Hierarchical Clustering Lab.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical Clustering Lab\n",
    "In this notebook, we will be using sklearn to conduct hierarchical clustering on the [Iris dataset](https://archive.ics.uci.edu/ml/datasets/iris) which contains 4 dimensions/attributes and 150 samples. Each sample is labeled as one of the three type of Iris flowers.\n",
    "\n",
    "In this exercise, we'll ignore the labeling and cluster based on the attributes, then we'll compare the results of different hierarchical clustering techniques with the original labels to see which one does a better job in this scenario. We'll then proceed to visualize the resulting cluster hierarchies.\n",
    "\n",
    "## 1. Importing the Iris dataset\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "iris = datasets.load_iris()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A look at the first 10 samples in the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.1,  3.5,  1.4,  0.2],\n",
       "       [ 4.9,  3. ,  1.4,  0.2],\n",
       "       [ 4.7,  3.2,  1.3,  0.2],\n",
       "       [ 4.6,  3.1,  1.5,  0.2],\n",
       "       [ 5. ,  3.6,  1.4,  0.2],\n",
       "       [ 5.4,  3.9,  1.7,  0.4],\n",
       "       [ 4.6,  3.4,  1.4,  0.3],\n",
       "       [ 5. ,  3.4,  1.5,  0.2],\n",
       "       [ 4.4,  2.9,  1.4,  0.2],\n",
       "       [ 4.9,  3.1,  1.5,  0.1]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.data[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```iris.target``` contains the labels that indicate which type of Iris flower each sample is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Clustering\n",
    "Let's now use sklearn's ```AgglomerativeClustering``` to conduct the heirarchical clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "# Hierarchical clustering\n",
    "# Ward is the default linkage algorithm, so we'll start with that\n",
    "ward = AgglomerativeClustering(n_clusters=3)\n",
    "ward_pred = ward.fit_predict(iris.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also try complete and average linkages\n",
    "\n",
    "**Exercise**:\n",
    "* Conduct hierarchical clustering with complete linkage, store the predicted labels in the variable ```complete_pred```\n",
    "* Conduct hierarchical clustering with average linkage, store the predicted labels in the variable ```avg_pred```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Hierarchical clustering using complete linkage\n",
    "# TODO: Create an instance of AgglomerativeClustering with the appropriate parameters\n",
    "complete = AgglomerativeClustering(n_clusters=3, linkage=\"complete\")\n",
    "# Fit & predict\n",
    "# TODO: Make AgglomerativeClustering fit the dataset and predict the cluster labels\n",
    "complete_pred = complete.fit_predict(iris.data)\n",
    "\n",
    "# Hierarchical clustering using average linkage\n",
    "# TODO: Create an instance of AgglomerativeClustering with the appropriate parameters\n",
    "avg = AgglomerativeClustering(n_clusters=3, linkage=\"average\")\n",
    "# Fit & predict\n",
    "# TODO: Make AgglomerativeClustering fit the dataset and predict the cluster labels\n",
    "avg_pred = avg.fit_predict(iris.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To determine which clustering result better matches the original labels of the samples, we can use ```adjusted_rand_score``` which is an *external cluster validation index* which results in a score between -1 and 1, where 1 means two clusterings are identical of how they grouped the samples in a dataset (regardless of what label is assigned to each cluster).\n",
    "\n",
    "Cluster validation indices are discussed later in the course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import adjusted_rand_score\n",
    "\n",
    "ward_ar_score = adjusted_rand_score(iris.target, ward_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:\n",
    "* Calculate the Adjusted Rand score of the clusters resulting from complete linkage and average linkage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO: Calculated the adjusted Rand score for the complete linkage clustering labels\n",
    "complete_ar_score = adjusted_rand_score(iris.target, complete_pred)\n",
    "\n",
    "# TODO: Calculated the adjusted Rand score for the average linkage clustering labels\n",
    "avg_ar_score = adjusted_rand_score(iris.target, avg_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which algorithm results in the higher Adjusted Rand Score?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scores: \n",
      "Ward: 0.731198556771 \n",
      "Complete:  0.642251251836 \n",
      "Average:  0.759198707107\n"
     ]
    }
   ],
   "source": [
    "print( \"Scores: \\nWard:\", ward_ar_score,\"\\nComplete: \", complete_ar_score, \"\\nAverage: \", avg_ar_score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. The Effect of Normalization on Clustering\n",
    "\n",
    "Can we improve on this clustering result?\n",
    "\n",
    "Let's take another look at the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.1,  3.5,  1.4,  0.2],\n",
       "       [ 4.9,  3. ,  1.4,  0.2],\n",
       "       [ 4.7,  3.2,  1.3,  0.2],\n",
       "       [ 4.6,  3.1,  1.5,  0.2],\n",
       "       [ 5. ,  3.6,  1.4,  0.2],\n",
       "       [ 5.4,  3.9,  1.7,  0.4],\n",
       "       [ 4.6,  3.4,  1.4,  0.3],\n",
       "       [ 5. ,  3.4,  1.5,  0.2],\n",
       "       [ 4.4,  2.9,  1.4,  0.2],\n",
       "       [ 4.9,  3.1,  1.5,  0.1],\n",
       "       [ 5.4,  3.7,  1.5,  0.2],\n",
       "       [ 4.8,  3.4,  1.6,  0.2],\n",
       "       [ 4.8,  3. ,  1.4,  0.1],\n",
       "       [ 4.3,  3. ,  1.1,  0.1],\n",
       "       [ 5.8,  4. ,  1.2,  0.2]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.data[:15]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at this, we can see that the forth column has smaller values than the rest of the columns, and so its variance counts for less in the clustering process (since clustering is based on distance). Let us [normalize](https://en.wikipedia.org/wiki/Feature_scaling) the dataset so that each dimension lies between 0 and 1, so they have equal weight in the clustering process.\n",
    "\n",
    "This is done by subtracting the minimum from each column then dividing the difference by the range.\n",
    "\n",
    "sklearn provides us with a useful utility called ```preprocessing.normalize()``` that can do that for us"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.80377277,  0.55160877,  0.22064351,  0.0315205 ],\n",
       "       [ 0.82813287,  0.50702013,  0.23660939,  0.03380134],\n",
       "       [ 0.80533308,  0.54831188,  0.2227517 ,  0.03426949],\n",
       "       [ 0.80003025,  0.53915082,  0.26087943,  0.03478392],\n",
       "       [ 0.790965  ,  0.5694948 ,  0.2214702 ,  0.0316386 ],\n",
       "       [ 0.78417499,  0.5663486 ,  0.2468699 ,  0.05808704],\n",
       "       [ 0.78010936,  0.57660257,  0.23742459,  0.0508767 ],\n",
       "       [ 0.80218492,  0.54548574,  0.24065548,  0.0320874 ],\n",
       "       [ 0.80642366,  0.5315065 ,  0.25658935,  0.03665562],\n",
       "       [ 0.81803119,  0.51752994,  0.25041771,  0.01669451]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import preprocessing\n",
    "\n",
    "normalized_X = preprocessing.normalize(iris.data)\n",
    "normalized_X[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now all the columns are in the range between 0 and 1. Would clustering the dataset after this transformation lead to a better clustering? (one that better matches the original labels of the samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scores: \n",
      "Ward: 0.885697031028 \n",
      "Complete:  0.644447235392 \n",
      "Average:  0.558371443754\n"
     ]
    }
   ],
   "source": [
    "ward = AgglomerativeClustering(n_clusters=3)\n",
    "ward_pred = ward.fit_predict(normalized_X)\n",
    "\n",
    "complete = AgglomerativeClustering(n_clusters=3, linkage=\"complete\")\n",
    "complete_pred = complete.fit_predict(normalized_X)\n",
    "\n",
    "avg = AgglomerativeClustering(n_clusters=3, linkage=\"average\")\n",
    "avg_pred = avg.fit_predict(normalized_X)\n",
    "\n",
    "\n",
    "ward_ar_score = adjusted_rand_score(iris.target, ward_pred)\n",
    "complete_ar_score = adjusted_rand_score(iris.target, complete_pred)\n",
    "avg_ar_score = adjusted_rand_score(iris.target, avg_pred)\n",
    "\n",
    "print( \"Scores: \\nWard:\", ward_ar_score,\"\\nComplete: \", complete_ar_score, \"\\nAverage: \", avg_ar_score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Dendrogram visualization with scipy\n",
    "\n",
    "Let's visualize the highest scoring clustering result. \n",
    "\n",
    "To do that, we'll need to use Scipy's [```linkage```](https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html) function to perform the clusteirng again so we can obtain the linkage matrix it will later use to visualize the hierarchy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import scipy's linkage function to conduct the clustering\n",
    "from scipy.cluster.hierarchy import linkage\n",
    "\n",
    "# Specify the linkage type. Scipy accepts 'ward', 'complete', 'average', as well as other values\n",
    "# Pick the one that resulted in the highest Adjusted Rand Score\n",
    "linkage_type = 'ward'\n",
    "\n",
    "linkage_matrix = linkage(normalized_X, linkage_type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot using scipy's [dendrogram](https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.cluster.hierarchy.dendrogram.html) function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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x3XF8t0wL5k4L1rqxxpYI6NGUvpFnkyPOFh1ldpygxXECFbsUmJhW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\n5xf3/P0r0rWzH0nPaKPR3/2fvgvnkTe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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116bf39b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.cluster.hierarchy import dendrogram\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(22,18))\n",
    "\n",
    "# plot using 'dendrogram()'\n",
    "dendrogram(linkage_matrix)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Visualization with Seaborn's ```clustermap``` \n",
    "\n",
    "The [seaborn](http://seaborn.pydata.org/index.html) plotting library for python can plot a [clustermap](http://seaborn.pydata.org/generated/seaborn.clustermap.html), which is a detailed dendrogram which also visualizes the dataset in more detail. It conducts the clustering as well, so we only need to pass it the dataset and the linkage type we want, and it will use scipy internally to conduct the clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/alammar/anaconda/envs/py3/lib/python3.6/site-packages/IPython/html.py:14: ShimWarning: The `IPython.html` package has been deprecated since IPython 4.0. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.\n",
      "  \"`IPython.html.widgets` has moved to `ipywidgets`.\", ShimWarning)\n",
      "/Users/alammar/anaconda/envs/py3/lib/python3.6/site-packages/matplotlib/cbook.py:136: MatplotlibDeprecationWarning: The axisbg attribute was deprecated in version 2.0. Use facecolor instead.\n",
      "  warnings.warn(message, mplDeprecation, stacklevel=1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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CQoLeeOMNHThwQGvXrtXll18ut9sti8ViKM8GtRBzOBzavXv3eY+dYW8RgAiQ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\nOMMsZdcklF0AAICKadq0qfLy8pSenq7x48dLkgoLC7Vr1y7DLGXXJE6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UKJ1//vlq27at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\n6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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119ee6fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "sns.clustermap(normalized_X, figsize=(12,18), method=linkage_type, cmap='viridis')\n",
    "\n",
    "# Expand figsize to a value like (18, 50) if you want the sample labels to be readable\n",
    "# Draw back is that you'll need more scrolling to observe the dendrogram\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the colors of the dimensions can you observe how they differ between the three type of flowers? You should at least be able to notice how one is vastly different from the two others (in the top third of the image)."
   ]
  },
  {
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}