5.4softmax_in_one_dimension_v2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork/Template/module%201/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Softmax Classifer 1D</h1>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Objective</h2><ul><li> How to build a Softmax classifier by using the Sequential module in pytorch.</li></ul> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of Contents</h2>\n",
    "<p>In this lab, you will use Softmax to classify three linearly separable classes, the features are in one dimension </p>\n",
    "<ul>\n",
    "    <li><a href=\"#Makeup_Data\">Make Some Data</a></li>\n",
    "    <li><a href=\"#Softmax\">Build Softmax Classifier</a></li>\n",
    "    <li><a href=\"#Model_Cost\">Train the Model</a></li>\n",
    "    <li><a href=\"#Result\">Analyze Results</a></li>\n",
    "</ul>\n",
    "<p>Estimated Time Needed: <strong>25 min</strong></p>\n",
    "\n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Preparation</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll need the following libraries:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the libraries we need for this lab\n",
    "\n",
    "import torch.nn as nn\n",
    "import torch\n",
    "import matplotlib.pyplot as plt \n",
    "import numpy as np\n",
    "from torch.utils.data import Dataset, DataLoader"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the helper function to plot labeled data points: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create class for plotting\n",
    "\n",
    "def plot_data(data_set, model = None, n = 1, color = False):\n",
    "    X = data_set[:][0]\n",
    "    Y = data_set[:][1]\n",
    "    plt.plot(X[Y == 0, 0].numpy(), Y[Y == 0].numpy(), 'bo', label = 'y = 0')\n",
    "    plt.plot(X[Y == 1, 0].numpy(), 0 * Y[Y == 1].numpy(), 'ro', label = 'y = 1')\n",
    "    plt.plot(X[Y == 2, 0].numpy(), 0 * Y[Y == 2].numpy(), 'go', label = 'y = 2')\n",
    "    plt.ylim((-0.1, 3))\n",
    "    plt.legend()\n",
    "    if model != None:\n",
    "        w = list(model.parameters())[0][0].detach()\n",
    "        b = list(model.parameters())[1][0].detach()\n",
    "        y_label = ['yhat=0', 'yhat=1', 'yhat=2']\n",
    "        y_color = ['b', 'r', 'g']\n",
    "        Y = []\n",
    "        for w, b, y_l, y_c in zip(model.state_dict()['0.weight'], model.state_dict()['0.bias'], y_label, y_color):\n",
    "            Y.append((w * X + b).numpy())\n",
    "            plt.plot(X.numpy(), (w * X + b).numpy(), y_c, label = y_l)\n",
    "        if color == True:\n",
    "            x = X.numpy()\n",
    "            x = x.reshape(-1)\n",
    "            top = np.ones(x.shape)\n",
    "            y0 = Y[0].reshape(-1)\n",
    "            y1 = Y[1].reshape(-1)\n",
    "            y2 = Y[2].reshape(-1)\n",
    "            plt.fill_between(x, y0, where = y1 > y1, interpolate = True, color = 'blue')\n",
    "            plt.fill_between(x, y0, where = y1 > y2, interpolate = True, color = 'blue')\n",
    "            plt.fill_between(x, y1, where = y1 > y0, interpolate = True, color = 'red')\n",
    "            plt.fill_between(x, y1, where = ((y1 > y2) * (y1 > y0)),interpolate = True, color = 'red')\n",
    "            plt.fill_between(x, y2, where = (y2 > y0) * (y0 > 0),interpolate = True, color = 'green')\n",
    "            plt.fill_between(x, y2, where = (y2 > y1), interpolate = True, color = 'green')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the random seed:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x7f64c3699a70>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Set the random seed\n",
    "\n",
    "torch.manual_seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Makeup_Data\">Make Some Data</h2> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create some linearly separable data with three classes: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the data class\n",
    "\n",
    "class Data(Dataset):\n",
    "    \n",
    "    # Constructor\n",
    "    def __init__(self):\n",
    "        self.x = torch.arange(-2, 2, 0.1).view(-1, 1)\n",
    "        self.y = torch.zeros(self.x.shape[0])\n",
    "        self.y[(self.x > -1.0)[:, 0] * (self.x < 1.0)[:, 0]] = 1\n",
    "        self.y[(self.x >= 1.0)[:, 0]] = 2\n",
    "        self.y = self.y.type(torch.LongTensor)\n",
    "        self.len = self.x.shape[0]\n",
    "        \n",
    "    # Getter\n",
    "    def __getitem__(self,index):      \n",
    "        return self.x[index], self.y[index]\n",
    "    \n",
    "    # Get Length\n",
    "    def __len__(self):\n",
    "        return self.len"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the dataset object:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the dataset object and plot the dataset object\n",
    "\n",
    "data_set = Data()\n",
    "data_set.x\n",
    "plot_data(data_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Softmax\">Build a Softmax Classifier </h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build a Softmax classifier by using the Sequential module:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('0.weight',\n",
       "              tensor([[-0.0075],\n",
       "                      [ 0.5364],\n",
       "                      [-0.8230]])),\n",
       "             ('0.bias', tensor([-0.7359, -0.3852,  0.2682]))])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Build Softmax Classifier technically you only need nn.Linear\n",
    "\n",
    "model = nn.Sequential(nn.Linear(1, 3)) #in_dim =1 , out_dim =3 \n",
    "model.state_dict()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Model\">Train the Model</h2> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the criterion function, the optimizer and the dataloader\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create criterion function, optimizer, and dataloader\n",
    "\n",
    "criterion = nn.CrossEntropyLoss() #notice that this is not BCE. It's CrossEntropyLoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr = 0.01)\n",
    "trainloader = DataLoader(dataset = data_set, batch_size = 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train the model for every 50 epochs plot, the line generated for each class.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the model\n",
    "\n",
    "LOSS = []\n",
    "def train_model(epochs):\n",
    "    for epoch in range(epochs):\n",
    "        if epoch % 50 == 0:\n",
    "            pass\n",
    "            plot_data(data_set, model)\n",
    "        for x, y in trainloader:\n",
    "            optimizer.zero_grad()\n",
    "            yhat = model(x)\n",
    "            loss = criterion(yhat, y)\n",
    "            LOSS.append(loss)\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "train_model(300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"Result\">Analyze Results</h2> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the predicted class on the test data: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 3.7019,  1.1621, -5.1287],\n",
      "        [ 3.4652,  1.1572, -4.9166],\n",
      "        [ 3.2285,  1.1523, -4.7044],\n",
      "        [ 2.9918,  1.1474, -4.4922],\n",
      "        [ 2.7551,  1.1425, -4.2800],\n",
      "        [ 2.5184,  1.1376, -4.0678],\n",
      "        [ 2.2818,  1.1326, -3.8556],\n",
      "        [ 2.0451,  1.1277, -3.6434],\n",
      "        [ 1.8084,  1.1228, -3.4312],\n",
      "        [ 1.5717,  1.1179, -3.2190],\n",
      "        [ 1.3350,  1.1130, -3.0069],\n",
      "        [ 1.0983,  1.1081, -2.7947],\n",
      "        [ 0.8617,  1.1032, -2.5825],\n",
      "        [ 0.6250,  1.0982, -2.3703],\n",
      "        [ 0.3883,  1.0933, -2.1581],\n",
      "        [ 0.1516,  1.0884, -1.9459],\n",
      "        [-0.0851,  1.0835, -1.7337],\n",
      "        [-0.3218,  1.0786, -1.5215],\n",
      "        [-0.5584,  1.0737, -1.3093],\n",
      "        [-0.7951,  1.0688, -1.0971],\n",
      "        [-1.0318,  1.0638, -0.8850],\n",
      "        [-1.2685,  1.0589, -0.6728],\n",
      "        [-1.5052,  1.0540, -0.4606],\n",
      "        [-1.7419,  1.0491, -0.2484],\n",
      "        [-1.9786,  1.0442, -0.0362],\n",
      "        [-2.2152,  1.0393,  0.1760],\n",
      "        [-2.4519,  1.0344,  0.3882],\n",
      "        [-2.6886,  1.0294,  0.6004],\n",
      "        [-2.9253,  1.0245,  0.8126],\n",
      "        [-3.1620,  1.0196,  1.0247],\n",
      "        [-3.3987,  1.0147,  1.2369],\n",
      "        [-3.6353,  1.0098,  1.4491],\n",
      "        [-3.8720,  1.0049,  1.6613],\n",
      "        [-4.1087,  1.0000,  1.8735],\n",
      "        [-4.3454,  0.9950,  2.0857],\n",
      "        [-4.5821,  0.9901,  2.2979],\n",
      "        [-4.8188,  0.9852,  2.5101],\n",
      "        [-5.0554,  0.9803,  2.7223],\n",
      "        [-5.2921,  0.9754,  2.9344],\n",
      "        [-5.5288,  0.9705,  3.1466]], grad_fn=<AddmmBackward>)\n",
      "torch.return_types.max(\n",
      "values=tensor([3.7019, 3.4652, 3.2285, 2.9918, 2.7551, 2.5184, 2.2818, 2.0451, 1.8084,\n",
      "        1.5717, 1.3350, 1.1081, 1.1032, 1.0982, 1.0933, 1.0884, 1.0835, 1.0786,\n",
      "        1.0737, 1.0688, 1.0638, 1.0589, 1.0540, 1.0491, 1.0442, 1.0393, 1.0344,\n",
      "        1.0294, 1.0245, 1.0247, 1.2369, 1.4491, 1.6613, 1.8735, 2.0857, 2.2979,\n",
      "        2.5101, 2.7223, 2.9344, 3.1466], grad_fn=<MaxBackward0>),\n",
      "indices=tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
      "        1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]))\n",
      "The prediction: tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
      "        1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])\n"
     ]
    }
   ],
   "source": [
    "# Make the prediction\n",
    "\n",
    "z =  model(data_set.x) \n",
    "print(z)\n",
    "print(z.max(1))\n",
    "item, index = z.max(1) #this max function is returning the index and the item that is largest.\n",
    "print(\"The prediction:\", index)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the accuracy on the test data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The accuracy:  0.975\n"
     ]
    }
   ],
   "source": [
    "# Print the accuracy\n",
    "\n",
    "correct = (data_set.y == yhat).sum().item()\n",
    "accuracy = correct / len(data_set)\n",
    "print(\"The accuracy: \", accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use the softmax function to convert the output to a probability,first, we create a Softmax object:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "Softmax_fn=nn.Softmax(dim=-1) #placeholder for dimension."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a tensor <code> Probability </code>, where each row corresponds to a different sample, and each column corresponds to that sample  belonging to a particular class\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "Probability =Softmax_fn(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can obtain the probability of the first sample belonging to the first, second and third class respectively as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'Tensor' object is not callable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-31-b07341af65d8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata_set\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mProbability\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'Tensor' object is not callable"
     ]
    }
   ],
   "source": [
    "for i in range(3):\n",
    "    print(\"probability of class {} isg given by  {}\".format(i, Probability[0,i]) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://dataplatform.cloud.ibm.com/registration/stepone?context=cpdaas&apps=data_science_experience,watson_machine_learning\"><img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork/Template/module%201/images/Watson_Studio.png\"/></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--Empty Space for separating topics-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>About the Authors:</h2> \n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\">Joseph Santarcangelo</a> has a PhD in Electrical Engineering, his research focused on using machine learning, signal processing, and computer vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other contributors: <a href=\"https://www.linkedin.com/in/michelleccarey/\">Michelle Carey</a>, <a href=\"www.linkedin.com/in/jiahui-mavis-zhou-a4537814a\">Mavis Zhou</a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                                          |\n",
    "| ----------------- | ------- | ---------- | ----------------------------------------------------------- |\n",
    "| 2020-09-23        | 2.0     | Shubham    | Migrated Lab to Markdown and added to course repo in GitLab |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
   ]
  }
 ],
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