{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", "\n", "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >\n", "\n", "\"Open\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# In Depth: Gaussian Mixture Models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The *k*-means clustering model explored in the previous section is simple and relatively easy to understand, but its simplicity leads to practical challenges in its application.\n", "In particular, the non-probabilistic nature of *k*-means and its use of simple distance-from-cluster-center to assign cluster membership leads to poor performance for many real-world situations.\n", "In this section we will take a look at Gaussian mixture models (GMMs), which can be viewed as an extension of the ideas behind *k*-means, but can also be a powerful tool for estimation beyond simple clustering.\n", "\n", "We begin with the standard imports:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/anaconda3/lib/python3.7/site-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n", " import pandas.util.testing as tm\n" ] } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Motivating GMM: Weaknesses of k-Means\n", "\n", "Let's take a look at some of the weaknesses of *k*-means and think about how we might improve the cluster model.\n", "As we saw in the previous section, given simple, well-separated data, *k*-means finds suitable clustering results.\n", "\n", "For example, if we have simple blobs of data, the *k*-means algorithm can quickly label those clusters in a way that closely matches what we might do by eye:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/anaconda3/lib/python3.7/site-packages/sklearn/utils/deprecation.py:144: FutureWarning: The sklearn.datasets.samples_generator module is deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n", " warnings.warn(message, FutureWarning)\n" ] } ], "source": [ "# Generate some data\n", "from sklearn.datasets.samples_generator import make_blobs\n", "X, y_true = make_blobs(n_samples=400, centers=4,\n", " cluster_std=0.60, random_state=0)\n", "X = X[:, ::-1] # flip axes for better plotting" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the data with K Means Labels\n", "from sklearn.cluster import KMeans\n", "kmeans = KMeans(4, random_state=0)\n", "labels = kmeans.fit(X).predict(X)\n", "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From an intuitive standpoint, we might expect that the clustering assignment for some points is more certain than others: for example, there appears to be a very slight overlap between the two middle clusters, such that we might not have complete confidence in the cluster assigment of points between them.\n", "Unfortunately, the *k*-means model has no intrinsic measure of probability or uncertainty of cluster assignments (although it may be possible to use a bootstrap approach to estimate this uncertainty).\n", "For this, we must think about generalizing the model.\n", "\n", "One way to think about the *k*-means model is that it places a circle (or, in higher dimensions, a hyper-sphere) at the center of each cluster, with a radius defined by the most distant point in the cluster.\n", "This radius acts as a hard cutoff for cluster assignment within the training set: any point outside this circle is not considered a member of the cluster.\n", "We can visualize this cluster model with the following function:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from sklearn.cluster import KMeans\n", "from scipy.spatial.distance import cdist\n", "\n", "def plot_kmeans(kmeans, X, n_clusters=4, rseed=0, ax=None):\n", " labels = kmeans.fit_predict(X)\n", "\n", " # plot the input data\n", " ax = ax or plt.gca()\n", " ax.axis('equal')\n", " ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n", "\n", " # plot the representation of the KMeans model\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='#CCCCCC', lw=3, alpha=0.5, zorder=1))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "kmeans = KMeans(n_clusters=4, random_state=0)\n", "plot_kmeans(kmeans, X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An important observation for *k*-means is that these cluster models *must be circular*: *k*-means has no built-in way of accounting for oblong or elliptical clusters.\n", "So, for example, if we take the same data and transform it, the cluster assignments end up becoming muddled:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rng = np.random.RandomState(13)\n", "X_stretched = np.dot(X, rng.randn(2, 2))\n", "\n", "kmeans = KMeans(n_clusters=4, random_state=0)\n", "plot_kmeans(kmeans, X_stretched)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By eye, we recognize that these transformed clusters are non-circular, and thus circular clusters would be a poor fit.\n", "Nevertheless, *k*-means is not flexible enough to account for this, and tries to force-fit the data into four circular clusters.\n", "This results in a mixing of cluster assignments where the resulting circles overlap: see especially the bottom-right of this plot.\n", "One might imagine addressing this particular situation by preprocessing the data with PCA (see [In Depth: Principal Component Analysis](05.09-Principal-Component-Analysis.ipynb)), but in practice there is no guarantee that such a global operation will circularize the individual data.\n", "\n", "These two disadvantages of *k*-means—its lack of flexibility in cluster shape and lack of probabilistic cluster assignment—mean that for many datasets (especially low-dimensional datasets) it may not perform as well as you might hope.\n", "\n", "You might imagine addressing these weaknesses by generalizing the *k*-means model: for example, you could measure uncertainty in cluster assignment by comparing the distances of each point to *all* cluster centers, rather than focusing on just the closest.\n", "You might also imagine allowing the cluster boundaries to be ellipses rather than circles, so as to account for non-circular clusters.\n", "It turns out these are two essential components of a different type of clustering model, Gaussian mixture models." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generalizing E–M: Gaussian Mixture Models\n", "\n", "A Gaussian mixture model (GMM) attempts to find a mixture of multi-dimensional Gaussian probability distributions that best model any input dataset.\n", "In the simplest case, GMMs can be used for finding clusters in the same manner as *k*-means:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.mixture import GaussianMixture\n", "gmm = GaussianMixture(n_components=4).fit(X)\n", "labels = gmm.predict(X)\n", "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But because GMM contains a probabilistic model under the hood, it is also possible to find probabilistic cluster assignments—in Scikit-Learn this is done using the ``predict_proba`` method.\n", "This returns a matrix of size ``[n_samples, n_clusters]`` which measures the probability that any point belongs to the given cluster:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0. 0.469 0. 0.531]\n", " [1. 0. 0. 0. ]\n", " [1. 0. 0. 0. ]\n", " [0. 0. 0. 1. ]\n", " [1. 0. 0. 0. ]]\n" ] } ], "source": [ "probs = gmm.predict_proba(X)\n", "print(probs[:5].round(3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can visualize this uncertainty by, for example, making the size of each point proportional to the certainty of its prediction; looking at the following figure, we can see that it is precisely the points at the boundaries between clusters that reflect this uncertainty of cluster assignment:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "size = 50 * probs.max(1) ** 2 # square emphasizes differences\n", "plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis', s=size);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Under the hood, a Gaussian mixture model is very similar to *k*-means: it uses an expectation–maximization approach which qualitatively does the following:\n", "\n", "1. Choose starting guesses for the location and shape\n", "\n", "2. Repeat until converged:\n", "\n", " 1. *E-step*: for each point, find weights encoding the probability of membership in each cluster\n", " 2. *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.\n", "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", "Let's create a function that will help us visualize the locations and shapes of the GMM clusters by drawing ellipses based on the GMM output:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "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", " \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,\n", " 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": "markdown", "metadata": {}, "source": [ "With this in place, we can take a look at what the four-component GMM gives us for our initial data:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[[ 0.36530305, 0.01293533],\n", " [ 0.01293533, 0.28921965]],\n", "\n", " [[ 0.40398685, -0.00235346],\n", " [-0.00235346, 0.36933794]],\n", "\n", " [[ 0.38465995, 0.02716798],\n", " [ 0.02716798, 0.37394003]],\n", "\n", " [[ 0.29768676, -0.02444193],\n", " [-0.02444193, 0.34173529]]])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gmm.covariances_" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gmm = GaussianMixture(n_components=4, random_state=42)\n", "plot_gmm(gmm, X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, we can use the GMM approach to fit our stretched dataset; allowing for a full covariance the model will fit even very oblong, stretched-out clusters:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gmm = GaussianMixture(n_components=4, covariance_type='full', random_state=42)\n", "plot_gmm(gmm, X_stretched)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This makes clear that GMM addresses the two main practical issues with *k*-means encountered before." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Choosing the covariance type\n", "\n", "If you look at the details of the preceding fits, you will see that the ``covariance_type`` option was set differently within each.\n", "This hyperparameter controls the degrees of freedom in the shape of each cluster; it is essential to set this carefully for any given problem.\n", "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.\n", "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.\n", "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", "We can see a visual representation of these three choices for a single cluster within the following figure:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![(Covariance Type)](05.12-covariance-type.png)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GMM as *Density Estimation*\n", "\n", "Though GMM is often categorized as a clustering algorithm, fundamentally it is an algorithm for *density estimation*.\n", "That is to say, the result of a GMM fit to some data is technically not a clustering model, but a generative probabilistic model describing the distribution of the data.\n", "\n", "As an example, consider some data generated from Scikit-Learn's ``make_moons`` function, which we saw in [In Depth: K-Means Clustering](05.11-K-Means.ipynb):" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_moons\n", "Xmoon, ymoon = make_moons(200, noise=.05, random_state=0)\n", "plt.scatter(Xmoon[:, 0], Xmoon[:, 1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we try to fit this with a two-component GMM viewed as a clustering model, the results are not particularly useful:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gmm2 = GaussianMixture(n_components=2, covariance_type='full', random_state=0)\n", "plot_gmm(gmm2, Xmoon)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But if we instead use many more components and ignore the cluster labels, we find a fit that is much closer to the input data:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gmm16 = GaussianMixture(n_components=16, covariance_type='full', random_state=0)\n", "plot_gmm(gmm16, Xmoon, label=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the mixture of 16 Gaussians serves not to find separated clusters of data, but rather to model the overall *distribution* of the input data.\n", "This is a generative model of the distribution, meaning that the GMM gives us the recipe to generate new random data distributed similarly to our input.\n", "For example, here are 400 new points drawn from this 16-component GMM fit to our original data:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Xnew = gmm16.sample(400)\n", "plt.scatter(Xnew[0][:, 0], Xnew[0][:, 1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "GMM is convenient as a flexible means of modeling an arbitrary multi-dimensional distribution of data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How many components?\n", "\n", "The fact that GMM is a generative model gives us a natural means of determining the optimal number of components for a given dataset.\n", "A generative model is inherently a probability distribution for the dataset, and so we can simply evaluate the *likelihood* of the data under the model, using cross-validation to avoid over-fitting.\n", "Another means of correcting for over-fitting is to adjust the model likelihoods using some analytic criterion such as the [Akaike information criterion (AIC)](https://en.wikipedia.org/wiki/Akaike_information_criterion) or the [Bayesian information criterion (BIC)](https://en.wikipedia.org/wiki/Bayesian_information_criterion).\n", "Scikit-Learn's ``GMM`` estimator actually includes built-in methods that compute both of these, and so it is very easy to operate on this approach.\n", "\n", "Let's look at the AIC and BIC as a function as the number of GMM components for our moon dataset:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_components = np.arange(1, 21)\n", "models = [GaussianMixture(n, covariance_type='full', random_state=0).fit(Xmoon)\n", " for n in n_components]\n", "\n", "plt.plot(n_components, [m.bic(Xmoon) for m in models], label='BIC')\n", "plt.plot(n_components, [m.aic(Xmoon) for m in models], label='AIC')\n", "plt.legend(loc='best')\n", "plt.xlabel('n_components');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimal number of clusters is the value that minimizes the AIC or BIC, depending on which approximation we wish to use. The AIC tells us that our choice of 16 components above was probably too many: around 8-12 components would have been a better choice.\n", "As is typical with this sort of problem, the BIC recommends a simpler model.\n", "\n", "Notice the important point: this choice of number of components measures how well GMM works *as a density estimator*, not how well it works *as a clustering algorithm*.\n", "I'd encourage you to think of GMM primarily as a density estimator, and use it for clustering only when warranted within simple datasets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: GMM for Generating New Data\n", "\n", "We just saw a simple example of using GMM as a generative model of data in order to create new samples from the distribution defined by the input data.\n", "Here we will run with this idea and generate *new handwritten digits* from the standard digits corpus that we have used before.\n", "\n", "To start with, let's load the digits data using Scikit-Learn's data tools:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1797, 64)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.datasets import load_digits\n", "digits = load_digits()\n", "digits.data.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next let's plot the first 100 of these to recall exactly what we're looking at:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_digits(data):\n", " fig, ax = plt.subplots(10, 10, figsize=(8, 8),\n", " subplot_kw=dict(xticks=[], yticks=[]))\n", " fig.subplots_adjust(hspace=0.05, wspace=0.05)\n", " for i, axi in enumerate(ax.flat):\n", " im = axi.imshow(data[i].reshape(8, 8), cmap='binary')\n", " im.set_clim(0, 16)\n", "plot_digits(digits.data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have nearly 1,800 digits in 64 dimensions, and we can build a GMM on top of these to generate more.\n", "GMMs can have difficulty converging in such a high dimensional space, so we will start with an invertible dimensionality reduction algorithm on the data.\n", "Here we will use a straightforward PCA, asking it to preserve 99% of the variance in the projected data:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1797, 41)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.decomposition import PCA\n", "pca = PCA(0.99, whiten=True)\n", "data = pca.fit_transform(digits.data)\n", "data.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is 41 dimensions, a reduction of nearly 1/3 with almost no information loss.\n", "Given this projected data, let's use the AIC to get a gauge for the number of GMM components we should use:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_components = np.arange(50, 210, 10)\n", "models = [GaussianMixture(n, covariance_type='full', random_state=0)\n", " for n in n_components]\n", "aics = [model.fit(data).aic(data) for model in models]\n", "plt.plot(n_components, aics);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It appears that around 110 components minimizes the AIC; we will use this model.\n", "Let's quickly fit this to the data and confirm that it has converged:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n" ] } ], "source": [ "gmm = GaussianMixture(110, covariance_type='full', random_state=0)\n", "gmm.fit(data)\n", "print(gmm.converged_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can draw samples of 100 new points within this 41-dimensional projected space, using the GMM as a generative model:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(100, 41)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data_new = gmm.sample(100)\n", "data_new[0].shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can use the inverse transform of the PCA object to construct the new digits:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "digits_new = pca.inverse_transform(data_new[0])\n", "plot_digits(digits_new)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results for the most part look like plausible digits from the dataset!\n", "\n", "Consider what we've done here: given a sampling of handwritten digits, we have modeled the distribution of that data in such a way that we can generate brand new samples of digits from the data: these are \"handwritten digits\" which do not individually appear in the original dataset, but rather capture the general features of the input data as modeled by the mixture model.\n", "Such a generative model of digits can prove very useful as a component of a Bayesian generative classifier, as we shall see in the next section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [In Depth: k-Means Clustering](05.11-K-Means.ipynb) | [Contents](Index.ipynb) | [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb) >\n", "\n", "\"Open\n" ] } ], "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }