape[0]), 100) # 100*400\n", + " sample_images = X[sample_idx, :]\n", + "\n", + " fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(8, 8))\n", + "\n", + " for r in range(10):\n", + " for c in range(10):\n", + " ax_array[r, c].matshow(sample_images[10 * r + c].reshape((size, size)),\n", + " cmap=matplotlib.cm.binary)\n", + " plt.xticks(np.array([]))\n", + " plt.yticks(np.array([])) \n", + " #绘图函数，画100张图片" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ttYDsxtTDtYHBpg1id5deeingY2DyKOhmjExkoOo7xciuueYal5Mg2TTnTZs2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8UZTJj797//DcDQoUNdiOK8884DfLiokPN7pQfZITiA5557DoCnn36acePGAT7EstFGGwFw8MEH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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_100_image(X)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(5000, 400)\n", + "(5000,)\n" + ] + } + ], + "source": [ + "raw_X, raw_y = load_data('ex3data1.mat')\n", + "print(raw_X.shape)\n", + "print(raw_y.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 准备数据" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(5000, 401)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# add intercept=1 for x0\n", + "X = np.insert(raw_X, 0, values=np.ones(raw_X.shape[0]), axis=1)#插入了第一列（全部为1）\n", + "X.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(10, 5000)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# y have 10 categories here. 1..10, they represent digit 0 as category 10 because matlab index start at 1\n", + "# I'll ditit 0, index 0 again\n", + "y_matrix = []\n", + "\n", + "for k in range(1, 11):\n", + " y_matrix.append((raw_y == k).astype(int))\n", + "\n", + "# last one is k==10, it's digit 0, bring it to the first position，最后一列k=10，都是0，把最后一列放到第一列\n", + "y_matrix = [y_matrix[-1]] + y_matrix[:-1]\n", + "y = np.array(y_matrix)\n", + "\n", + "y.shape\n", + "\n", + "# 扩展 5000*1 到 5000*10\n", + "# 比如 y=10 -> [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]: ndarray\n", + "# \"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 1, 1, ..., 0, 0, 0],\n", + " [0, 0, 0, ..., 0, 0, 0],\n", + " [0, 0, 0, ..., 0, 0, 0],\n", + " ..., \n", + " [0, 0, 0, ..., 0, 0, 0],\n", + " [0, 0, 0, ..., 0, 0, 0],\n", + " [0, 0, 0, ..., 1, 1, 1]])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# train 1 model（训练一维模型）" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def cost(theta, X, y):\n", + " ''' cost fn is -l(theta) for you to minimize'''\n", + " return np.mean(-y * np.log(sigmoid(X @ theta)) - (1 - y) * np.log(1 - sigmoid(X @ theta)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def regularized_cost(theta, X, y, l=1):\n", + " '''you don't penalize theta_0'''\n", + " theta_j1_to_n = theta[1:]\n", + " regularized_term = (l / (2 * len(X))) * np.power(theta_j1_to_n, 2).sum()\n", + "\n", + " return cost(theta, X, y) + regularized_term" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def regularized_gradient(theta, X, y, l=1):\n", + " '''still, leave theta_0 alone'''\n", + " theta_j1_to_n = theta[1:]\n", + " regularized_theta = (l / len(X)) * theta_j1_to_n\n", + "\n", + " # by doing this, no offset is on theta_0\n", + " regularized_term = np.concatenate([np.array([0]), regularized_theta])\n", + "\n", + " return gradient(theta, X, y) + regularized_term" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sigmoid(z):\n", + " return 1 / (1 + np.exp(-z))" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gradient(theta, X, y):\n", + " '''just 1 batch gradient'''\n", + " return (1 / len(X)) * X.T @ (sigmoid(X @ theta) - y)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def logistic_regression(X, y, l=1):\n", + " \"\"\"generalized logistic regression\n", + " args:\n", + " X: feature matrix, (m, n+1) # with incercept x0=1\n", + " y: target vector, (m, )\n", + " l: lambda constant for regularization\n", + "\n", + " return: trained parameters\n", + " \"\"\"\n", + " # init theta\n", + " theta = np.zeros(X.shape[1])\n", + "\n", + " # train it\n", + " res = opt.minimize(fun=regularized_cost,\n", + " x0=theta,\n", + " args=(X, y, l),\n", + " method='TNC',\n", + " jac=regularized_gradient,\n", + " options={'disp': True})\n", + " # get trained parameters\n", + " final_theta = res.x\n", + "\n", + " return final_theta" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def predict(x, theta):\n", + " prob = sigmoid(x @ theta)\n", + " return (prob >= 0.5).astype(int)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t0 = logistic_regression(X, y[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(401,)\n", + "Accuracy=0.9974\n" + ] + } + ], + "source": [ + "print(t0.shape)\n", + "y_pred = predict(X, t0)\n", + "print('Accuracy={}'.format(np.mean(y[0] == y_pred)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# train k model（训练k维模型）" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(10, 401)\n" + ] + } + ], + "source": [ + "k_theta = np.array([logistic_regression(X, y[k]) for k in range(10)])\n", + "print(k_theta.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 进行预测\n", + "* think about the shape of k_theta, now you are making $X\\times\\theta^T$\n", + "> $(5000, 401) \\times (10, 401).T = (5000, 10)$\n", + "* after that, you run sigmoid to get probabilities and for each row, you find the highest prob as the answer" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "prob_matrix = sigmoid(X @ k_theta.T)" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.9957736 , 0. , 0.0005348 , ..., 0.0000647 ,\n", + " 0.00003918, 0.00172193],\n", + " [ 0.99834617, 0.0000001 , 0.00005609, ..., 0.00009687,\n", + " 0.0000029 , 0.00008485],\n", + " [ 0.99139702, 0. , 0.00056824, ..., 0.00000655,\n", + " 0.02654595, 0.00197376],\n", + " ..., \n", + " [ 0.00000068, 0.0414034 , 0.00320872, ..., 0.00012718,\n", + " 0.00297474, 0.70751222],\n", + " [ 0.00001843, 0.00000013, 0.00000009, ..., 0.00164846,\n", + " 0.06810645, 0.86109385],\n", + " [ 0.02881702, 0. , 0.00012984, ..., 0.36623328,\n", + " 0.00498066, 0.14826916]])" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.set_printoptions(suppress=True)\n", + "prob_matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "y_pred = np.argmax(prob_matrix, axis=1)#返回沿轴axis最大值的索引，axis=1代表行" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0, 0, 0, ..., 9, 9, 7], dtype=int64)" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y_pred" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "y_answer = raw_y.copy()\n", + "y_answer[y_answer==10] = 0" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " precision recall f1-score support\n", + "\n", + " 0 0.97 0.99 0.98 500\n", + " 1 0.95 0.99 0.97 500\n", + " 2 0.95 0.92 0.93 500\n", + " 3 0.95 0.91 0.93 500\n", + " 4 0.95 0.95 0.95 500\n", + " 5 0.92 0.92 0.92 500\n", + " 6 0.97 0.98 0.97 500\n", + " 7 0.95 0.95 0.95 500\n", + " 8 0.93 0.92 0.92 500\n", + " 9 0.92 0.92 0.92 500\n", + "\n", + "avg / total 0.94 0.94 0.94 5000\n", + "\n" + ] + } + ], + "source": [ + "print(classification_report(y_answer, y_pred))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 神经网络模型图示\n", + "" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def load_weight(path):\n", + " data = sio.loadmat(path)\n", + " return data['Theta1'], data['Theta2']\n" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((25, 401), (10, 26))" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta1, theta2 = load_weight('ex3weights.mat')\n", + "\n", + "theta1.shape, theta2.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " 因此在数据加载函数中，原始数据做了转置，然而，转置的数据与给定的参数不兼容，因为这些参数是由原始数据训练的。 所以为了应用给定的参数，我需要使用原始数据（不转置）" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((5000, 401), (5000,))" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X, y = load_data('ex3data1.mat',transpose=False)\n", + "\n", + "X = np.insert(X, 0, values=np.ones(X.shape[0]), axis=1) # intercept\n", + "\n", + "X.shape, y.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# feed forward prediction（前馈预测）" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "a1 = X" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(5000, 25)" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "z2 = a1 @ theta1.T # (5000, 401) @ (25,401).T = (5000, 25)\n", + "z2.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "z2 = np.insert(z2, 0, values=np.ones(z2.shape[0]), axis=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(5000, 26)" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a2 = sigmoid(z2)\n", + "a2.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(5000, 10)" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "z3 = a2 @ theta2.T\n", + "z3.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.00013825, 0.0020554 , 0.00304012, ..., 0.00049102,\n", + " 0.00774326, 0.99622946],\n", + " [ 0.00058776, 0.00285027, 0.00414688, ..., 0.00292311,\n", + " 0.00235617, 0.99619667],\n", + " [ 0.00010868, 0.0038266 , 0.03058551, ..., 0.07514539,\n", + " 0.0065704 , 0.93586278],\n", + " ..., \n", + " [ 0.06278247, 0.00450406, 0.03545109, ..., 0.0026367 ,\n", + " 0.68944816, 0.00002744],\n", + " [ 0.00101909, 0.00073436, 0.00037856, ..., 0.01456166,\n", + " 0.97598976, 0.00023337],\n", + " [ 0.00005908, 0.00054172, 0.0000259 , ..., 0.00700508,\n", + " 0.73281465, 0.09166961]])" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a3 = sigmoid(z3)\n", + "a3" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(5000,)" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y_pred = np.argmax(a3, axis=1) + 1 # numpy is 0 base index, +1 for matlab convention，返回沿轴axis最大值的索引，axis=1代表行\n", + "y_pred.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 准确率\n", + " \n", + "虽然人工神经网络是非常强大的模型，但训练数据的准确性并不能完美预测实际数据，在这里很容易过拟合。" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " precision recall f1-score support\n", + "\n", + " 1 0.97 0.98 0.97 500\n", + " 2 0.98 0.97 0.97 500\n", + " 3 0.98 0.96 0.97 500\n", + " 4 0.97 0.97 0.97 500\n", + " 5 0.98 0.98 0.98 500\n", + " 6 0.97 0.99 0.98 500\n", + " 7 0.98 0.97 0.97 500\n", + " 8 0.98 0.98 0.98 500\n", + " 9 0.97 0.96 0.96 500\n", + " 10 0.98 0.99 0.99 500\n", + "\n", + "avg / total 0.98 0.98 0.98 5000\n", + "\n" + ] + } + ], + "source": [ + "print(classification_report(y, y_pred))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/code/ex3-neural network/ML-Exercise3.ipynb b/code/ex3-neural network/ML-Exercise3.ipynb new file mode 100644 index 00000000..c41b5e7f --- /dev/null +++ b/code/ex3-neural network/ML-Exercise3.ipynb @@ -0,0 +1,503 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 机器学习练习 3 - 多类分类" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "该代码涵盖了基于Python的解决方案，用于Coursera机器学习课程的第三个编程练习。 有关详细说明和方程式，请参阅[exercise text](ex3.pdf)。\n", + "\n", + "\n", + "代码修改并注释：黄海广，haiguang2000@qq.com" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "对于此练习，我们将使用逻辑回归来识别手写数字（0到9）。 我们将扩展我们在练习2中写的逻辑回归的实现，并将其应用于一对一的分类。 让我们开始加载数据集。 它是在MATLAB的本机格式，所以要加载它在Python，我们需要使用一个SciPy工具。" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from scipy.io import loadmat" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'X': array([[ 0., 0., 0., ..., 0., 0., 0.],\n", + " [ 0., 0., 0., ..., 0., 0., 0.],\n", + " [ 0., 0., 0., ..., 0., 0., 0.],\n", + " ..., \n", + " [ 0., 0., 0., ..., 0., 0., 0.],\n", + " [ 0., 0., 0., ..., 0., 0., 0.],\n", + " [ 0., 0., 0., ..., 0., 0., 0.]]),\n", + " '__globals__': [],\n", + " '__header__': b'MATLAB 5.0 MAT-file, Platform: GLNXA64, Created on: Sun Oct 16 13:09:09 2011',\n", + " '__version__': '1.0',\n", + " 'y': array([[10],\n", + " [10],\n", + " [10],\n", + " ..., \n", + " [ 9],\n", + " [ 9],\n", + " [ 9]], dtype=uint8)}" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = loadmat('ex3data1.mat')\n", + "data" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((5000, 400), (5000, 1))" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data['X'].shape, data['y'].shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "好的，我们已经加载了我们的数据。图像在martix X中表示为400维向量（其中有5,000个）。 400维“特征”是原始20 x 20图像中每个像素的灰度强度。类标签在向量y中作为表示图像中数字的数字类。\n", + "\n", + "\n", + "第一个任务是将我们的逻辑回归实现修改为完全向量化（即没有“for”循环）。这是因为向量化代码除了简洁外，还能够利用线性代数优化，并且通常比迭代代码快得多。但是，如果从练习2中看到我们的代价函数已经完全向量化实现了，所以我们可以在这里重复使用相同的实现。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# sigmoid 函数\n", + "g 代表一个常用的逻辑函数（logistic function）为S形函数（Sigmoid function），公式为： \\\\[g\\left( z \\right)=\\frac{1}{1+{{e}^{-z}}}\\\\] \n", + "合起来，我们得到逻辑回归模型的假设函数： \n", + "\t\\\\[{{h}_{\\theta }}\\left( x \\right)=\\frac{1}{1+{{e}^{-{{\\theta }^{T}}X}}}\\\\] " + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def sigmoid(z):\n", + " return 1 / (1 + np.exp(-z))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "代价函数：\n", + "$J\\left( \\theta \\right)=\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[-{{y}^{(i)}}\\log \\left( {{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)-\\left( 1-{{y}^{(i)}} \\right)\\log \\left( 1-{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right) \\right)]}$" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [], + "source": [ + "def cost(theta, X, y, learningRate):\n", + " theta = np.matrix(theta)\n", + " X = np.matrix(X)\n", + " y = np.matrix(y)\n", + " first = np.multiply(-y, np.log(sigmoid(X * theta.T)))\n", + " second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))\n", + " reg = (learningRate / (2 * len(X))) * np.sum(np.power(theta[:,1:theta.shape[1]], 2))\n", + " return np.sum(first - second) / len(X) + reg" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "如果我们要使用梯度下降法令这个代价函数最小化，因为我们未对${{\\theta }_{0}}$ 进行正则化，所以梯度下降算法将分两种情形：\n", + "\\begin{align}\n", + " & Repeat\\text{ }until\\text{ }convergence\\text{ }\\!\\!\\{\\!\\!\\text{ } \\\\ \n", + " & \\text{ }{{\\theta }_{0}}:={{\\theta }_{0}}-a\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}}]x_{_{0}}^{(i)}} \\\\ \n", + " & \\text{ }{{\\theta }_{j}}:={{\\theta }_{j}}-a\\frac{1}{m}\\sum\\limits_{i=1}^{m}{[{{h}_{\\theta }}\\left( {{x}^{(i)}} \\right)-{{y}^{(i)}}]x_{j}^{(i)}}+\\frac{\\lambda }{m}{{\\theta }_{j}} \\\\ \n", + " & \\text{ }\\!\\!\\}\\!\\!\\text{ } \\\\ \n", + " & Repeat \\\\ \n", + "\\end{align}\n", + "\n", + "以下是原始代码是使用for循环的梯度函数：" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gradient_with_loop(theta, X, y, learningRate):\n", + " theta = np.matrix(theta)\n", + " X = np.matrix(X)\n", + " y = np.matrix(y)\n", + " \n", + " parameters = int(theta.ravel().shape[1])\n", + " grad = np.zeros(parameters)\n", + " \n", + " error = sigmoid(X * theta.T) - y\n", + " \n", + " for i in range(parameters):\n", + " term = np.multiply(error, X[:,i])\n", + " \n", + " if (i == 0):\n", + " grad[i] = np.sum(term) / len(X)\n", + " else:\n", + " grad[i] = (np.sum(term) / len(X)) + ((learningRate / len(X)) * theta[:,i])\n", + " \n", + " return grad" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "向量化的梯度函数" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gradient(theta, X, y, learningRate):\n", + " theta = np.matrix(theta)\n", + " X = np.matrix(X)\n", + " y = np.matrix(y)\n", + " \n", + " parameters = int(theta.ravel().shape[1])\n", + " error = sigmoid(X * theta.T) - y\n", + " \n", + " grad = ((X.T * error) / len(X)).T + ((learningRate / len(X)) * theta)\n", + " \n", + " # intercept gradient is not regularized\n", + " grad[0, 0] = np.sum(np.multiply(error, X[:,0])) / len(X)\n", + " \n", + " return np.array(grad).ravel()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在我们已经定义了代价函数和梯度函数，现在是构建分类器的时候了。 对于这个任务，我们有10个可能的类，并且由于逻辑回归只能一次在2个类之间进行分类，我们需要多类分类的策略。 在本练习中，我们的任务是实现一对一全分类方法，其中具有k个不同类的标签就有k个分类器，每个分类器在“类别 i”和“不是 i”之间决定。 我们将把分类器训练包含在一个函数中，该函数计算10个分类器中的每个分类器的最终权重，并将权重返回为k X（n + 1）数组，其中n是参数数量。" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from scipy.optimize import minimize\n", + "\n", + "def one_vs_all(X, y, num_labels, learning_rate):\n", + " rows = X.shape[0]\n", + " params = X.shape[1]\n", + " \n", + " # k X (n + 1) array for the parameters of each of the k classifiers\n", + " all_theta = np.zeros((num_labels, params + 1))\n", + " \n", + " # insert a column of ones at the beginning for the intercept term\n", + " X = np.insert(X, 0, values=np.ones(rows), axis=1)\n", + " \n", + " # labels are 1-indexed instead of 0-indexed\n", + " for i in range(1, num_labels + 1):\n", + " theta = np.zeros(params + 1)\n", + " y_i = np.array([1 if label == i else 0 for label in y])\n", + " y_i = np.reshape(y_i, (rows, 1))\n", + " \n", + " # minimize the objective function\n", + " fmin = minimize(fun=cost, x0=theta, args=(X, y_i, learning_rate), method='TNC', jac=gradient)\n", + " all_theta[i-1,:] = fmin.x\n", + " \n", + " return all_theta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "这里需要注意的几点：首先，我们为theta添加了一个额外的参数（与训练数据一列），以计算截距项（常数项）。 其次，我们将y从类标签转换为每个分类器的二进制值（要么是类i，要么不是类i）。 最后，我们使用SciPy的较新优化API来最小化每个分类器的代价函数。 如果指定的话，API将采用目标函数，初始参数集，优化方法和jacobian（渐变）函数。 然后将优化程序找到的参数分配给参数数组。\n", + "\n", + "实现向量化代码的一个更具挑战性的部分是正确地写入所有的矩阵，保证维度正确。" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((5000, 401), (5000, 1), (401,), (10, 401))" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rows = data['X'].shape[0]\n", + "params = data['X'].shape[1]\n", + "\n", + "all_theta = np.zeros((10, params + 1))\n", + "\n", + "X = np.insert(data['X'], 0, values=np.ones(rows), axis=1)\n", + "\n", + "theta = np.zeros(params + 1)\n", + "\n", + "y_0 = np.array([1 if label == 0 else 0 for label in data['y']])\n", + "y_0 = np.reshape(y_0, (rows, 1))\n", + "\n", + "X.shape, y_0.shape, theta.shape, all_theta.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "注意，theta是一维数组，因此当它被转换为计算梯度的代码中的矩阵时，它变为（1×401）矩阵。 我们还检查y中的类标签，以确保它们看起来像我们想象的一致。" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dtype=uint8)" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.unique(data['y'])#看下有几类标签" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们确保我们的训练函数正确运行，并且得到合理的输出。" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ -2.38335105e+00, 0.00000000e+00, 0.00000000e+00, ...,\n", + " 1.30434941e-03, -7.35542490e-10, 0.00000000e+00],\n", + " [ -3.18549977e+00, 0.00000000e+00, 0.00000000e+00, ...,\n", + " 4.45902426e-03, -5.08371406e-04, 0.00000000e+00],\n", + " [ -4.79997891e+00, 0.00000000e+00, 0.00000000e+00, ...,\n", + " -2.87612799e-05, -2.47948035e-07, 0.00000000e+00],\n", + " ..., \n", + " [ -7.98390460e+00, 0.00000000e+00, 0.00000000e+00, ...,\n", + " -8.96271728e-05, 7.22810041e-06, 0.00000000e+00],\n", + " [ -4.57356699e+00, 0.00000000e+00, 0.00000000e+00, ...,\n", + " -1.33528780e-03, 9.97862678e-05, 0.00000000e+00],\n", + " [ -5.40564903e+00, 0.00000000e+00, 0.00000000e+00, ...,\n", + " -1.16550490e-04, 7.87549333e-06, 0.00000000e+00]])" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "all_theta = one_vs_all(data['X'], data['y'], 10, 1)\n", + "all_theta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们现在准备好最后一步 - 使用训练完毕的分类器预测每个图像的标签。 对于这一步，我们将计算每个类的类概率，对于每个训练样本（使用当然的向量化代码），并将输出类标签为具有最高概率的类。" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def predict_all(X, all_theta):\n", + " rows = X.shape[0]\n", + " params = X.shape[1]\n", + " num_labels = all_theta.shape[0]\n", + " \n", + " # same as before, insert ones to match the shape\n", + " X = np.insert(X, 0, values=np.ones(rows), axis=1)\n", + " \n", + " # convert to matrices\n", + " X = np.matrix(X)\n", + " all_theta = np.matrix(all_theta)\n", + " \n", + " # compute the class probability for each class on each training instance\n", + " h = sigmoid(X * all_theta.T)\n", + " \n", + " # create array of the index with the maximum probability\n", + " h_argmax = np.argmax(h, axis=1)\n", + " \n", + " # because our array was zero-indexed we need to add one for the true label prediction\n", + " h_argmax = h_argmax + 1\n", + " \n", + " return h_argmax" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在我们可以使用predict_all函数为每个实例生成类预测，看看我们的分类器是如何工作的。" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "accuracy = 94.46%\n" + ] + } + ], + "source": [ + "y_pred = predict_all(data['X'], all_theta)\n", + "correct = [1 if a == b else 0 for (a, b) in zip(y_pred, data['y'])]\n", + "accuracy = (sum(map(int, correct)) / float(len(correct)))\n", + "print ('accuracy = {0}%'.format(accuracy * 100))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在下一个练习中，我们将介绍如何从头开始实现前馈神经网络。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 神经网络模型图示\n", + "" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.1" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/code/ex3-neural network/ex3.pdf b/code/ex3-neural network/ex3.pdf new file mode 100644 index 00000000..93ad46a2 Binary files /dev/null and b/code/ex3-neural network/ex3.pdf differ diff --git a/code/ex3-neural network/ex3data1.mat b/code/ex3-neural network/ex3data1.mat new file mode 100644 index 00000000..371bd0c0 Binary files /dev/null and b/code/ex3-neural network/ex3data1.mat differ diff --git a/code/ex3-neural network/ex3weights.mat b/code/ex3-neural network/ex3weights.mat new file mode 100644 index 00000000..ace2a090 Binary files /dev/null and b/code/ex3-neural network/ex3weights.mat differ diff --git a/code/ex4-NN back propagation/1- NN back propagation.ipynb b/code/ex4-NN back propagation/1- NN back propagation.ipynb new file mode 100644 index 00000000..a75d5ef1 --- /dev/null +++ b/code/ex4-NN back propagation/1- NN back propagation.ipynb @@ -0,0 +1,1855 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# NN back propagation（神经网络反向传播）" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import scipy.io as sio\n", + "import matplotlib\n", + "import scipy.optimize as opt\n", + "from sklearn.metrics import classification_report#这个包是评价报告" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def load_data(path, transpose=True):\n", + " data = sio.loadmat(path)\n", + " y = data.get('y') # (5000,1)\n", + " y = y.reshape(y.shape[0]) # make it back to column vector\n", + "\n", + " X = data.get('X') # (5000,400)\n", + "\n", + " if transpose:\n", + " # for this dataset, you need a transpose to get the orientation right\n", + " X = np.array([im.reshape((20, 20)).T for im in X])\n", + "\n", + " # and I flat the image again to preserve the vector presentation\n", + " X = np.array([im.reshape(400) for im in X])\n", + "\n", + " return X, y" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "X, _ = load_data('ex4data1.mat')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_100_image(X):\n", + " \"\"\" sample 100 image and show them\n", + " assume the image is square\n", + "\n", + " X : (5000, 400)\n", + " \"\"\"\n", + " size = int(np.sqrt(X.shape[1]))\n", + "\n", + " # sample 100 image, reshape, reorg it\n", + " sample_idx = np.random.choice(np.arange(X.shape[0]), 100) # 100*400\n", + " sample_images = X[sample_idx, :]\n", + "\n", + " fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(8, 8))\n", + "\n", + " for r in range(10):\n", + " for c in range(10):\n", + " ax_array[r, c].matshow(sample_images[10 * r + c].reshape((size, size)),\n", + " cmap=matplotlib.cm.binary)\n", + " plt.xticks(np.array([]))\n", + " plt.yticks(np.array([]))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support.' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " this.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
')\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('