{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cluster Analysis" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import addutils.toc ; addutils.toc.js(ipy_notebook=True)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "from sklearn.manifold import TSNE\n", "from sklearn.cluster import KMeans, DBSCAN\n", "from sklearn.datasets import make_blobs\n", "from addutils import css_notebook\n", "from sklearn import metrics\n", "from sklearn.preprocessing import StandardScaler\n", "css_notebook()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " Loading BokehJS ...\n", "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", "(function(root) {\n", " function now() {\n", " return new Date();\n", " }\n", "\n", " var force = true;\n", "\n", " if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n", " root._bokeh_onload_callbacks = [];\n", " root._bokeh_is_loading = undefined;\n", " }\n", "\n", " var JS_MIME_TYPE = 'application/javascript';\n", " var HTML_MIME_TYPE = 'text/html';\n", " var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n", " var CLASS_NAME = 'output_bokeh rendered_html';\n", "\n", " /**\n", " * Render data to the DOM node\n", " */\n", " function render(props, node) {\n", " var script = document.createElement(\"script\");\n", " node.appendChild(script);\n", " }\n", "\n", " /**\n", " * Handle when an output is cleared or removed\n", " */\n", " function handleClearOutput(event, handle) {\n", " var cell = handle.cell;\n", "\n", " var id = cell.output_area._bokeh_element_id;\n", " var server_id = cell.output_area._bokeh_server_id;\n", " // Clean up Bokeh references\n", " if (id !== undefined) {\n", " Bokeh.index[id].model.document.clear();\n", " delete Bokeh.index[id];\n", " }\n", "\n", " if (server_id !== undefined) {\n", " // Clean up Bokeh references\n", " var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n", " cell.notebook.kernel.execute(cmd, {\n", " iopub: {\n", " output: function(msg) {\n", " var element_id = msg.content.text.trim();\n", " Bokeh.index[element_id].model.document.clear();\n", " delete Bokeh.index[element_id];\n", " }\n", " }\n", " });\n", " // Destroy server and session\n", " var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n", " cell.notebook.kernel.execute(cmd);\n", " }\n", " }\n", "\n", " /**\n", " * Handle when a new output is added\n", " */\n", " function handleAddOutput(event, handle) {\n", " var output_area = handle.output_area;\n", " var output = handle.output;\n", "\n", " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n", " if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n", " return\n", " }\n", "\n", " var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n", "\n", " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n", " toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n", " // store reference to embed id on output_area\n", " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n", " }\n", " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n", " var bk_div = document.createElement(\"div\");\n", " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n", " var script_attrs = bk_div.children[0].attributes;\n", " for (var i = 0; i < script_attrs.length; i++) {\n", " toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n", " }\n", " // store reference to server id on output_area\n", " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n", " }\n", " }\n", "\n", " function register_renderer(events, OutputArea) {\n", "\n", " function append_mime(data, metadata, element) {\n", " // create a DOM node to render to\n", " var toinsert = this.create_output_subarea(\n", " metadata,\n", " CLASS_NAME,\n", " EXEC_MIME_TYPE\n", " );\n", " this.keyboard_manager.register_events(toinsert);\n", " // Render to node\n", " var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n", " render(props, toinsert[0]);\n", " element.append(toinsert);\n", " return toinsert\n", " }\n", "\n", " /* Handle when an output is cleared or removed */\n", " events.on('clear_output.CodeCell', handleClearOutput);\n", " events.on('delete.Cell', handleClearOutput);\n", "\n", " /* Handle when a new output is added */\n", " events.on('output_added.OutputArea', handleAddOutput);\n", "\n", " /**\n", " * Register the mime type and append_mime function with output_area\n", " */\n", " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n", " /* Is output safe? */\n", " safe: true,\n", " /* Index of renderer in `output_area.display_order` */\n", " index: 0\n", " });\n", " }\n", "\n", " // register the mime type if in Jupyter Notebook environment and previously unregistered\n", " if (root.Jupyter !== undefined) {\n", " var events = require('base/js/events');\n", " var OutputArea = require('notebook/js/outputarea').OutputArea;\n", "\n", " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n", " register_renderer(events, OutputArea);\n", " }\n", " }\n", "\n", " \n", " if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n", " root._bokeh_timeout = Date.now() + 5000;\n", " root._bokeh_failed_load = false;\n", " }\n", "\n", " var NB_LOAD_WARNING = {'data': {'text/html':\n", " \"
\\n\"+\n", " \"

\\n\"+\n", " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n", " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n", " \"

\\n\"+\n", " \"
    \\n\"+\n", " \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
  • \\n\"+\n", " \"
  • use INLINE resources instead, as so:
  • \\n\"+\n", " \"
\\n\"+\n", " \"\\n\"+\n", " \"from bokeh.resources import INLINE\\n\"+\n", " \"output_notebook(resources=INLINE)\\n\"+\n", " \"\\n\"+\n", " \"
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\\n\"+\n \"

\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"

\\n\"+\n \"
    \\n\"+\n \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
  • \\n\"+\n \"
  • use INLINE resources instead, as so:
  • \\n\"+\n \"
\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\n\n function display_loaded() {\n var el = document.getElementById(\"f1bc2f24-9fdc-4f45-9765-0e81bc434962\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n }\n finally {\n delete root._bokeh_onload_callbacks\n }\n console.info(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(js_urls, callback) {\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null || js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = js_urls.length;\n for (var i = 0; i < js_urls.length; i++) {\n var url = js_urls[i];\n var s = document.createElement('script');\n s.src = url;\n s.async = false;\n s.onreadystatechange = s.onload = function() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.log(\"Bokeh: all BokehJS libraries loaded\");\n run_callbacks()\n }\n };\n s.onerror = function() {\n console.warn(\"failed to load library \" + url);\n };\n console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.getElementsByTagName(\"head\")[0].appendChild(s);\n }\n };var element = document.getElementById(\"f1bc2f24-9fdc-4f45-9765-0e81bc434962\");\n if (element == null) {\n console.log(\"Bokeh: ERROR: autoload.js configured with elementid 'f1bc2f24-9fdc-4f45-9765-0e81bc434962' but no matching script tag was found. \")\n return false;\n }\n\n var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n var inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n \n function(Bokeh) {\n \n },\n function(Bokeh) {\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n }\n ];\n\n function run_inline_js() {\n \n if ((root.Bokeh !== undefined) || (force === true)) {\n for (var i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n var cell = $(document.getElementById(\"f1bc2f24-9fdc-4f45-9765-0e81bc434962\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._bokeh_is_loading === 0) {\n console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(js_urls, function() {\n console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import bokeh.plotting as bk\n", "from bokeh import palettes\n", "bk.output_notebook()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib.cm as cm\n", "%matplotlib notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1 Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is Clustering? *Given a set of data points, partition them into groups (clusters) containing very similar data points.*\n", "\n", "This is a rough description of what clustering, for example it does not define what is the **number of clusters**, or what we mean for **similar**. \n", "\n", "Clustering has many applications, for example: data summarization, customer segmentation, social network analysis, preprocessing step for classification or outlier detection.\n", "\n", "There are many kind of clustering algorithm we will briefly sketch the main ideas of each typology, but first we will briefly define what is **similarity (or distance)**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 Distances" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given two objects $O_1$ and $O_2$, determine a value of the similarity $Sim(O_1 , O_2)$ (or distance $Dist(O_1, O_2))$ between the two objects. \n", "\n", "In similarity functions, larger values imply greater similarity, while in distance functions, smaller values imply greater similarity. When we are dealing with spatial data, it is more natural to talk about distance function. \n", "\n", "The most common distance function for **quantitative data** is the $L_p$*-norm*, given two data points $X = (x_1, \\ldots, x_n)$ and $Y = (y_1, \\ldots, y_n)$ it is defined as:\n", "$$ Dist(X,Y) = \\Bigg(\\sum_{i=1}^d \\mid x_i - y_i \\mid^p \\Bigg)^{1/p}$$\n", "Two special cases are the Euclidean ($p=2$) and Manhattan ($p=1$). The Euclidean distance is the straight line between two points:\n", "\"Euclidean\n", "The Manhattan distance is the \"city block\" distance in a region where the street are arranged as rectangular blocks:\n", "\"Manhattan\n", "These two distances are the most popular and widely used distances." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2 Representative-Based Algorithms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the symplest way of clustering, because this algorithms rely directly on the notion of distance (or similarity) to cluster data points. Each cluster is represented by a representative, that could be a function of the points or a point in the cluster. Finding a good clustering here, means finding a good set of representatives. With a good set of representatives and the distance function it is possible to assign points to the closest representative." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 KMeans" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The KMeans algorithm clusters data by trying to separate samples in n groups of equal variance, minimizing a criterion known as the inertia or within-cluster sum-of-squares. This algorithm requires the number of clusters to be specified. It scales well to large number of samples and has been used across a large range of application areas in many different fields.\n", "\n", "The k-means algorithm divides a set of N samples X into K disjoint clusters C, each described by the mean $\\mu_j$ of the samples in the cluster. The means are commonly called the cluster “centroids”; note that they are not, in general, points from X, although they live in the same space. The K-means algorithm aims to choose centroids that minimise the inertia, or within-cluster sum of squared criterion:\n", "\n", "$\\sum_{i=0}^{n}\\min_{\\mu_j \\in C}(\\|x_j - \\mu_i\\|^2)$\n", "\n", "Inertia, or the within-cluster sum of squares criterion, can be recognized as a measure of how internally coherent clusters are. It suffers from various drawbacks:\n", "* Inertia makes the assumption that clusters are convex and isotropic, which is not always the case. It responds poorly to elongated clusters, or manifolds with irregular shapes.\n", "* Inertia is not a normalized metric: we just know that lower values are better and zero is optimal. But in very high-dimensional spaces, Euclidean distances tend to become inflated (this is an instance of the so-called “curse of dimensionality”). Running a dimensionality reduction algorithm such as PCA prior to k-means clustering can alleviate this problem and speed up the computations." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7, 7))\n", "\n", "n_samples = 1500\n", "random_state = 170\n", "X, y = make_blobs(n_samples=n_samples, random_state=random_state)\n", "\n", "# Incorrect number of clusters\n", "y_pred = KMeans(n_clusters=2, random_state=random_state).fit_predict(X)\n", "\n", "plt.subplot(221)\n", "plt.scatter(X[:, 0], X[:, 1], c=y_pred)\n", "plt.title(\"Incorrect Number of Blobs\")\n", "\n", "# Anisotropicly distributed data\n", "transformation = [[ 0.60834549, -0.63667341], [-0.40887718, 0.85253229]]\n", "X_aniso = np.dot(X, transformation)\n", "y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_aniso)\n", "\n", "plt.subplot(222)\n", "plt.scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred)\n", "plt.title(\"Anisotropicly Distributed Blobs\")\n", "\n", "# Different variance\n", "X_varied, y_varied = make_blobs(n_samples=n_samples,\n", " cluster_std=[1.0, 2.5, 0.5],\n", " random_state=random_state)\n", "y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_varied)\n", "\n", "plt.subplot(223)\n", "plt.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred)\n", "plt.title(\"Unequal Variance\")\n", "\n", "# Unevenly sized blobs\n", "X_filtered = np.vstack((X[y == 0][:500], X[y == 1][:100], X[y == 2][:10]))\n", "y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_filtered)\n", "\n", "plt.subplot(224)\n", "plt.scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_pred)\n", "plt.title(\"Unevenly Sized Blobs\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Silhouette Plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First of all we will create a synthetic dataset that we will use for each example throughout the notebook." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1500, 10)\n" ] } ], "source": [ "n_samples = 1500\n", "n_features = 10\n", "random_state = 0\n", "X, _ = make_blobs(n_samples=n_samples, n_features=n_features, \n", " random_state=random_state, centers=4, cluster_std=0.4)\n", "print(X.shape)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1500, 2)\n" ] } ], "source": [ "tsne = TSNE(n_components=2, random_state=0, perplexity=30)\n", "Y = tsne.fit_transform(X)\n", "print(Y.shape)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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\",\"dtype\":\"float32\",\"shape\":[1500]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float32\",\"shape\":[1500]}}},\"id\":\"d5ef79f6-120f-4e75-b5d6-4d17b826e3d7\",\"type\":\"ColumnDataSource\"}],\"root_ids\":[\"f5881514-a573-426a-bb75-01c93aeee83d\"]},\"title\":\"Bokeh 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= bk.figure(plot_width=750, \n", " plot_height=450,\n", " title=\"Data\")\n", "#fig.scatter(Y[:,0], Y[:,1], fill_color=[pal[i] for i in y_pred], line_color=None)\n", "fig.scatter(Y[:,0], Y[:,1], line_color=None)\n", "bk.show(fig)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Silhouette analysis can be used to study the separation distance between the resulting clusters. The silhouette plot displays a measure of how close each point in one cluster is to points in the neighboring clusters and thus provides a way to assess parameters like number of clusters visually. This measure has a range of [-1, 1].\n", "\n", "Silhouette coefficients (as these values are referred to as) near +1 indicate that the sample is far away from the neighboring clusters. A value of 0 indicates that the sample is on or very close to the decision boundary between two neighboring clusters and negative values indicate that those samples might have been assigned to the wrong cluster.\n", "\n", "In this example the silhouette analysis is used to choose an optimal value for n_clusters. The silhouette plot shows that the n_clusters value of 4, 5 and 6 are a bad pick for the given data due to the presence of clusters with below average silhouette scores and also due to wide fluctuations in the size of the silhouette plots. Silhouette analysis is more ambivalent in deciding between 2 and 3.\n", "\n", "Also from the thickness of the silhouette plot the cluster size can be visualized. The silhouette plot for cluster 0 when n_clusters is equal to 2, is bigger in size owing to the grouping of the 2 sub clusters into one big cluster. However when the n_clusters is equal to 3, all the plots are more or less of similar thickness and hence are of similar sizes as can be also verified from the labelled scatter plot on the right." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "For n_clusters = 3 The average silhouette_score is : 0.7392830922762088\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "For n_clusters = 4 The average silhouette_score is : 0.8857123183962275\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "For n_clusters = 5 The average silhouette_score is : 0.6827500786110825\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "range_n_clusters = [3, 4, 5]\n", "\n", "for n_clusters in range_n_clusters:\n", " # Create a subplot with 1 row and 2 columns\n", " fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(7, 4))\n", " # fig.set_size_inches(18, 7)\n", "\n", " # The 1st subplot is the silhouette plot\n", " # The silhouette coefficient can range from -1, 1 but in this example all\n", " # lie within [-0.1, 1]\n", " ax1.set_xlim([-0.1, 1])\n", " # The (n_clusters+1)*10 is for inserting blank space between silhouette\n", " # plots of individual clusters, to demarcate them clearly.\n", " ax1.set_ylim([0, len(X) + (n_clusters + 1) * 10])\n", "\n", " # Initialize the clusterer with n_clusters value and a random generator\n", " # seed of 10 for reproducibility.\n", " clusterer = KMeans(n_clusters=n_clusters, random_state=10)\n", " cluster_labels = clusterer.fit_predict(X)\n", "\n", " # The silhouette_score gives the average value for all the samples.\n", " # This gives a perspective into the density and separation of the formed\n", " # clusters\n", " silhouette_avg = metrics.silhouette_score(X, cluster_labels)\n", " print(\"For n_clusters =\", n_clusters,\n", " \"The average silhouette_score is :\", silhouette_avg)\n", "\n", " # Compute the silhouette scores for each sample\n", " sample_silhouette_values = metrics.silhouette_samples(X, cluster_labels)\n", "\n", " y_lower = 10\n", " for i in range(n_clusters):\n", " # Aggregate the silhouette scores for samples belonging to\n", " # cluster i, and sort them\n", " ith_cluster_silhouette_values = \\\n", " sample_silhouette_values[cluster_labels == i]\n", "\n", " ith_cluster_silhouette_values.sort()\n", "\n", " size_cluster_i = ith_cluster_silhouette_values.shape[0]\n", " y_upper = y_lower + size_cluster_i\n", "\n", " color = cm.spectral(float(i) / n_clusters)\n", " ax1.fill_betweenx(np.arange(y_lower, y_upper),\n", " 0, ith_cluster_silhouette_values,\n", " facecolor=color, edgecolor=color, alpha=0.7)\n", "\n", " # Label the silhouette plots with their cluster numbers at the middle\n", " ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))\n", "\n", " # Compute the new y_lower for next plot\n", " y_lower = y_upper + 10 # 10 for the 0 samples\n", "\n", " #ax1.set_title(\"The silhouette plot for the various clusters.\", fontsize=8)\n", " ax1.set_xlabel(\"The silhouette coefficient values\", fontsize=8)\n", " ax1.set_ylabel(\"Cluster label\", fontsize=8)\n", "\n", " # The vertical line for average silhouette score of all the values\n", " ax1.axvline(x=silhouette_avg, color=\"red\", linestyle=\"--\")\n", "\n", " ax1.set_yticks([]) # Clear the yaxis labels / ticks\n", " ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])\n", "\n", " # 2nd Plot showing the actual clusters formed\n", " colors = cm.spectral(cluster_labels.astype(float) / n_clusters)\n", " ax2.scatter(Y[:, 0], Y[:, 1], marker='.', s=30, lw=0, alpha=0.7,\n", " c=colors)\n", "\n", " # Labeling the clusters\n", " centers = clusterer.cluster_centers_\n", " closest, _ = metrics.pairwise_distances_argmin_min(centers, X)\n", " \n", " # Draw white circles at cluster centers\n", " # ax2.scatter(centers[:, 0], centers[:, 1],\n", " ax2.scatter(Y[closest, 0], Y[closest, 1],\n", " marker='o', c=\"white\", alpha=1, s=200)\n", "\n", " # for i, c in enumerate(centers):\n", " # ax2.scatter(c[0], c[1], marker='$%d$' % i, alpha=1, s=50)\n", " for i, c in enumerate(closest):\n", " ax2.scatter(Y[c, 0], Y[c, 1], marker='$%d$' % i, alpha=1, s=50) \n", "\n", " #ax2.set_title(\"The visualization of the clustered data.\", fontsize=8)\n", "\n", " plt.suptitle((\"Silhouette analysis for KMeans clustering on sample data \"\n", " \"with n_clusters = %d\" % n_clusters),\n", " fontsize=10, fontweight='bold')\n", " #fig.tight_layout()\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3 Density-Based Algorithms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the problems of distance-based clustering is that the shape of underlying cluster is implicitly defined by the distance function. For example k-means assumes a spherical shape for the clusters. Density-Based clusters are very helpful in situation where the form and number of clusters is unknown. The idea is to first identify dense region in the data that forms the building blocks for constructing cluster of arbitrary shape." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 DBSCAN" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The DBSCAN algorithm views clusters as areas of high density separated by areas of low density. Due to this rather generic view, clusters found by DBSCAN can be any shape, as opposed to k-means which assumes that clusters are convex shaped. The central component to the DBSCAN is the concept of core samples, which are samples that are in areas of high density. A cluster is therefore a set of core samples, each close to each other (measured by some distance measure) and a set of non-core samples that are close to a core sample (but are not themselves core samples). There are two parameters to the algorithm, min_samples and eps, which define formally what we mean when we say dense. Higher min_samples or lower eps indicate higher density necessary to form a cluster.\n", "\n", "More formally, we define a core sample as being a sample in the dataset such that there exist `min_samples` other samples within a distance of `eps`, which are defined as neighbors of the core sample. This tells us that the core sample is in a dense area of the vector space. A cluster is a set of core samples that can be built by recursively taking a core sample, finding all of its neighbors that are core samples, finding all of their neighbors that are core samples, and so on. A cluster also has a set of non-core samples, which are samples that are neighbors of a core sample in the cluster but are not themselves core samples. Intuitively, these samples are on the fringes of a cluster.\n", "\n", "Any core sample is part of a cluster, by definition. Any sample that is not a core sample, and is at least eps in distance from any core sample, is considered an outlier by the algorithm.\n", "\n", "In the figure below, the color indicates cluster membership, with large circles indicating core samples found by the algorithm. Smaller circles are non-core samples that are still part of a cluster. Moreover, the outliers are indicated by black points below." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "centers = [[1, 1], [-1, -1], [1, -1], [-1, 1]]\n", "X, _ = make_blobs(n_samples=750, centers=centers, cluster_std=0.4,\n", " random_state=0)\n", "\n", "X = StandardScaler().fit_transform(X)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "metrics.pairwise.pairwise_distances(X).mean()\n", "pal = palettes.Category10[5]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated number of clusters: 4\n", "Silhouette Coefficient: 0.548\n" ] } ], "source": [ "db = DBSCAN(eps=0.3, min_samples=20).fit(X)\n", "core_samples_mask = np.zeros_like(db.labels_, dtype=bool)\n", "core_samples_mask[db.core_sample_indices_] = True\n", "labels = db.labels_\n", "\n", "# Number of clusters in labels, ignoring noise if present.\n", "n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)\n", "\n", "print('Estimated number of clusters: %d' % n_clusters_)\n", "print(\"Silhouette Coefficient: %0.3f\"\n", " % metrics.silhouette_score(X, labels))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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= bk.figure(plot_width=750, plot_height=450, \n", " title='Estimated number of clusters: {}'.format(n_clusters_))\n", "# Black removed and is used for noise instead.\n", "unique_labels = set(labels)\n", "colors = plt.cm.Spectral(np.linspace(0, 1, len(unique_labels)))\n", "for k, col in zip(unique_labels, pal):\n", " if k == -1:\n", " # Black used for noise.\n", " col = '#000000'\n", " \n", " class_member_mask = (labels == k)\n", "\n", " xy = X[class_member_mask & core_samples_mask]\n", " fig.scatter(xy[:, 0], xy[:, 1], fill_color=col, \n", " line_color=None, size=14)\n", "\n", " xy = X[class_member_mask & ~core_samples_mask]\n", " fig.scatter(xy[:,0], xy[:,1], fill_color=col, \n", " line_color=None, size=6)\n", "\n", "fig.title.text_font_size = '14pt'\n", "bk.show(fig)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4 Probabilistic Model-Based Algorithms " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The k-means clustering model explored before is simple and relatively easy to understand, but its simplicity leads to practical challenges in its application. In particular, the nonprobabilistic nature of k-means and its use of simple distance-from-cluster-center to assign cluster membership may lead to poor performance in many real applications.\n", "\n", "There’s another way to deal with clustering problems: a model-based approach, which consists in using certain models for clusters and attempting to optimize the fit between the data and the model.\n", "\n", "In practice, each cluster can be mathematically represented by a parametric distribution, like a Gaussian (continuous) or a Poisson (discrete). The entire data set is therefore modelled by a mixture of these distributions. An individual distribution used to model a specific cluster is often referred to as a component distribution.\n", "\n", "A mixture model with high likelihood tends to have the following traits:\n", "\n", "* component distributions have high \"peaks\" (data in one cluster are tight);\n", "* the mixture model \"covers\" the data well (dominant patterns in the data are captured by component distributions).\n", "\n", "Main advantages of model-based clustering:\n", "\n", "* well-studied statistical inference techniques available;\n", "* flexibility in choosing the component distribution;\n", "* obtain a density estimation for each cluster;\n", "* a \"soft\" classification is available." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1 Mixture of Gaussians" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X, y_true = make_blobs(n_samples=400, centers=4,\n", " cluster_std=0.60, random_state=0)\n", "X = X[:, ::-1] " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n", " labels = kmeans.fit_predict(X)\n", "\n", " ax = ax or plt.gca()\n", " ax.axis('equal')\n", " ax.scatter(X[:, 0], X[:, 1], c=labels, s=20, cmap='viridis', zorder=2)\n", "\n", " centers = kmeans.cluster_centers_\n", " radii = [cdist(X[labels == i], [center]).max() \n", " for i, center in enumerate(centers)]\n", " for c, r in zip(centers, radii):\n", " ax.add_patch(plt.Circle(c, r, fc='lightblue', lw=3, alpha=0.5, zorder=1))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.spatial.distance import cdist\n", "kmeans = KMeans(4, random_state=42)\n", "labels = kmeans.fit(X).predict(X)\n", "fig, ax = plt.subplots()\n", "plot_kmeans(kmeans, X, ax)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.RandomState(13)\n", "X_stretched = np.dot(X, rng.randn(2, 2))\n", "fig, ax = plt.subplots()\n", "kmeans = KMeans(n_clusters=4, random_state=42)\n", "plot_kmeans(kmeans, X_stretched, ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One possible solution is to use PCA or other transformations but since we are in an unsupervised environment there is no guarantee that it will work as expected. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most widely used clustering method for this kind of problems is the one based on learning a mixture of Gaussians: we can actually consider clusters as Gaussian distributions centred on their barycentres.\n", "\n", "The GaussianMixture object implements the expectation-maximization (EM) algorithm for fitting mixture-of-Gaussian models, that qualitatively does the following:\n", "\n", "1. Choose starting guesses for the location and shape\n", "\n", "1. Repeat until converged:\n", " - E-step: for each point, find weights encoding the probability of membership in each cluster\n", " - M-step: for each cluster, update its location, normalization, and shape based on all data points, making use of the weights\n", "\n", "The result of this is that each cluster is associated not with a hard-edged sphere, but with a smooth Gaussian model. Just as in the k-means expectation–maximization approach, this algorithm can sometimes miss the globally optimal solution, and thus in practice multiple random initializations are used.\n", "\n", "It can also draw confidence ellipsoids for multivariate models, and compute the Bayesian Information Criterion to assess the number of clusters in the data. A GaussianMixture.fit method is provided that learns a Gaussian Mixture Model from train data. Given test data, it can assign to each sample the Gaussian it mostly probably belong to using the GaussianMixture.predict method.\n", "\n", "The GaussianMixture comes with different options to constrain the covariance of the difference classes estimated: spherical, diagonal, tied or full covariance." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from matplotlib.patches import Ellipse\n", "\n", "def draw_ellipse(position, covariance, ax=None, **kwargs):\n", " \"\"\"Draw an ellipse with a given position and covariance\"\"\"\n", " ax = ax or plt.gca()\n", " # Convert covariance to principal axes\n", " if covariance.shape == (2, 2):\n", " U, s, Vt = np.linalg.svd(covariance)\n", " angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n", " width, height = 2 * np.sqrt(s)\n", " else:\n", " angle = 0\n", " width, height = 2 * np.sqrt(covariance)\n", " \n", " # Draw the ellipse\n", " for nsig in range(1, 4):\n", " ax.add_patch(Ellipse(position, nsig * width, nsig * height, angle, **kwargs))\n", "\n", "def plot_gmm(gmm, X, label=True, ax=None):\n", " ax = ax or plt.gca()\n", " labels = gmm.fit(X).predict(X)\n", " if label:\n", " ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n", " else:\n", " ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)\n", " ax.axis('equal')\n", " \n", " w_factor = 0.2 / gmm.weights_.max()\n", " for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\n", " draw_ellipse(pos, covar, alpha=w * w_factor)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.mixture import GaussianMixture\n", "fig, ax = plt.subplots()\n", "gmm = GaussianMixture(n_components=4, random_state=42)\n", "plot_gmm(gmm, X, ax)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "gmm = GaussianMixture(n_components=4, covariance_type='full', random_state=42)\n", "plot_gmm(gmm, X_stretched, ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Choosing the covariance type:* If you look at the details of the preceding fits, you will see that the covariance_type option was set differently within each. This hyperparameter controls the degrees of freedom in the shape of each cluster; it is essential to set this carefully for any given problem. The default is covariance_type=\"diag\" , which means that the size of the cluster along each dimension can be set independently, with the resulting ellipse constrained to align with the axes. A slightly simpler and faster model is covariance_type=\"spherical\" , which constrains the shape of the cluster such that all dimensions are equal. The resulting clustering will have similar characteristics to that of k-means, though it is not entirely equivalent. A more complicated and computationally expensive model (especially as the number of dimensions grows) is to use covariance_type=\"full\" , which allows each cluster to be modeled as an ellipse with arbitrary orientation.\n", "\n", "The main difficulty in learning Gaussian mixture models from unlabeled data is that it is one usually doesn’t know which points came from which latent component (if one has access to this information it gets very easy to fit a separate Gaussian distribution to each set of points). Expectation-maximization is a well-founded statistical algorithm to get around this problem by an iterative process. First one assumes random components (randomly centered on data points, learned from k-means, or even just normally distributed around the origin) and computes for each point a probability of being generated by each component of the model. Then, one tweaks the parameters to maximize the likelihood of the data given those assignments. Repeating this process is guaranteed to always converge to a local optimum.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "Visit [www.add-for.com]() for more tutorials and updates.\n", "\n", "This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda env:addfor_tutorials]", "language": "python", "name": "conda-env-addfor_tutorials-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 1 }