2_Kmeans_Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering\n",
    "\n",
    "Clustering is the grouping of data points which are similar to each other. It can be a powerful technique for identifying patterns in data. Clustering analysis does not usually require any training and is known as an unsupervised learning technique. The lack of a need for training means it can be applied quickly. Typical applications are:\n",
    "\n",
    " * Looking for trends in data\n",
    " * Data compression, all data clustering around a point can be reduced to just that point. For example reducing colour depth of an image.\n",
    " * Pattern recognition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-means Clustering\n",
    "\n",
    "The K-means clustering algorithm is a simple clustering algorithm that tries to identify the centre of each cluster. It does this by searching for a point which minimises the distance between the centre and all the points in the cluster. The algorithm needs to be told how many clusters to look for, but a common technique is to try different numbers of clusters and combine it with other tests to decide on the best combination. Let's try this using skikit-learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Necessary imports\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn.cluster as skl_cluster\n",
    "import sklearn.datasets.samples_generator as skl_smpl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate 4 clusters in a 400-point dataset\n",
    "data, cluster_id = skl_smpl.make_blobs(n_samples=400, cluster_std=0.75,\n",
    "                                       centers=4, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialise a Kmean object to do the analysis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run the kmeans algorithm on the data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use the kmeans predictor to work out which class each item is in\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot the data, colouring it by cluster\n",
    "plt.scatter(data[:, 0], data[:, 1], s=5, linewidth=0,c=clusters)\n",
    "\n",
    "# plot the centres of each cluster as an X\n",
    "for cluster_x, cluster_y in Kmean.cluster_centers_:\n",
    "    plt.scatter(cluster_x, cluster_y, s=100, c='r', marker='x')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Advantages of K-Means\n",
    " * Simple algorithm, fast to compute. A good choice as the first thing to try when attempting to cluster data.\n",
    " * Suitable for large datasets due to its low memory and computing requirements.\n",
    "\n",
    "### Limitations of K-Means\n",
    "\n",
    " * Requires number of clusters to be known in advance\n",
    " * Struggles when clusters have irregular shapes\n",
    " * Will always produce an answer finding the required number of clusters even if the data isn't clustered (or clustered in that many clusters).\n",
    " * Requires linear cluster boundaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: more and overlapping clusters \n",
    "\n",
    "Adjust the program above to increase the standard deviation of the blobs (the cluster_std parameter to make_blobs) and increase the number of samples (n_samples) to 4000. You should start to see the clusters overlapping. Do the clusters that are identified make sense? Is there any strange behaviour from this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SOLUTION:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: How many clusters should we look for?\n",
    "\n",
    "As K-Means requires us to specify the number of clusters to expect a common strategy to get around this is to vary the number of clusters we are looking for. Modify the program to loop through searching for between 2 and 10 clusters. Which (if any) of the results look more sensible? What criteria might you use to select the best one?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SOLUTION\n"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spectral Clustering\n",
    "\n",
    "Spectral clustering is a technique that attempts to overcome the linear boundary problem of k-means clustering. It works by treating clustering as a graph partitioning problem, its looking for nodes in a graph with a small distance between them. See [this](http://www.cvl.isy.liu.se:82/education/graduate/spectral-clustering/SC_course_part1.pdf) introduction to Spectral Clustering if you are interested in more details about how spectral clustering works.\n",
    "\n",
    "Here is an example of using spectral clustering on two concentric circles:\n",
    "![image.png](attachment:image.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Necessary imports\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "import mpl_toolkits.mplot3d as plt3d\n",
    "import sklearn.cluster as skl_cluster\n",
    "import sklearn.datasets as skl_data\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the circles\n",
    "circles, circles_clusters = \\\n",
    "    skl_data.make_circles(n_samples=400, \n",
    "    noise=.01, random_state=0)\n",
    "plt.scatter(circles[:, 0], circles[:, 1], s=5, c=circles_clusters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# See how standard kmeans fails"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now try spectral clustering\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a plotting function to show the clustering in 3D\n",
    "def plot_3d_separation(circles,labels):\n",
    "\n",
    "    #create two empty arrays for the points inside a list\n",
    "    circles2 = [np.zeros([200,3]),np.zeros([200,3])]\n",
    "\n",
    "    circle_indicies = [0,0]\n",
    "    for i in range(0,400):\n",
    "        x = circles[i][0]\n",
    "        y = circles[i][1]\n",
    "        label = labels[i]\n",
    "        j = circle_indicies[label]\n",
    "        circles2[label][j][0] = x\n",
    "        circles2[label][j][1] = y\n",
    "        circles2[label][j][2] = label\n",
    "        circle_indicies[label] = circle_indicies[label] + 1\n",
    "\n",
    "    fig = plt.figure()\n",
    "    ax = fig.gca(projection='3d')\n",
    "    ax.scatter(circles2[0][:, 0],circles2[0][:, 1],circles2[0][:, 2],c=matplotlib.cm.flag(0))\n",
    "    ax.scatter(circles2[1][:, 0],circles2[1][:, 1],circles2[1][:, 2],c=matplotlib.cm.flag(255))\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "# Plot the data in 3D    \n",
    "plot_3d_separation(circles,labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}