{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%run ../../../common_functions/import_all.py\n", "\n", "from common_functions.setup_notebook import set_css_style, setup_matplotlib, config_ipython\n", "\n", "from sklearn.cluster import KMeans\n", "from sklearn.preprocessing import scale\n", "\n", "from common_functions.kmeans_helpers import (retrieve_cluster_points, \n", " compute_wcss, \n", " compute_gap_statistic, \n", " evaluate_gap_statistic_best_k)\n", "\n", "dataset = '../../datasets/oldfaithful.txt'\n", "\n", "config_ipython()\n", "setup_matplotlib()\n", "set_css_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# k-means: trying it!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Let's use the \"old faithful\" dataset\n", "\n", "We will use the Old Faithful classic dataset, a copy of which is available in this repo under folder `datasets/` for convenience. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
eruptionswaiting
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" ], "text/plain": [ " eruptions waiting\n", "0 3.600 79\n", "1 1.800 54\n", "2 3.333 74\n", "3 2.283 62\n", "4 4.533 85" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's read the Old Faithful dataset into a Pandas Dataframe, choosing the columns\n", "\n", "data = pd.read_csv(dataset, delimiter=' ')[['eruptions', 'waiting']]\n", "\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Scale the data so that each column is in the same scale" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "scaled_data = scale(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First, see how it looks like\n", "\n", "It looks that 2 groups are naturally emerging from the data." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 396, "width": 609 } }, "output_type": "display_data" } ], "source": [ "data.plot.scatter('eruptions', 'waiting')\n", "plt.title('Scatter of the data in the \"old faithful\" dataset')\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What does the rule of thumb say?" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " * Rule of thumb asserts optimal k = 11.66\n" ] } ], "source": [ "thumb_k = np.sqrt(data.shape[0]/2)\n", "print(' * Rule of thumb asserts optimal k =', round(thumb_k, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using the elbow method\n", "\n", "You'll see the elbow seems to appear quite soon." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k = 1\n", "k = 2\n", "k = 3\n", "k = 4\n", "k = 5\n", "k = 6\n", "k = 7\n", "k = 8\n", "k = 9\n", "k = 10\n", "k = 11\n", "k = 12\n", "k = 13\n", "k = 14\n", "k = 15\n", "k = 16\n", "k = 17\n", "k = 18\n", "k = 19\n", "k = 20\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 396, "width": 615 } }, "output_type": "display_data" } ], "source": [ "k_range = range(1, 21) # range of K (decide arbitrarily how many Ks to test)\n", "inertia_k = dict() # inertia for each k\n", "wcss_k = dict() # WCSS for each k\n", "p_k = dict() # percentage of variance explained for each k\n", "\n", "# Loop over the value of K\n", "for k in k_range:\n", " print('k = ', k)\n", " \n", " # Fit the model\n", " fit = KMeans(n_clusters=k).fit(scaled_data)\n", "\n", " # Retrieve centroids for fitted model\n", " # A centroid is the cluster center, given as the vector of coordinates over the n_features dimensions\n", " # So there will be K number of n_features-dimensional centroids\n", " centroids = fit.cluster_centers_\n", " \n", " # Retrieve cluster labels for fitted model\n", " labels = fit.labels_\n", "\n", " # Retrieve the inertia of the fitted model\n", " inertia_k[k] = fit.inertia_\n", " \n", " # Compute the WCSS of the fitted model\n", " wcss_k[k] = compute_wcss(centroids, labels, scaled_data)\n", " \n", "plt.title('WCSS vs. K')\n", "plt.plot(k_range, list(wcss_k.values()), marker='o')\n", "plt.xlabel('K')\n", "plt.xticks(k_range)\n", "plt.ylabel('WCSS')\n", "plt.savefig('elbow.png', dpi=200)\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run a clustering" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3, 2, 3, 0, 4, 0, 4, 4, 2, 4, 2, 4, 1, 2, 4, 2, 0, 4, 2, 1, 2, 2,\n", " 3, 3, 1, 3, 2, 3, 3, 1, 1, 1, 3, 1, 3, 2, 2, 1, 0, 4, 1, 0, 4, 0,\n", " 1, 3, 3, 2, 1, 0, 1, 4, 2, 1, 2, 4, 3, 0, 1, 1, 0, 4, 2, 1, 0, 4,\n", " 1, 1, 0, 1, 1, 0, 1, 3, 0, 1, 0, 1, 3, 3, 3, 1, 3, 0, 3, 4, 3, 1,\n", " 2, 4, 0, 4, 2, 1, 0, 1, 4, 3, 2, 1, 0, 4, 2, 4, 1, 2, 4, 2, 4, 3,\n", " 1, 0, 4, 1, 0, 1, 2, 4, 0, 4, 2, 3, 1, 0, 4, 3, 2, 1, 2, 4, 2, 4,\n", " 0, 4, 2, 1, 2, 4, 2, 3, 1, 0, 1, 1, 1, 0, 1, 2, 4, 2, 1, 3, 0, 1,\n", " 3, 3, 1, 4, 2, 4, 2, 4, 0, 3, 3, 1, 0, 4, 2, 4, 2, 0, 1, 3, 1, 1,\n", " 1, 2, 4, 3, 2, 1, 4, 3, 2, 1, 4, 2, 4, 2, 1, 0, 1, 4, 3, 1, 4, 1,\n", " 2, 1, 0, 1, 4, 2, 1, 2, 1, 4, 2, 4, 0, 1, 2, 3, 3, 1, 2, 4, 2, 1,\n", " 2, 1, 2, 1, 3, 1, 1, 1, 3, 1, 3, 2, 4, 2, 4, 2, 2, 1, 3, 0, 3, 2,\n", " 4, 0, 4, 3, 0, 1, 0, 1, 2, 4, 3, 1, 4, 3, 3, 4, 0, 1, 1, 4, 0, 4,\n", " 2, 0, 1, 1, 2, 4, 2, 1], dtype=int32)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = 5 # choose K\n", "\n", "fit = KMeans(n_clusters=k).fit(scaled_data)\n", "centroids = fit.cluster_centers_\n", "labels = fit.labels_\n", "\n", "labels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute the gap statistic\n", "\n", "Note that this takes a bit to run." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('The best k according to the gap statistic is: ', 2)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k_gap = {}\n", "for k in k_range:\n", " gap = compute_gap_statistic(scaled_data, k, scale_data=False)\n", " k_gap[k] = gap \n", " \n", "k_gapdiff = {}\n", "for k in range(min(k_range), max(k_range)-1):\n", " k_gapdiff[k] = k_gap[k][0] - k_gap[k+1][0] - k_gap[k + 1][2]\n", " \n", "'The best k according to the gap statistic is: ', evaluate_gap_statistic_best_k(scaled_data)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 396, "width": 612 } }, "output_type": "display_data" } ], "source": [ "plt.plot(list(k_gap.keys()), [value[0] for value in k_gap.values()])\n", "plt.title('Gap statistic')\n", "plt.ylabel('$G$')\n", "plt.xlabel('$K$')\n", "#plt.grid()\n", "plt.savefig('gap.png', dpi=200)\n", "plt.show();" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 396, "width": 621 } }, "output_type": "display_data" } ], "source": [ "plt.bar(list(k_gapdiff.keys()), k_gapdiff.values())\n", "plt.title('Gap diff')\n", "plt.ylabel('$G_K - G_{K+1} + s_{K+1}$')\n", "plt.xlabel('$K$')\n", "plt.ylim(-0.8, 0.1)\n", "plt.savefig('gapdiff.png', dpi=200)\n", "plt.show();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Scatter plot of two given features with the respective cluster colour and centroid" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 393, "width": 621 } }, "output_type": "display_data" } ], "source": [ "# Choose feature indices from the header\n", "f1 = 1\n", "f2 = 2\n", "\n", "k = 4\n", "\n", "# List of colours: if len is < k, add some\n", "colours = {\n", " 'red': 'r',\n", " 'black': 'k',\n", " 'blue': 'b',\n", " 'green': 'g',\n", " 'grey': '#929090',\n", " 'pink': '#FFB6C1',\n", " 'light_blue': '#00BFFF',\n", " 'light_green': '#29E191'\n", "}\n", "\n", "plt.title('Scatter plot of two features, k clusters', fontweight='bold', fontsize=16)\n", "plt.xlabel('eruptions')\n", "plt.ylabel('waiting')\n", "plt.grid()\n", "\n", "# Note: plot displays the scaled data\n", "for cluster_index in range(k):\n", " cluster_color = colours[list(colours)[cluster_index]]\n", " cluster_points = retrieve_cluster_points(cluster_index, labels, scaled_data)\n", " plt.scatter([point[f1-1] for point in cluster_points], \n", " [point[f2-1] for point in cluster_points], color=cluster_color)\n", " plt.scatter(centroids[cluster_index,f1-1], centroids[cluster_index, f2-1], marker='x', s=200, color=cluster_color)\n", "\n", "plt.savefig('cluster.png', dpi=200)\n", "plt.show();" ] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }