{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# code for loading the format for the notebook\n", "import os\n", "\n", "# path : store the current path to convert back to it later\n", "path = os.getcwd()\n", "os.chdir(os.path.join('..', 'notebook_format'))\n", "from formats import load_style\n", "load_style(plot_style = False)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ethen 2017-09-27 21:21:42 \n", "\n", "CPython 3.5.2\n", "IPython 6.1.0\n", "\n", "numpy 1.13.1\n", "pandas 0.20.3\n", "matplotlib 2.0.0\n", "sklearn 0.18.1\n", "scipy 0.19.1\n" ] } ], "source": [ "os.chdir(path)\n", "\n", "# 1. magic for inline plot\n", "# 2. magic to print version\n", "# 3. magic so that the notebook will reload external python modules\n", "# 4. magic to enable retina (high resolution) plots\n", "# https://gist.github.com/minrk/3301035\n", "%matplotlib inline\n", "%load_ext watermark\n", "%load_ext autoreload\n", "%autoreload 2\n", "%config InlineBackend.figure_format = 'retina'\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm\n", "from sklearn.cluster import KMeans\n", "from sklearn.mixture import GaussianMixture\n", "from sklearn.metrics import pairwise_distances\n", "from sklearn.datasets.samples_generator import make_blobs\n", "\n", "%watermark -a 'Ethen' -d -t -v -p numpy,pandas,matplotlib,sklearn,scipy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# K-means" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clustering algorithms are a typical example of unsupervised clustering. Its task is to gathering similar samples (we'll need to define which similarity or distance (dissimilarity) measure we want to use) into groups based on the data attributes (features) alone. Let's start by creating a simple, 2-dimensional, synthetic dataset." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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+jLDPJq96eZeVFGvxnKgOvfF24GsBAPiPQBwoUGOH0LTsOe17ID67IqKL/fnX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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 364, "width": 369 } }, "output_type": "display_data" } ], "source": [ "X, y = make_blobs(n_samples = 300, centers = 4,\n", " random_state = 0, cluster_std = 0.6)\n", "\n", "# change default figure and font size\n", "plt.rcParams['figure.figsize'] = 8, 6 \n", "plt.rcParams['font.size'] = 12\n", "\n", "# scatter plot\n", "plt.scatter(X[:, 0], X[:, 1], s = 50)\n", "plt.ylim(-2, 10)\n", "plt.xlim(-6, 6)\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the scatter plot above, we can see 4 separate groups of data points and we would like to recover them using clustering -- think of \"discovering\" the class labels that we've taken for granted in a classification task. Even though the groups are pretty obvious here, it becomes hard to find them when the data lives in a high-dimensional space, where we simply can't visualize them in a single scatterplot.\n", "\n", "Now we will use one of the simplest clustering algorithms, **K-means**. This is an iterative algorithm which searches for 4 cluster centroids (we need to specify the number of clusters before we run the algorithm) such that the distance from each point to its cluster is minimized. \n", "\n", "It starts by choosing an initial set of centroids $\\mu_j$ (in our case $j$ will count up to 4, since we want to have 4 clusters). A common practice is to choose randomly from the data points. After initialization, the K-means algorithm iterates between the following two steps:\n", "\n", "1. Assign each data point $\\mathbf{x}_i$ to the closest centroid $z_i$ using standard euclidean distance.\n", "\n", "$$\n", "z_i \\gets \\mathrm{argmin}_j \\| \\mathbf{x}_i - \\mu_j \\|_2\n", "$$\n", "\n", "2. Revise each centroids as the mean of the assigned data points.\n", "\n", "$$\n", "\\mu_j \\gets \\frac{1}{n_j}\\sum_{i:z_i=j} \\mathbf{x}_i\n", "$$\n", "\n", "Where $n_j$ is the number of data points that belongs to cluster $j$.\n", "\n", "One sidenote, the standard implementation of K-means uses the euclidean distance, thus we need to make sure all our variables are measured on the same scale if we are working with real-world datastets. Or else our distance measure will get dominated by features that have a large scale, leading to unexpected results.\n", "\n", "Let's now implement a vanilla K-means algorithm." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def kmeans(X, k, maxiter, seed = None):\n", " \"\"\"\n", " specify the number of clusters k and\n", " the maximum iteration to run the algorithm\n", " \"\"\"\n", " n_row, n_col = X.shape\n", "\n", " # randomly choose k data points as initial centroids\n", " if seed is not None:\n", " np.random.seed(seed)\n", " \n", " rand_indices = np.random.choice(n_row, size = k)\n", " centroids = X[rand_indices]\n", "\n", " for itr in range(maxiter):\n", " # compute distances between each data point and the set of centroids\n", " # and assign each data point to the closest centroid\n", " distances_to_centroids = pairwise_distances(X, centroids, metric = 'euclidean')\n", " cluster_assignment = np.argmin(distances_to_centroids, axis = 1)\n", "\n", " # select all data points that belong to cluster i and compute\n", " # the mean of these data points (each feature individually)\n", " # this will be our new cluster centroids\n", " new_centroids = np.array([X[cluster_assignment == i].mean(axis = 0) for i in range(k)])\n", " \n", " # if the updated centroid is still the same,\n", " # then the algorithm converged\n", " if np.all(centroids == new_centroids):\n", " break\n", " \n", " centroids = new_centroids\n", " \n", " return centroids, cluster_assignment" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([75, 75, 75, 75])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = 4\n", "centers, label = kmeans(X, k, maxiter = 100)\n", "\n", "# we can count occurrences of each cluster label\n", "np.bincount(label)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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qTMSJurGDueedmv/bdzfCaPrpYchtWbk438aOsidcSMZ1pjqorQZI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\n0NjJV1U6jO/Wo5NGT7xcdQpr7+8E2YkgDgBAGiR7U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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 364, "width": 369 } }, "output_type": "display_data" } ], "source": [ "# plot the cluster and cluster's centroid\n", "plt.scatter(X[:, 0], X[:, 1], s = 50, c = label, cmap = 'viridis')\n", "plt.scatter(centers[:, 0], centers[:, 1], s = 200, alpha = 0.5)\n", "plt.ylim(-2, 10)\n", "plt.xlim(-6, 6)\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The algorithm identifies the four clusters of points in a manner very similar to what we would do by eye! We can also use the pre-implemented `Kmeans` from scikit-learn to confirm the outputs." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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UKWlQpaZBoTcWSC/lapZG3aez/2Hz9uKXkRSXjKNbT1o0Tv+3e6LPuK4QQuCn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\nRpPF9e4aNVr2bYKSlUrkeFx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GVX4Vk3vOxMF1kTCZLFtC0F5a9H6qQK+Xk0vHruLswQvO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kkiLsQpRGuNjuxFh9ehw5vRpoWa3OEVKTlyEq9spx+XPYw/fPLuddJ0ECLHV3Txh0yc9jDZrjQc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\n9K/f1lnHHl5tn/EWTYt0yagh+sOPzlPL0pJ6rhDIP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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 364, "width": 369 } }, "output_type": "display_data" } ], "source": [ "km = KMeans(n_clusters = 4)\n", "kmeans_y = km.fit_predict(X)\n", "kmeans_centers = km.cluster_centers_\n", "\n", "plt.scatter(X[:, 0], X[:, 1], s = 50, c = kmeans_y, cmap = 'viridis')\n", "plt.scatter(kmeans_centers[:, 0], kmeans_centers[:, 1], s = 200, alpha = 0.5)\n", "plt.ylim(-2, 10)\n", "plt.xlim(-6, 6)\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assessing Convergence\n", "\n", "One weakness of K-means is, the algorithm's performance is closely tied with the randomly generated initial centroids' quality. If the algorithm starts with a set of bad inital centers, it will get stuck in a local minimum.\n", "\n", "Before we get into that, we need to take a step back and ask ourselves how can we tell if the K-means algorithm is converging? Well, we can look at the cluster assignments and see if they stabilize over time. In fact, that's what we did in the toy implementation above, we ran the algorithm until the cluster assignments stop changing at all. But after running the clustering algorithm we want to have a measure that assesses the algorithm's performance. Hence, we'll introduce an additional measurement, **Total within Sum of Squares** (or refered to as inertia or heterogeneity). Mathematically, this is defined as:\n", "\n", "$$ \\sum_{j=1}^k \\sum_{i:z_i = j} \\|\\mathbf{x}_i - \\mu_j\\|_2^2 $$\n", "\n", "Where $k$ denotes the total number of clusters, $x_i$ is the $i_{th}$ data point, $\\mu_j$ is the $j_{th}$ cluster, and $\\|\\mathbf{x}_i - \\mu_j\\|_2^2$ denotes the squared L2 norm (Euclidean distance) between the two vectors.\n", "\n", "The formula computes the sum of all squared distances between data points and its centroids. It computation can be divided into two small parts. The within sum of squares for a single cluster, $\\sum_{i:z_i = j} \\|\\mathbf{x}_i - \\mu_j\\|_2^2$ is the squared distance (note that it is \"squared\" distance!, do not square root it like we usually do for euclidean distance) of each point in the cluster from that cluster’s centroid. And the total within sum of squares, $\\sum_{j=1}^k$, is the sum of the within sum of squares of all the clusters.\n", "\n", "> It might be a bit confusing, as to why, in the objective function we're using, $\\|\\mathbf{x}_i - \\mu_j\\|_2^2$, the squared L2 norm (euclidean distance) between the two vectors, while earlier in the cluster assignment section, we use $z_i \\gets \\mathrm{argmin}_j \\| \\mathbf{x}_i - \\mu_j \\|_2$, the euclidean distance (without squaring it). The fact that we can use still use euclidean distance (without squaring) it to assign data points to its closest cluster centers is because squaring or not squaring the distance doesn’t affect the order, and it saves us a computation to square it back to squared euclidean distance.\n", "\n", "To see that the convergence of this algorithm is not guaranteed, we'll add the new code to our original `kmeans` function to compute the heterogeneity. After that we'll run K-means multiple times. Each time, we use a different random seed to get different set of initial centroids." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def kmeans(X, k, maxiter, seed = None):\n", " \"\"\"\n", " specify the number of clusters k and\n", " the maximum iteration to run the algorithm\n", " \"\"\"\n", " n_row, n_col = X.shape\n", "\n", " # randomly choose k data points as initial centroids\n", " if seed is not None:\n", " np.random.seed(seed)\n", " \n", " rand_indices = np.random.choice(n_row, size = k)\n", " centroids = X[rand_indices]\n", "\n", " for itr in range(maxiter):\n", " # compute distances between each data point and the set of centroids\n", " # and assign each data point to the closest centroid\n", " distances_to_centroids = pairwise_distances(X, centroids, metric = 'euclidean')\n", " cluster_assignment = np.argmin(distances_to_centroids, axis = 1)\n", "\n", " # select all data points that belong to cluster i and compute\n", " # the mean of these data points (each feature individually)\n", " # this will be our new cluster centroids\n", " new_centroids = np.array([X[cluster_assignment == i].mean(axis = 0) for i in range(k)])\n", " \n", " # if the updated centroid is still the same,\n", " # then the algorithm converged\n", " if np.all(centroids == new_centroids):\n", " break\n", " \n", " centroids = new_centroids\n", " \n", " heterogeneity = 0\n", " for i in range(k):\n", " # note that pairwise_distance only accepts 2d-array\n", " cluster_data = X[cluster_assignment == i]\n", " distances = pairwise_distances(cluster_data, [centroids[i]], metric = 'euclidean')\n", " heterogeneity += np.sum(distances ** 2)\n", " \n", " return centroids, cluster_assignment, heterogeneity" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "seed = 0, heterogeneity = 212.00599621083518\n", "seed = 1000, heterogeneity = 212.00599621083518\n", "seed = 8181, heterogeneity = 523.7150139149792\n", "seed = 555, heterogeneity = 528.0315740282444\n", "seed = 10000, heterogeneity = 212.00599621083518\n", "seed = 120000, heterogeneity = 528.5562600476272\n" ] } ], "source": [ "heterogeneity_kmeans = {}\n", "\n", "for seed in [0, 1000, 8181, 555, 10000, 120000]:\n", " _, _, heterogeneity = kmeans(X, k, maxiter = 100, seed = seed)\n", " heterogeneity_kmeans[seed] = heterogeneity\n", " print('seed = {}, heterogeneity = {}'.format(seed, heterogeneity_kmeans[seed]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the variation in heterogeneity for different initializations. This shows K-means does in fact get stuck at a bad local minimum from time to time. So, the next question is, is there anything we can do about this?\n", "\n", "\n", "## K-means++\n", "\n", "One effective way to counter this issue is to use **K-means++** to provide a smart initialization. This method tries to spread out the initial set of centroids so that they are not too close together. It is known to improve the quality of local optima and lower average runtime (link to the original paper if you're interested in the theoretical guarantee [K-means++: The Advantages of Careful Seeding](http://ilpubs.stanford.edu:8090/778/1/2006-13.pdf)). \n", "\n", "The workflow of K-means++ is as follows:\n", "\n", "1. Choose a data point at random from the dataset, this serves as the first centroid\n", "2. Compute the **squared** euclidean distance of all other data points to the randomly chosen first centroid\n", "3. To generate the next centroid, each data point is chosen with the probability (weight) of its squared distance to the chosen center of this round divided by the the total squared distance (to make sure the probability adds up to 1). Roughtly speaking, a new centroid should be as far as from the other centroids as possible\n", "4. Next, recompute the probability (weight) of each data point as the minimum of the distance between it and all the centers that are already generated (e.g. for the second iteration, compare the data point's distance between the first and second center and choose the smaller one)\n", "5. Repeat step 3 and 4 until we have $K$ centers\n", "\n", "We'll now add the functionality of using K-means++ to initialize the initial cluster centroid to our original `kmeans` function." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def kmeans(X, k, init, maxiter, seed = None):\n", " \"\"\"\n", " specify the number of clusters k and\n", " the maximum iteration to run the algorithm\n", " \"\"\"\n", " n_row, n_col = X.shape\n", "\n", " if seed is not None:\n", " np.random.seed(seed)\n", " \n", " if init == 'kmeanspp':\n", " # randomly choose the first centroid\n", " centroids = np.zeros((k, n_col))\n", " rand_index = np.random.choice(n_row)\n", " centroids[0] = X[rand_index]\n", " \n", " # compute distances from the first centroid chosen to all the other data points\n", " distances = pairwise_distances(X, [centroids[0]], metric = 'euclidean').flatten()\n", " \n", " for i in range(1, k):\n", " # choose the next centroid, the probability for each data point to be chosen\n", " # is directly proportional to its squared distance from the nearest centroid\n", " prob = distances ** 2\n", " rand_index = np.random.choice(n_row, size = 1, p = prob / np.sum(prob))\n", " centroids[i] = X[rand_index]\n", " \n", " if i == k - 1:\n", " break\n", " \n", " # if we still need another cluster,\n", " # compute distances from the centroids to all data points\n", " # and update the squared distance as the minimum distance to all centroid\n", " distances_new = pairwise_distances(X, [centroids[i]], metric = 'euclidean').flatten()\n", " distances = np.min(np.vstack((distances, distances_new)), axis = 0)\n", " \n", " else: # random\n", " rand_indices = np.random.choice(n_row, size = k)\n", " centroids = X[rand_indices]\n", "\n", " for itr in range(maxiter):\n", " # compute distances between each data point and the set of centroids\n", " # and assign each data point to the closest centroid\n", " distances_to_centroids = pairwise_distances(X, centroids, metric = 'euclidean')\n", " cluster_assignment = np.argmin(distances_to_centroids, axis = 1)\n", "\n", " # select all data points that belong to cluster i and compute\n", " # the mean of these data points (each feature individually)\n", " # this will be our new cluster centroids\n", " new_centroids = np.array([X[cluster_assignment == i].mean(axis = 0) for i in range(k)])\n", " \n", " # if the updated centroid is still the same,\n", " # then the algorithm converged\n", " if np.all(centroids == new_centroids):\n", " break\n", " \n", " centroids = new_centroids\n", " \n", " heterogeneity = 0\n", " for i in range(k):\n", " # note that pairwise_distance only accepts 2d-array\n", " cluster_data = X[cluster_assignment == i]\n", " distances = pairwise_distances(cluster_data, [centroids[i]], metric = 'euclidean')\n", " heterogeneity += np.sum(distances ** 2)\n", " \n", " return centroids, cluster_assignment, heterogeneity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now rerun K-means using the same set of seeds as before, but this time we will always using K-means++ to initialize the centroid. Then, we'll compare the set of cluster heterogeneities we got from using K-means++ initialization versus using random initialization." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "seed = 0, heterogeneity = 212.00599621083518\n", "seed = 1000, heterogeneity = 212.00599621083518\n", "seed = 8181, heterogeneity = 212.00599621083518\n", "seed = 555, heterogeneity = 212.00599621083518\n", "seed = 10000, heterogeneity = 212.00599621083518\n", "seed = 120000, heterogeneity = 212.00599621083518\n", "\n", "kmeans average: 369.38680610389275\n", "kmeans++ average: 212.0059962108352\n" ] } ], "source": [ "heterogeneity_kmeanspp = {}\n", "\n", "for seed in [0, 1000, 8181, 555, 10000, 120000]:\n", " _, _, heterogeneity = kmeans(X, k, init = 'kmeanspp', maxiter = 100, seed = seed)\n", " heterogeneity_kmeanspp[seed] = heterogeneity\n", " print( 'seed = {}, heterogeneity = {}'.format(seed, heterogeneity_kmeanspp[seed]) )\n", "\n", "print()\n", "print('kmeans average: {}'.format( np.mean( list(heterogeneity_kmeans.values()) ) ))\n", "print('kmeans++ average: {}'.format( np.mean( list(heterogeneity_kmeanspp.values()) ) ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the result, we can see that random initialization results in a worse clustering heterogeneity than K-means++ on average. \n", "\n", "Although it looks like K-means++ worked pretty well in this simple example, it is not a panacea. It can still get stuck at local minima from time to time. Thus, in practice, we should run K-means at least a few times with different initializations and then return the best one (one that resulted in the lowest heterogeneity). For scikit-learn's [Kmeans](http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html), the default behavior is to run the algorithm for 10 times (`n_init` parameter) using the kmeans++ (`init` parameter) initialization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Elbow Method for Choosing K\n", "\n", "Another \"short-comings\" of K-means is that we have to specify the number of clusters before running the algorithm, which we often don't know apriori. For example, let's have a look what happens if we set the number of clusters to 3 in our synthetic dataset." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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T5un1QQC6j+kIIQR+vjofB9cfxYZFW3Hl5HXERcfD1VOHqo0qovPIdqjbpkam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\nqQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": { "image/png": { "height": 364, "width": 369 } }, "output_type": "display_data" } ], "source": [ "km = KMeans(n_clusters = 3, random_state = 42)\n", "labels = km.fit_predict(X)\n", "\n", "plt.scatter(X[:, 0], X[:, 1], s = 50, c = labels, cmap = 'viridis')\n", "plt.ylim(-2, 10)\n", "plt.xlim(-6, 6)\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "K-means can still run perfectly fine, but this the probably not the result we're looking for.\n", "\n", "There're many different heuristics for choosing the suitable $K$, the simplest one being the **Elbow method**. The way it works is we run the algorithm using different values of $K$ and plot the heterogeneity. This measure will decrease as the number of clusters increases, because each cluster will be smaller and tighter. And what we’re hoping for is the measure will keep on decreasing up till the optimal cluster number, and the decrease will start to flat out after that." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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rkiRJkiQDAmnI1dUFSxYdfYpgxZrNJVYjSZIkSRkDAqkElfMQrFzTTHt7KrEa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\nOpRzrsnMzpX0JUkfl1QnqVPSWkk/kvQD51yfYzydc583sxck/Z2iuxo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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 377, "width": 516 } }, "output_type": "display_data" } ], "source": [ "heterogeneities = []\n", "for i in range(2, 10):\n", " km = KMeans(n_clusters = i, random_state = 0)\n", " km.fit(X)\n", " heterogeneities.append(km.inertia_)\n", "\n", "plt.plot(range(2, 10), heterogeneities, marker = 'o')\n", "plt.xlabel('Number of clusters')\n", "plt.ylabel('heterogeneities')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "As we can see, the plot suggests we should choose 4 as our cluster number, since starting from $K=4$ the magnitude of the decease starts dropping (it looks like the pit of an elbow, that's why it was given the name the elbow method), which makes sense given our visual expection of the dataset previously. In practice, this \"elbow\" can sometimes be hard to see and can be quite subjective.\n", "\n", "Now that we gotten a bit familiar with how K-means works, we'll start addressing the assumption that K-means is making and its caveats.\n", "\n", "\n", "## Kmeans Caveats\n", "\n", "Different algorithm makes different assumptions, hence the quality and interpretability of the result will depend on whether these assumptions are valid for our goal. For K-means clustering, the model assumes that **all clusters have equal, spherical variance**. To let the notion sink in, let's look at some cases where K-means will generate results that might not match our intuition.\n", "\n", "Suppose our data looks like the following:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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ERERCBIKBG4KTMZlj8NuPfov2q+2yz1HmKkPd0jpd9hKrXXWLDCr/+cg/Y8vp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\nyAYnWYIcZsxOXBUM0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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 361, "width": 487 } }, "output_type": "display_data" } ], "source": [ "sizes = 20, 100, 500\n", "sizes_cumsum = 0, 20, 120, 620\n", "x_mean = 1, 4, 6\n", "y_mean = 5, 0, 6\n", "\n", "shape = np.sum(sizes), 2\n", "coordinates = np.zeros(shape)\n", "\n", "for idx, (s, xm, ym) in enumerate(zip(sizes, x_mean, y_mean)):\n", " x = norm(xm).rvs(size = s)\n", " y = norm(ym).rvs(size = s)\n", " plt.scatter(x, y, s = 50)\n", " \n", " coord = np.vstack((x, y)).T\n", " index = slice(sizes_cumsum[idx], sizes_cumsum[idx + 1])\n", " coordinates[index] = coord" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we randomly generated three cluster of data points drawn from three different normal distribution, each having 20, 100 and 500 data points. Let’s try K-means on this dataset." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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JW/zq3iJLAB3VFhERkYr59N253Hru3dw14wG6WvvuCi6z0hR2PmQHdjxwW2ob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RFXFNY9QegEry8ZRaPO9XC5XHQy9/O4Tzovqt5RicP7juFyFHZNtGeULJvFgt/+zrcdwbcYQBcF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exBf37uBodmaPolZCHg9LQ8LwXFw8nSk0wNQevv1R6XT4wYkj+GbzM3BTKCw6t6WxLIu6tlY0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\nhLh2TeFoTR4wUE9t2qinNm/Qp812hU5KSNDfDR2uBcU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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 361, "width": 487 } }, "output_type": "display_data" } ], "source": [ "km = KMeans(n_clusters = 3, random_state = 42)\n", "labels = km.fit_predict(coordinates)\n", "centers = km.cluster_centers_\n", "\n", "plt.scatter(coordinates[:, 0], coordinates[:, 1], s = 50, \n", " c = labels, cmap = 'viridis')\n", "plt.scatter(centers[:, 0], centers[:, 1], s = 200, alpha = 0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ouch. In its quest to minimize the within-cluster sum of squares, K-means algorithm will give more \"weight\" to larger clusters. As we can see from the plot, a lot of data points from the smaller cluster (of size 20) end up being far away from any centroid, while the larger cluster (of size 500) gets chopped in half. This is because K-means assumes **all clusters have equal, spherical variance**, meaning that each cluster has roughly equal number of observations and the cluster's will tend to form a sphere shape.\n", "\n", "Let's fit a different kind of clustering algorithm, Gaussian Mixture Model and visualize its clustering result:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n" ] }, { "data": { "image/png": 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WS5pvK2xq6JU4b05NltTqyhB/dw98tOIxrNqxxaaJs6+LK7495b4en00PDML0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krtFiZz1PN3fGwcgyMimZzYl8mJfRkcEen0oFkURY5eucyy3GP8+8ghiqur6e0jrZd3YXoWFquV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\nms6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6zqz0UCgUuHPmAS78czW3GRgDWDtaod3AFqjb2g2D5/XB+vHbtf5cA2Mxfmgzv8jZ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\nOepfaYi++tNUdgBA/sWIMwDkU9nZ2dq7bb9OHj2luPg4JVco6db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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 361, "width": 487 } }, "output_type": "display_data" } ], "source": [ "gmm = GaussianMixture(n_components = 3, random_state = 42)\n", "gmm.fit(coordinates)\n", "print(gmm.converged_)\n", "\n", "labels = gmm.predict(coordinates)\n", "centers = gmm.means_\n", "\n", "plt.scatter(coordinates[:, 0], coordinates[:, 1], s = 50, \n", " c = labels, cmap = 'viridis')\n", "plt.scatter(centers[:, 0], centers[:, 1], s = 200, alpha = 0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In general, there is no guarantee that structure found by a clustering algorithm has anything to do with what we were interested in. And there will always be edge cases where a clustering algorithm might lead to unintuitive results (for higher dimensions where we can't visualize the dataset easily, we might not even know whether the result matches our intuition or not). For visualization of comparing different clustering algorithms on toy 2d datasets, refer to the following link, [scikit-learn doc: Plot cluster comparison](http://scikit-learn.org/stable/auto_examples/cluster/plot_cluster_comparison.html).\n", "\n", "The take away message for this section is that: K-means is usually \"go-to\" clustering algorithm for many, because it is fast, easy to understand, and available in lots of statistical or machine learning toolkit. If we have an EXTREMELY LARGE dataset then K-means might be our only option. But we must also understand that it is still making some assumptions and sometimes these assumptions can lead to unsatisfying or misleading results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Reference\n", "\n", "- [Coursera: Washington Clustering & Retrieval](https://www.coursera.org/learn/ml-clustering-and-retrieval)\n", "- [Notebook: K-Means In-Depth](http://nbviewer.jupyter.org/github/jakevdp/sklearn_pycon2015/blob/master/notebooks/04.2-Clustering-KMeans.ipynb)\n", "- [Notebook: Unsupervised Learning Part 2 -- Clustering](http://nbviewer.jupyter.org/github/amueller/scipy-2016-sklearn/blob/master/notebooks/08%20Unsupervised%20Learning%20-%20Clustering.ipynb)\n", "- [Blog: K-means clustering is not a free lunch](http://varianceexplained.org/r/kmeans-free-lunch/)\n", "- [Blog: Improved Seeding For Clustering With K-Means++](https://datasciencelab.wordpress.com/2014/01/15/improved-seeding-for-clustering-with-k-means/)" ] } ], "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" }, "toc": { "nav_menu": { "height": "206px", "width": "252px" }, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": "block", "toc_window_display": true }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }