{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Copyright (c) 2015, 2016 [Sebastian Raschka](sebastianraschka.com)\n", "\n", "https://github.com/rasbt/python-machine-learning-book\n", "\n", "[MIT License](https://github.com/rasbt/python-machine-learning-book/blob/master/LICENSE.txt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Python Machine Learning - Code Examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 11 - Working with Unlabeled Data – Clustering Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sebastian Raschka \n", "last updated: 2016-09-29 \n", "\n", "CPython 3.5.2\n", "IPython 5.1.0\n", "\n", "numpy 1.11.1\n", "pandas 0.18.1\n", "matplotlib 1.5.1\n", "scipy 0.18.1\n", "sklearn 0.18\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,pandas,matplotlib,scipy,sklearn" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "*The use of `watermark` is optional. You can install this IPython extension via \"`pip install watermark`\". For more information, please see: https://github.com/rasbt/watermark.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Overview" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [Grouping objects by similarity using k-means](#Grouping-objects-by-similarity-using-k-means)\n", " - [K-means++](#K-means++)\n", " - [Hard versus soft clustering](#Hard-versus-soft-clustering)\n", " - [Using the elbow method to find the optimal number of clusters](#Using-the-elbow-method-to-find-the-optimal-number-of-clusters)\n", " - [Quantifying the quality of clustering via silhouette plots](#Quantifying-the-quality-of-clustering-via-silhouette-plots)\n", "- [Organizing clusters as a hierarchical tree](#Organizing-clusters-as-a-hierarchical-tree)\n", " - [Performing hierarchical clustering on a distance matrix](#Performing-hierarchical-clustering-on-a-distance-matrix)\n", " - [Attaching dendrograms to a heat map](#Attaching-dendrograms-to-a-heat-map)\n", " - [Applying agglomerative clustering via scikit-learn](#Applying-agglomerative-clustering-via-scikit-learn)\n", "- [Locating regions of high density via DBSCAN](#Locating-regions-of-high-density-via-DBSCAN)\n", "- [Summary](#Summary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from IPython.display import Image\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Grouping objects by similarity using k-means" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.datasets import make_blobs\n", "\n", "X, y = make_blobs(n_samples=150, \n", " n_features=2, \n", " centers=3, \n", " cluster_std=0.5, \n", " shuffle=True, \n", " random_state=0)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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NZqOqqqqw9PD777+f1qxZo5nRGO3c0aaRpiPd1azMQpVTeYnU1qeyNiK19cHE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\nJqNhAyUB1X3FKutTWRugtj6VtQHq69M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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c='white', marker='o', s=50)\n", "plt.grid()\n", "plt.tight_layout()\n", "#plt.savefig('./figures/spheres.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZSc8xXWEymXh77BjWzH4vJ4A5+z3eHjvGq+utvh7HcBcj6zOyNjC2Pmfaypcv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\nCS+e9z2+qkUPlIEyGF27duWNt8bw885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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.cluster import KMeans\n", "\n", "km = KMeans(n_clusters=3, \n", " init='random', \n", " n_init=10, \n", " max_iter=300,\n", " tol=1e-04,\n", " random_state=0)\n", "y_km = km.fit_predict(X)\n", "\n", "plt.scatter(X[y_km == 0, 0],\n", " X[y_km == 0, 1],\n", " s=50,\n", " c='lightgreen',\n", " marker='s',\n", " label='cluster 1')\n", "plt.scatter(X[y_km == 1, 0],\n", " X[y_km == 1, 1],\n", " s=50,\n", " c='orange',\n", " marker='o',\n", " label='cluster 2')\n", "plt.scatter(X[y_km == 2, 0],\n", " X[y_km == 2, 1],\n", " s=50,\n", " c='lightblue',\n", " marker='v',\n", " label='cluster 3')\n", "plt.scatter(km.cluster_centers_[:, 0],\n", " km.cluster_centers_[:, 1],\n", " s=250,\n", " marker='*',\n", " c='red',\n", " label='centroids')\n", "plt.legend()\n", "plt.grid()\n", "plt.tight_layout()\n", "#plt.savefig('./figures/centroids.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## K-means++" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hard versus soft clustering" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the elbow method to find the optimal number of clusters " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Distortion: 72.48\n" ] } ], "source": [ "print('Distortion: %.2f' % km.inertia_)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "distortions = []\n", "for i in range(1, 11):\n", " km = KMeans(n_clusters=i, \n", " init='k-means++', \n", " n_init=10, \n", " max_iter=300, \n", " random_state=0)\n", " km.fit(X)\n", " distortions.append(km.inertia_)\n", "plt.plot(range(1, 11), distortions, marker='o')\n", "plt.xlabel('Number of clusters')\n", "plt.ylabel('Distortion')\n", "plt.tight_layout()\n", "#plt.savefig('./figures/elbow.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quantifying the quality of clustering via silhouette plots" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import cm\n", "from sklearn.metrics import silhouette_samples\n", "\n", "km = KMeans(n_clusters=3, \n", " init='k-means++', \n", " n_init=10, \n", " max_iter=300,\n", " tol=1e-04,\n", " random_state=0)\n", "y_km = km.fit_predict(X)\n", "\n", "cluster_labels = np.unique(y_km)\n", "n_clusters = cluster_labels.shape[0]\n", "silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n", "y_ax_lower, y_ax_upper = 0, 0\n", "yticks = []\n", "for i, c in enumerate(cluster_labels):\n", " c_silhouette_vals = silhouette_vals[y_km == c]\n", " c_silhouette_vals.sort()\n", " y_ax_upper += len(c_silhouette_vals)\n", " color = cm.jet(float(i) / n_clusters)\n", " plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n", " edgecolor='none', color=color)\n", "\n", " yticks.append((y_ax_lower + y_ax_upper) / 2.)\n", " y_ax_lower += len(c_silhouette_vals)\n", " \n", "silhouette_avg = np.mean(silhouette_vals)\n", "plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n", "\n", "plt.yticks(yticks, cluster_labels + 1)\n", "plt.ylabel('Cluster')\n", "plt.xlabel('Silhouette coefficient')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('./figures/silhouette.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparison to \"bad\" clustering:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Ccf1g5ihQiSmcceZZIbmufHexi+n6/KHe+aACTe8Siii2umQR8NTv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\nPZSVV9K/f38GDRoU8f7LtrnbDqKlP6L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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "km = KMeans(n_clusters=2,\n", " init='k-means++',\n", " n_init=10,\n", " max_iter=300,\n", " tol=1e-04,\n", " random_state=0)\n", "y_km = km.fit_predict(X)\n", "\n", "plt.scatter(X[y_km == 0, 0],\n", " X[y_km == 0, 1],\n", " s=50,\n", " c='lightgreen',\n", " marker='s',\n", " label='cluster 1')\n", "plt.scatter(X[y_km == 1, 0],\n", " X[y_km == 1, 1],\n", " s=50,\n", " c='orange',\n", " marker='o',\n", " label='cluster 2')\n", "\n", "plt.scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1],\n", " s=250, marker='*', c='red', label='centroids')\n", "plt.legend()\n", "plt.grid()\n", "plt.tight_layout()\n", "#plt.savefig('./figures/centroids_bad.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cluster_labels = np.unique(y_km)\n", "n_clusters = cluster_labels.shape[0]\n", "silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n", "y_ax_lower, y_ax_upper = 0, 0\n", "yticks = []\n", "for i, c in enumerate(cluster_labels):\n", " c_silhouette_vals = silhouette_vals[y_km == c]\n", " c_silhouette_vals.sort()\n", " y_ax_upper += len(c_silhouette_vals)\n", " color = cm.jet(float(i) / n_clusters)\n", " plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n", " edgecolor='none', color=color)\n", "\n", " yticks.append((y_ax_lower + y_ax_upper) / 2.)\n", " y_ax_lower += len(c_silhouette_vals)\n", " \n", "silhouette_avg = np.mean(silhouette_vals)\n", "plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n", "\n", "plt.yticks(yticks, cluster_labels + 1)\n", "plt.ylabel('Cluster')\n", "plt.xlabel('Silhouette coefficient')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('./figures/silhouette_bad.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Organizing clusters as a hierarchical tree" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Cg5VEMfGU3Kc7mTVCVWW0c/suhVsxHT6ssD4lkXom96MB/Wz+ODKYjcS6oZj2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QGSlvt8Wl2pnmlZWueAOtx1j39gC5fXNoHX3lYf2jy3Acw0TcHGCBl3nyAzW25eZa8HIHnXc3Pt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\nXl9F0uspB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Ng0FyGnI2FS4Y5sSH/yyAHJFDKGrNEhpbjxAxRR3FFZNz18kT1xUNYCsMTj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h+UBzBvOErOIDZFlTf/vtt3swS9xBgwb50wo4tYBxwdjV+JVb7PSI9YsUiBSIFIgAthN5QEIG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\njLvrOqFWschIgUiBVlO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"text/plain": [ "" ] }, "execution_count": 12, "metadata": { "image/png": { "width": 400 } }, "output_type": "execute_result" } ], "source": [ "Image(filename='./images/11_05.png', width=400) " ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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XYZ
ID_06.9646922.8613932.268515
ID_15.5131487.1946904.231065
ID_29.8076426.8482974.809319
ID_33.9211753.4317807.290497
ID_44.3857220.5967793.980443
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" ], "text/plain": [ " X Y Z\n", "ID_0 6.964692 2.861393 2.268515\n", "ID_1 5.513148 7.194690 4.231065\n", "ID_2 9.807642 6.848297 4.809319\n", "ID_3 3.921175 3.431780 7.290497\n", "ID_4 4.385722 0.596779 3.980443" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "\n", "np.random.seed(123)\n", "\n", "variables = ['X', 'Y', 'Z']\n", "labels = ['ID_0', 'ID_1', 'ID_2', 'ID_3', 'ID_4']\n", "\n", "X = np.random.random_sample([5, 3])*10\n", "df = pd.DataFrame(X, columns=variables, index=labels)\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Performing hierarchical clustering on a distance matrix" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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ID_0ID_1ID_2ID_3ID_4
ID_00.0000004.9735345.5166535.8998853.835396
ID_14.9735340.0000004.3470735.1043116.698233
ID_25.5166534.3470730.0000007.2442628.316594
ID_35.8998855.1043117.2442620.0000004.382864
ID_43.8353966.6982338.3165944.3828640.000000
\n", "
" ], "text/plain": [ " ID_0 ID_1 ID_2 ID_3 ID_4\n", "ID_0 0.000000 4.973534 5.516653 5.899885 3.835396\n", "ID_1 4.973534 0.000000 4.347073 5.104311 6.698233\n", "ID_2 5.516653 4.347073 0.000000 7.244262 8.316594\n", "ID_3 5.899885 5.104311 7.244262 0.000000 4.382864\n", "ID_4 3.835396 6.698233 8.316594 4.382864 0.000000" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.spatial.distance import pdist, squareform\n", "\n", "row_dist = pd.DataFrame(squareform(pdist(df, metric='euclidean')),\n", " columns=labels,\n", " index=labels)\n", "row_dist" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can either pass a condensed distance matrix (upper triangular) from the `pdist` function, or we can pass the \"original\" data array and define the `metric='euclidean'` argument in `linkage`. However, we should not pass the squareform distance matrix, which would yield different distance values although the overall clustering could be the same." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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row label 1row label 2distanceno. of items in clust.
cluster 10.04.06.5219732.0
cluster 21.02.06.7296032.0
cluster 33.05.08.5392473.0
cluster 46.07.012.4448245.0
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" ], "text/plain": [ " row label 1 row label 2 distance no. of items in clust.\n", "cluster 1 0.0 4.0 6.521973 2.0\n", "cluster 2 1.0 2.0 6.729603 2.0\n", "cluster 3 3.0 5.0 8.539247 3.0\n", "cluster 4 6.0 7.0 12.444824 5.0" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 1. incorrect approach: Squareform distance matrix\n", "\n", "from scipy.cluster.hierarchy import linkage\n", "\n", "row_clusters = linkage(row_dist, method='complete', metric='euclidean')\n", "pd.DataFrame(row_clusters,\n", " columns=['row label 1', 'row label 2',\n", " 'distance', 'no. of items in clust.'],\n", " index=['cluster %d' % (i + 1)\n", " for i in range(row_clusters.shape[0])])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
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row label 1row label 2distanceno. of items in clust.
cluster 10.04.03.8353962.0
cluster 21.02.04.3470732.0
cluster 33.05.05.8998853.0
cluster 46.07.08.3165945.0
\n", "
" ], "text/plain": [ " row label 1 row label 2 distance no. of items in clust.\n", "cluster 1 0.0 4.0 3.835396 2.0\n", "cluster 2 1.0 2.0 4.347073 2.0\n", "cluster 3 3.0 5.0 5.899885 3.0\n", "cluster 4 6.0 7.0 8.316594 5.0" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 2. correct approach: Condensed distance matrix\n", "\n", "row_clusters = linkage(pdist(df, metric='euclidean'), method='complete')\n", "pd.DataFrame(row_clusters,\n", " columns=['row label 1', 'row label 2',\n", " 'distance', 'no. of items in clust.'],\n", " index=['cluster %d' % (i + 1) \n", " for i in range(row_clusters.shape[0])])" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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row label 1row label 2distanceno. of items in clust.
cluster 10.04.03.8353962.0
cluster 21.02.04.3470732.0
cluster 33.05.05.8998853.0
cluster 46.07.08.3165945.0
\n", "
" ], "text/plain": [ " row label 1 row label 2 distance no. of items in clust.\n", "cluster 1 0.0 4.0 3.835396 2.0\n", "cluster 2 1.0 2.0 4.347073 2.0\n", "cluster 3 3.0 5.0 5.899885 3.0\n", "cluster 4 6.0 7.0 8.316594 5.0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 3. correct approach: Input sample matrix\n", "\n", "pd.DataFrame(row_clusters,\n", " columns=['row label 1', 'row label 2',\n", " 'distance', 'no. of items in clust.'],\n", " index=['cluster %d' % (i + 1)\n", " for i in range(row_clusters.shape[0])])" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.cluster.hierarchy import dendrogram\n", "\n", "# make dendrogram black (part 1/2)\n", "# from scipy.cluster.hierarchy import set_link_color_palette\n", "# set_link_color_palette(['black'])\n", "\n", "row_dendr = dendrogram(row_clusters, \n", " labels=labels,\n", " # make dendrogram black (part 2/2)\n", " # color_threshold=np.inf\n", " )\n", "plt.tight_layout()\n", "plt.ylabel('Euclidean distance')\n", "#plt.savefig('./figures/dendrogram.png', dpi=300, \n", "# bbox_inches='tight')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Attaching dendrograms to a heat map" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot row dendrogram\n", "fig = plt.figure(figsize=(8, 8), facecolor='white')\n", "axd = fig.add_axes([0.09, 0.1, 0.2, 0.6])\n", "\n", "# note: for matplotlib < v1.5.1, please use orientation='right'\n", "row_dendr = dendrogram(row_clusters, orientation='left')\n", "\n", "# reorder data with respect to clustering\n", "df_rowclust = df.ix[row_dendr['leaves'][::-1]]\n", "\n", "axd.set_xticks([])\n", "axd.set_yticks([])\n", "\n", "# remove axes spines from dendrogram\n", "for i in axd.spines.values():\n", " i.set_visible(False)\n", "\n", "# plot heatmap\n", "axm = fig.add_axes([0.23, 0.1, 0.6, 0.6]) # x-pos, y-pos, width, height\n", "cax = axm.matshow(df_rowclust, interpolation='nearest', cmap='hot_r')\n", "fig.colorbar(cax)\n", "axm.set_xticklabels([''] + list(df_rowclust.columns))\n", "axm.set_yticklabels([''] + list(df_rowclust.index))\n", "\n", "# plt.savefig('./figures/heatmap.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Applying agglomerative clustering via scikit-learn" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cluster labels: [0 1 1 0 0]\n" ] } ], "source": [ "from sklearn.cluster import AgglomerativeClustering\n", "\n", "ac = AgglomerativeClustering(n_clusters=2, \n", " affinity='euclidean', \n", " linkage='complete')\n", "labels = ac.fit_predict(X)\n", "print('Cluster labels: %s' % labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Locating regions of high density via DBSCAN" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ncW2Q/hYBn0nHrY9TOl/V6Z14ZmXuRWNPtmpOVjrvVBfy947h/C0CgtOq5gCC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\nHQUJp3MOgjIvDAFDoB4QoIxCUP75z3/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Mg12nRiC1Nkj9TeSeSPip7Lbddlsfv/CyEZGL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\n8cUXe+v3EUcc4U477TRfnvgmCvJfNKQLAUZoOfbZZx+/krMEBHM8ioN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BlPGVXFNuuVZD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\n3EW8ZE1Cj6O7ITtcA4FFP9PNBwGDaKG76fbSbLqkSI/ySH7IH8Tr6aefD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vzvuBmjfQY9mDepPyzcAjzvNHgFsKbBeEevdShzcDfwlgrf1HYLUx\n5jwaz+v3H7jEIGvtU8DrRTYJap17KTsEs85/bK097jw/DZxk6T2jgax3j2WHMuu90ScfryzwbWPM\npDHm1kYXpgxBvUn57dba1yB9YAFvL7BdEOrdSx3mb/OKyzaN4PX7f4/TXfO4MeZd9Sla1YJa514F\nus6NMb2kW4H/mPdW4Ou9SNmhzHr3M83clU83+v6StfZVY0w36RPmSecqqabCfJNykbK79fsWypRp\nSL0vM8eAi6y1/2aMeT/wN8DlDS5Tswt0nRtj2oH/DexxWiOhUaLsZdd7zQOUtXa7D/t41fk3aYz5\nP6S7Tmp+ovSh7K8AF2X9fKHzWs0VK7szgHyetfY1Y8w7gESBfTSk3vN4qcNXgHeW2KYRSpY9+4/Y\nWvtNY8x+Y8xaa+1P6lTGSgW1zksKcp0bY1pIn+C/bK39qssmga33UmWvpN6D1MXn2jdpjFnlRGWM\nMW3ArwL/VM+CeVDyJmVjTIT0Tcpfq1+xCvoa8PvO898DlhxMAap3L3X4NeC/wMLMJT/NdGE2WMmy\nZ48fGGOuJX3rR8NPlA5D4WM7qHWeUbDsAa/zvwCmrbUPFXg/yPVetOwV1XuDMz9uId2fmiI9y8Q3\nndfPB77uPL+YdPbTFOnlPe5uZJnLKbvz842kM1peCFDZ1wKjTrm+BXQFud7d6hDYBXw4a5vPk86Y\ne5YiGaFBKzvwEdKBfwr4HvDuRpfZKddh4EfAGeAl4A9CVOdFyx7gOv8l4M2sv7tnnOMn8PXupeyV\n1Ltu1BURkUAKUhefiIjIAgUoEREJJAUoEREJJAUoEREJJAUoEREJJAUoEREJJAUoEREJJAUoEREJ\npP8PAbPAgYqzUNwAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_moons\n", "\n", "X, y = make_moons(n_samples=200, noise=0.05, random_state=0)\n", "plt.scatter(X[:, 0], X[:, 1])\n", "plt.tight_layout()\n", "# plt.savefig('./figures/moons.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "K-means and hierarchical clustering:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/QEqWPDOBYUOHcuzIET758H22fPUlmzdtpNsVHfjqo/cYM30+D/37P0x57T3G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\nLP9oB1nvZ1NWAbfeM4gFH3xK1vsfse3Lr5iUmWmYdm5ufjk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 3))\n", "\n", "km = KMeans(n_clusters=2, random_state=0)\n", "y_km = km.fit_predict(X)\n", "ax1.scatter(X[y_km == 0, 0], X[y_km == 0, 1],\n", " c='lightblue', marker='o', s=40, label='cluster 1')\n", "ax1.scatter(X[y_km == 1, 0], X[y_km == 1, 1],\n", " c='red', marker='s', s=40, label='cluster 2')\n", "ax1.set_title('K-means clustering')\n", "\n", "ac = AgglomerativeClustering(n_clusters=2,\n", " affinity='euclidean',\n", " linkage='complete')\n", "y_ac = ac.fit_predict(X)\n", "ax2.scatter(X[y_ac == 0, 0], X[y_ac == 0, 1], c='lightblue',\n", " marker='o', s=40, label='cluster 1')\n", "ax2.scatter(X[y_ac == 1, 0], X[y_ac == 1, 1], c='red',\n", " marker='s', s=40, label='cluster 2')\n", "ax2.set_title('Agglomerative clustering')\n", "\n", "plt.legend()\n", "plt.tight_layout()\n", "#plt.savefig('./figures/kmeans_and_ac.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Density-based clustering:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GC3M51xC6lFLPrVwN31osFiSnpGDx+sbp6VmDMtBCCBw+xJ14qflxiC9EOb9b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\nSrk+UA0jIqLIJqSUvp9EiM0A8qSU3yl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.cluster import DBSCAN\n", "\n", "db = DBSCAN(eps=0.2, min_samples=5, metric='euclidean')\n", "y_db = db.fit_predict(X)\n", "plt.scatter(X[y_db == 0, 0], X[y_db == 0, 1],\n", " c='lightblue', marker='o', s=40,\n", " label='cluster 1')\n", "plt.scatter(X[y_db == 1, 0], X[y_db == 1, 1],\n", " c='red', marker='s', s=40,\n", " label='cluster 2')\n", "plt.legend()\n", "plt.tight_layout()\n", "#plt.savefig('./figures/moons_dbscan.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Summary" ] }, { "cell_type": "markdown", "metadata": {}, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }