├── .gitignore ├── README.md ├── LICENSE └── CorrelationMatrixClustering.ipynb /.gitignore: -------------------------------------------------------------------------------- 1 | .ipynb_checkpoints 2 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # CorrelationMatrixClustering 2 | An example on how Correlation Matrix can be displayed and clustered. 3 | See https://thelonenutblog.wordpress.com/2017/03/30/correlation-matrix-clustering/ for details. 4 | 5 | Added a Generalized version (recursive) of the Correlation Matrix Clustering, blog post coming up later. 6 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2017 Pascal Potvin 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /CorrelationMatrixClustering.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Correlation Matrix Clustering example" 8 | ] 9 | }, 10 | { 11 | "cell_type": "markdown", 12 | "metadata": {}, 13 | "source": [ 14 | "## Function to plot the correlation matrix of a dataframe." 15 | ] 16 | }, 17 | { 18 | "cell_type": "code", 19 | "execution_count": 37, 20 | "metadata": { 21 | "collapsed": true 22 | }, 23 | "outputs": [], 24 | "source": [ 25 | "def plot_corr(df,size=10):\n", 26 | " '''Plot a graphical correlation matrix for a dataframe.\n", 27 | "\n", 28 | " Input:\n", 29 | " df: pandas DataFrame\n", 30 | " size: vertical and horizontal size of the plot'''\n", 31 | " \n", 32 | " %matplotlib inline\n", 33 | " import matplotlib.pyplot as plt\n", 34 | "\n", 35 | " # Compute the correlation matrix for the received dataframe\n", 36 | " corr = df.corr()\n", 37 | " \n", 38 | " # Plot the correlation matrix\n", 39 | " fig, ax = plt.subplots(figsize=(size, size))\n", 40 | " cax = ax.matshow(corr, cmap='RdYlGn')\n", 41 | " plt.xticks(range(len(corr.columns)), corr.columns, rotation=90);\n", 42 | " plt.yticks(range(len(corr.columns)), corr.columns);\n", 43 | " \n", 44 | " # Add the colorbar legend\n", 45 | " cbar = fig.colorbar(cax, ticks=[-1, 0, 1], aspect=40, shrink=.8)" 46 | ] 47 | }, 48 | { 49 | "cell_type": "markdown", 50 | "metadata": {}, 51 | "source": [ 52 | "## Generate example data" 53 | ] 54 | }, 55 | { 56 | "cell_type": "code", 57 | "execution_count": 38, 58 | "metadata": { 59 | "collapsed": false 60 | }, 61 | "outputs": [], 62 | "source": [ 63 | "import pandas as pd\n", 64 | "import numpy as np\n", 65 | "\n", 66 | "# Generate 50 variables with 1000 samples\n", 67 | "n_variables = 50\n", 68 | "n_samples = 1000\n", 69 | "\n", 70 | "# Those variables will be spread over 3 clusters of variable sizes\n", 71 | "cluster_size = [5,22,28]\n", 72 | "n_clusters = len(cluster_size)\n", 73 | "\n", 74 | "# Assign each variable to a cluster\n", 75 | "belongs_to_cluster = [i for i, c in enumerate(cluster_size) for n in range(c)]\n", 76 | "np.random.shuffle(belongs_to_cluster)\n", 77 | "\n", 78 | "# This latent data is used to make variables that belong\n", 79 | "# to the same cluster correlated.\n", 80 | "latent = np.random.randn(n_clusters, n_samples)\n", 81 | "\n", 82 | "variables = []\n", 83 | "for i in range(n_variables):\n", 84 | " variables.append(np.random.randn(n_samples) + latent[belongs_to_cluster[i], :])\n", 85 | "\n", 86 | "df = pd.DataFrame(np.array(variables).transpose())" 87 | ] 88 | }, 89 | { 90 | "cell_type": "markdown", 91 | "metadata": {}, 92 | "source": [ 93 | "## Visualize the correlation matrix" 94 | ] 95 | }, 96 | { 97 | "cell_type": "code", 98 | "execution_count": 39, 99 | "metadata": { 100 | "collapsed": false 101 | }, 102 | "outputs": [ 103 | { 104 | "data": { 105 | "image/png": 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CAAAAQNXJZiqzr8wQWQAAAABAKuhgAgAAAABSwRBZAAAAAKgipl46i6yZDTGz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\n6fRaZ2B7te31ttfv2bN/imUCAAAAABrdpG5TEhG9ku6V9A5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106 | "text/plain": [ 107 | "" 108 | ] 109 | }, 110 | "metadata": {}, 111 | "output_type": "display_data" 112 | } 113 | ], 114 | "source": [ 115 | "plot_corr(df, size=18)" 116 | ] 117 | }, 118 | { 119 | "cell_type": "markdown", 120 | "metadata": {}, 121 | "source": [ 122 | "## Cluster the correlation matrix and visualize it\n", 123 | "We use hierarchical clustering to determine which columns belongs to which cluster." 124 | ] 125 | }, 126 | { 127 | "cell_type": "code", 128 | "execution_count": 40, 129 | "metadata": { 130 | "collapsed": false 131 | }, 132 | "outputs": [ 133 | { 134 | "data": { 135 | "image/png": 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Wn11999YqHNUGZitaOtCY7jo/25pJzX/f/p2p/Njg6lT+4UtflcqfdMkHU/ld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\nlMqvqI+m8rPNmVS+GY1Ufmx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DqiUHr1wqXTcwI+Ibkp4sSbbrkv5d0ucqKhcAAAAAoM9U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\nJdtfsf2Y7fec9PNbbSeHbgEAAAAA9LtOrmAuSLo8ImZtVyR9wfZ/jYh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136 | "text/plain": [ 137 | "" 138 | ] 139 | }, 140 | "metadata": {}, 141 | "output_type": "display_data" 142 | } 143 | ], 144 | "source": [ 145 | "import scipy\n", 146 | "import scipy.cluster.hierarchy as sch\n", 147 | "\n", 148 | "X = df.corr().values\n", 149 | "d = sch.distance.pdist(X) # vector of ('55' choose 2) pairwise distances\n", 150 | "L = sch.linkage(d, method='complete')\n", 151 | "ind = sch.fcluster(L, 0.5*d.max(), 'distance')\n", 152 | "columns = [df.columns.tolist()[i] for i in list((np.argsort(ind)))]\n", 153 | "df = df.reindex_axis(columns, axis=1)\n", 154 | "\n", 155 | "plot_corr(df, size=18)" 156 | ] 157 | }, 158 | { 159 | "cell_type": "markdown", 160 | "metadata": {}, 161 | "source": [ 162 | "## Do a two-pass clustering on the biggest clusters\n", 163 | "In the first pass we do as earlier, then for bigger clusters we re-cluster them individually. We could easily extend this to an n-pass clustering until all sub-clusters are smaller than a threshold." 164 | ] 165 | }, 166 | { 167 | "cell_type": "code", 168 | "execution_count": 41, 169 | "metadata": { 170 | "collapsed": false 171 | }, 172 | "outputs": [ 173 | { 174 | "data": { 175 | "image/png": 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2SW+UdMfJ+yLi8Yh4pkt1AQAAAAD6TKezyN4q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\npvKSVC3VUvmSc29CpVRN5bOakXsP5xq5nWgs+fpDazvr5Xw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uQmCC\n", 176 | "text/plain": [ 177 | "" 178 | ] 179 | }, 180 | "metadata": {}, 181 | "output_type": "display_data" 182 | } 183 | ], 184 | "source": [ 185 | "# Two pass clustering\n", 186 | "# 1-We cluster the corr matrix\n", 187 | "# We sort the survey data according to this clustering\n", 188 | "# 2-For cluster bigger than a threshold we cluster those sub-clusters\n", 189 | "# We sort the survey data according to these clustering\n", 190 | "\n", 191 | "import scipy\n", 192 | "import scipy.cluster.hierarchy as sch\n", 193 | "\n", 194 | "cluster_th = 4\n", 195 | "\n", 196 | "X = df.corr().values\n", 197 | "d = sch.distance.pdist(X)\n", 198 | "L = sch.linkage(d, method='complete')\n", 199 | "ind = sch.fcluster(L, 0.5*d.max(), 'distance')\n", 200 | "\n", 201 | "columns = [df.columns.tolist()[i] for i in list(np.argsort(ind))]\n", 202 | "df = df.reindex_axis(columns, axis=1)\n", 203 | "\n", 204 | "unique, counts = np.unique(ind, return_counts=True)\n", 205 | "counts = dict(zip(unique, counts))\n", 206 | "\n", 207 | "i = 0\n", 208 | "j = 0\n", 209 | "columns = []\n", 210 | "for cluster_l1 in set(sorted(ind)):\n", 211 | " j += counts[cluster_l1]\n", 212 | " sub = df[df.columns.values[i:j]]\n", 213 | " if counts[cluster_l1]>cluster_th: \n", 214 | " X = sub.corr().values\n", 215 | " d = sch.distance.pdist(X)\n", 216 | " L = sch.linkage(d, method='complete')\n", 217 | " ind = sch.fcluster(L, 0.5*d.max(), 'distance')\n", 218 | " col = [sub.columns.tolist()[i] for i in list((np.argsort(ind)))]\n", 219 | " sub = sub.reindex_axis(col, axis=1)\n", 220 | " cols = sub.columns.tolist()\n", 221 | " columns.extend(cols)\n", 222 | " i = j\n", 223 | "df = df.reindex_axis(columns, axis=1)\n", 224 | "\n", 225 | "plot_corr(df, 18)" 226 | ] 227 | }, 228 | { 229 | "cell_type": "code", 230 | "execution_count": null, 231 | "metadata": { 232 | "collapsed": true 233 | }, 234 | "outputs": [], 235 | "source": [] 236 | } 237 | ], 238 | "metadata": { 239 | "kernelspec": { 240 | "display_name": "Python 3", 241 | "language": "python", 242 | "name": "python3" 243 | }, 244 | "language_info": { 245 | "codemirror_mode": { 246 | "name": "ipython", 247 | "version": 3 248 | }, 249 | "file_extension": ".py", 250 | "mimetype": "text/x-python", 251 | "name": "python", 252 | "nbconvert_exporter": "python", 253 | "pygments_lexer": "ipython3", 254 | "version": "3.5.2" 255 | } 256 | }, 257 | "nbformat": 4, 258 | "nbformat_minor": 2 259 | } 260 | --------------------------------------------------------------------------------