W7-1 Clustering Introduction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Clustering Introduction With Random Data</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## About clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### Supervised vs unsupervised methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "In **supervised methods**, we start with some sort of \"ground truth.\" And we use that ground truth both to train and test our machine learning models.\n",
    "\n",
    "In **unsupervised methods**, we don't start with any ground truth. We have the data and look for patterns.\n",
    "\n",
    "Clearly unsupervised methods are more cool."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create some random data: Points on a plane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "def scatter_plot(dvectors, dnames = []):\n",
    "    plt.axhline(xmin = -1, xmax = 1)\n",
    "    plt.axvline(ymin = -1, ymax = 1)\n",
    "    plt.grid(True)\n",
    "    plt.axis('on')\n",
    "    xvals = []\n",
    "    yvals = []\n",
    "    if dnames == []:\n",
    "        dnames = range(len(dvectors))\n",
    "    for d in dvectors:\n",
    "        xvals.append(d[0])\n",
    "        yvals.append(d[1])\n",
    "    plt.scatter(xvals, yvals)\n",
    "    for i in range(len(dnames)):\n",
    "        loc = [dvectors[i][0] + .02, dvectors[i][1] + .02]\n",
    "        plt.annotate(dnames[i], loc, size = \"large\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "Xtest, y = make_blobs(n_samples=10, centers=3, n_features=2, shuffle=True, random_state=42)\n",
    "scatter_plot(Xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xtest.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "Xtest[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### Hierarachical clustering"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "![image.png](https://www.statisticshowto.com/wp-content/uploads/2016/11/clustergram.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Do the clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**We'll use sklearn rather than nltk**\n",
    "\n",
    "https://scikit-learn.org/stable/modules/classes.html#module-sklearn.cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "clusterer = AgglomerativeClustering(n_clusters=3, linkage=\"ward\", affinity=\"euclidean\")\n",
    "clusterer.fit(Xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "clusterer.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import NearestCentroid\n",
    "def get_centroids(X, labels):\n",
    "    clf = NearestCentroid()\n",
    "    clf.fit(X, labels)\n",
    "    centroids = clf.centroids_\n",
    "    return centroids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "centroids = get_centroids(Xtest, clusterer.labels_)\n",
    "scatter_plot(centroids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.cluster.hierarchy import dendrogram\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "import numpy as np\n",
    "\n",
    "def plot_dendrogram(model, **kwargs):\n",
    "\n",
    "    # Children of hierarchical clustering\n",
    "    children = model.children_\n",
    "\n",
    "    # Distances between each pair of children\n",
    "    # Since we don't have this information, we can use a uniform one for plotting\n",
    "    distance = np.arange(children.shape[0])\n",
    "\n",
    "    # The number of observations contained in each cluster level\n",
    "    no_of_observations = np.arange(2, children.shape[0]+2)\n",
    "\n",
    "    # Create linkage matrix and then plot the dendrogram\n",
    "    linkage_matrix = np.column_stack([children, distance, no_of_observations]).astype(float)\n",
    "\n",
    "    # Plot the corresponding dendrogram\n",
    "    dendrogram(linkage_matrix, **kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_dendrogram(clusterer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "silhouette_score(Xtest, clusterer.labels_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kmeans clustering\n",
    "\n",
    "A kind of flat clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How it works:\n",
    "\n",
    "1. It randomly picks a number of points equal to the number of clusters. These are the first guesses at centers for the clusters.\n",
    "2. Each sample in the data set is assigned to the cluster corresponding to the center to which it is closest.\n",
    "3. Find the average of the points in each cluster. These become the new centers.\n",
    "4. The process iterates it converges within some measure of tolerance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kclusterer = KMeans(n_clusters=3).fit(Xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "kclusterer.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "centroids = kclusterer.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scatter_plot(centroids)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determining the right number of clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_rss(X, centroids, labels):\n",
    "    rss = 0\n",
    "    for dnum in range(X.shape[0]):\n",
    "        vec = X[dnum]\n",
    "        centroid = centroids[labels[dnum]]\n",
    "        res_vec = vec - centroid\n",
    "        rss += np.dot(res_vec, res_vec)\n",
    "    return rss\n",
    "\n",
    "def compute_rss_data(X, start, end):\n",
    "    results = []\n",
    "    for k in range(start, end):\n",
    "        kcluster = KMeans(n_clusters=k)\n",
    "        kcluster.fit(X)\n",
    "        centroids = kcluster.cluster_centers_\n",
    "        labels = kcluster.labels_\n",
    "        rss = compute_rss(X, centroids, labels)\n",
    "        results.append([k, rss])\n",
    "    return results\n",
    "\n",
    "def compute_rss_data_agglomerative(X, start, end):\n",
    "    results = []\n",
    "    for k in range(start, end):\n",
    "        clusterer = AgglomerativeClustering(n_clusters=k, linkage=\"ward\", affinity=\"euclidean\")\n",
    "        clusterer.fit(X)\n",
    "        labels = clusterer.labels_\n",
    "        centroids = get_centroids(X, labels)\n",
    "        rss = compute_rss(X, centroids, labels)\n",
    "        results.append([k, rss])\n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rss_list = compute_rss_data(Xtest, 2, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.clf()\n",
    "x = [res[0] for res in rss_list]\n",
    "y = [res[1] for res in rss_list]\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Elbow visualizer\n",
    "explained [here](https://www.scikit-yb.org/en/latest/api/cluster/elbow.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from yellowbrick.cluster import KElbowVisualizer \n",
    "from sklearn.cluster import KMeans\n",
    "clusterer = KMeans()\n",
    "visualizer = KElbowVisualizer(clusterer, k=(2, 10), metric='distortion')\n",
    "visualizer.fit(Xtest)\n",
    "visualizer.poof()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Silhouette score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Silhouette Coefficient is calculated using the mean intra-cluster distance (a) and the mean nearest-cluster distance (b) for each sample. The Silhouette Coefficient for a sample is (b - a) / max(a, b). Note that Silhouette Coefficient is only defined if number of labels is 2 <= n_labels <= n_samples - 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from yellowbrick.cluster import KElbowVisualizer \n",
    "from sklearn.cluster import KMeans\n",
    "clusterer = KMeans()\n",
    "visualizer = KElbowVisualizer(clusterer, k=(2, 10), metric=\"silhouette\")\n",
    "visualizer.fit(Xtest)\n",
    "visualizer.poof()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from yellowbrick.cluster import SilhouetteVisualizer \n",
    "from sklearn.cluster import KMeans\n",
    "visualizer = SilhouetteVisualizer(KMeans(n_clusters=3))\n",
    "visualizer.fit(Xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_samples\n",
    "silhouette_samples(Xtest, visualizer.labels_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "visualizer.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from yellowbrick.cluster import SilhouetteVisualizer \n",
    "from sklearn.cluster import KMeans\n",
    "visualizer = SilhouetteVisualizer(KMeans(n_clusters=5))\n",
    "visualizer.fit(Xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "visualizer.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "list(visualizer.labels_).count(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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