Pushing the docs for revision for branch: master, commit a4f632f02f0e66bf3533e5df64e936d87f6e57ee

Author: sklearn-ci

dev/_downloads/plot_bayesian_gaussian_mixture.ipynb

@@ -0,0 +1,54 @@
+{
+  "nbformat_minor": 0, 
+  "nbformat": 4, 
+  "cells": [
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "%matplotlib inline"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }, 
+    {
+      "source": [
+        "\n# Bayesian Gaussian Mixture Concentration Prior Analysis\n\n\nPlot the resulting ellipsoids of a mixture of three Gaussians with\nvariational Bayesian Gaussian Mixture for three different values on the\nprior the dirichlet concentration.\n\nFor all models, the Variationnal Bayesian Gaussian Mixture adapts its number of\nmixture automatically. The parameter `dirichlet_concentration_prior` has a\ndirect link with the resulting number of components. Specifying a high value of\n`dirichlet_concentration_prior` leads more often to uniformly-sized mixture\ncomponents, while specifying small (under 0.1) values will lead to some mixture\ncomponents getting almost all the points while most mixture components will be\ncentered on just a few of the remaining points.\n"
+      ], 
+      "cell_type": "markdown", 
+      "metadata": {}
+    }, 
+    {
+      "execution_count": null, 
+      "cell_type": "code", 
+      "source": [
+        "# Author: Thierry Guillemot <[email protected]>\n# License: BSD 3 clause\n\nimport numpy as np\nimport matplotlib as mpl\nimport matplotlib.pyplot as plt\nimport matplotlib.gridspec as gridspec\n\nfrom sklearn.mixture import BayesianGaussianMixture\n\nprint(__doc__)\n\n\ndef plot_ellipses(ax, weights, means, covars):\n    for n in range(means.shape[0]):\n        v, w = np.linalg.eigh(covars[n][:2, :2])\n        u = w[0] / np.linalg.norm(w[0])\n        angle = np.arctan2(u[1], u[0])\n        angle = 180 * angle / np.pi  # convert to degrees\n        v = 2 * np.sqrt(2) * np.sqrt(v)\n        ell = mpl.patches.Ellipse(means[n, :2], v[0], v[1], 180 + angle)\n        ell.set_clip_box(ax.bbox)\n        ell.set_alpha(weights[n])\n        ax.add_artist(ell)\n\n\ndef plot_results(ax1, ax2, estimator, dirichlet_concentration_prior, X, y, plot_title=False):\n    estimator.dirichlet_concentration_prior = dirichlet_concentration_prior\n    estimator.fit(X)\n    ax1.set_title(\"Bayesian Gaussian Mixture for \"\n                  r\"$dc_0=%.1e$\" % dirichlet_concentration_prior)\n    # ax1.axis('equal')\n    ax1.scatter(X[:, 0], X[:, 1], s=5, marker='o', color=colors[y], alpha=0.8)\n    ax1.set_xlim(-2., 2.)\n    ax1.set_ylim(-3., 3.)\n    ax1.set_xticks(())\n    ax1.set_yticks(())\n    plot_ellipses(ax1, estimator.weights_, estimator.means_,\n                  estimator.covariances_)\n\n    ax2.get_xaxis().set_tick_params(direction='out')\n    ax2.yaxis.grid(True, alpha=0.7)\n    for k, w in enumerate(estimator.weights_):\n        ax2.bar(k - .45, w, width=0.9, color='royalblue', zorder=3)\n        ax2.text(k, w + 0.007, \"%.1f%%\" % (w * 100.),\n                 horizontalalignment='center')\n    ax2.set_xlim(-.6, 2 * n_components - .4)\n    ax2.set_ylim(0., 1.1)\n    ax2.tick_params(axis='y', which='both', left='off',\n                    right='off', labelleft='off')\n    ax2.tick_params(axis='x', which='both', top='off')\n\n    if plot_title:\n        ax1.set_ylabel('Estimated Mixtures')\n        ax2.set_ylabel('Weight of each component')\n\n# Parameters\nrandom_state = 2\nn_components, n_features = 3, 2\ncolors = np.array(['mediumseagreen', 'royalblue', 'r', 'gold',\n                   'orchid', 'indigo', 'darkcyan', 'tomato'])\ndirichlet_concentration_prior = np.logspace(-3, 3, 3)\ncovars = np.array([[[.7, .0], [.0, .1]],\n                   [[.5, .0], [.0, .1]],\n                   [[.5, .0], [.0, .1]]])\nsamples = np.array([200, 500, 200])\nmeans = np.array([[.0, -.70],\n                  [.0, .0],\n                  [.0, .70]])\n\n\n# Here we put beta_prior to 0.8 to minimize the influence of the prior for this\n# dataset\nestimator = BayesianGaussianMixture(n_components=2 * n_components,\n                                    init_params='random', max_iter=1500,\n                                    mean_precision_prior=.8, tol=1e-9,\n                                    random_state=random_state)\n\n# Generate data\nrng = np.random.RandomState(random_state)\nX = np.vstack([\n    rng.multivariate_normal(means[j], covars[j], samples[j])\n    for j in range(n_components)])\ny = np.concatenate([j * np.ones(samples[j], dtype=int)\n                    for j in range(n_components)])\n\n# Plot Results\nplt.figure(figsize=(4.7 * 3, 8))\nplt.subplots_adjust(bottom=.04, top=0.95, hspace=.05, wspace=.05,\n                    left=.03, right=.97)\n\ngs = gridspec.GridSpec(3, len(dirichlet_concentration_prior))\nfor k, dc in enumerate(dirichlet_concentration_prior):\n    plot_results(plt.subplot(gs[0:2, k]), plt.subplot(gs[2, k]),\n                 estimator, dc, X, y, plot_title=k == 0)\n\nplt.show()"
+      ], 
+      "outputs": [], 
+      "metadata": {
+        "collapsed": false
+      }
+    }
+  ], 
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 2", 
+      "name": "python2", 
+      "language": "python"
+    }, 
+    "language_info": {
+      "mimetype": "text/x-python", 
+      "nbconvert_exporter": "python", 
+      "name": "python", 
+      "file_extension": ".py", 
+      "version": "2.7.12", 
+      "pygments_lexer": "ipython2", 
+      "codemirror_mode": {
+        "version": 2, 
+        "name": "ipython"
+      }
+    }
+  }
+}

dev/_downloads/plot_bayesian_gaussian_mixture.py

@@ -0,0 +1,114 @@
+"""
+======================================================
+Bayesian Gaussian Mixture Concentration Prior Analysis
+======================================================
+
+Plot the resulting ellipsoids of a mixture of three Gaussians with
+variational Bayesian Gaussian Mixture for three different values on the
+prior the dirichlet concentration.
+
+For all models, the Variationnal Bayesian Gaussian Mixture adapts its number of
+mixture automatically. The parameter `dirichlet_concentration_prior` has a
+direct link with the resulting number of components. Specifying a high value of
+`dirichlet_concentration_prior` leads more often to uniformly-sized mixture
+components, while specifying small (under 0.1) values will lead to some mixture
+components getting almost all the points while most mixture components will be
+centered on just a few of the remaining points.
+"""
+# Author: Thierry Guillemot <[email protected]>
+# License: BSD 3 clause
+
+import numpy as np
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+import matplotlib.gridspec as gridspec
+
+from sklearn.mixture import BayesianGaussianMixture
+
+print(__doc__)
+
+
+def plot_ellipses(ax, weights, means, covars):
+    for n in range(means.shape[0]):
+        v, w = np.linalg.eigh(covars[n][:2, :2])
+        u = w[0] / np.linalg.norm(w[0])
+        angle = np.arctan2(u[1], u[0])
+        angle = 180 * angle / np.pi  # convert to degrees
+        v = 2 * np.sqrt(2) * np.sqrt(v)
+        ell = mpl.patches.Ellipse(means[n, :2], v[0], v[1], 180 + angle)
+        ell.set_clip_box(ax.bbox)
+        ell.set_alpha(weights[n])
+        ax.add_artist(ell)
+
+
+def plot_results(ax1, ax2, estimator, dirichlet_concentration_prior, X, y, plot_title=False):
+    estimator.dirichlet_concentration_prior = dirichlet_concentration_prior
+    estimator.fit(X)
+    ax1.set_title("Bayesian Gaussian Mixture for "
+                  r"$dc_0=%.1e$" % dirichlet_concentration_prior)
+    # ax1.axis('equal')
+    ax1.scatter(X[:, 0], X[:, 1], s=5, marker='o', color=colors[y], alpha=0.8)
+    ax1.set_xlim(-2., 2.)
+    ax1.set_ylim(-3., 3.)
+    ax1.set_xticks(())
+    ax1.set_yticks(())
+    plot_ellipses(ax1, estimator.weights_, estimator.means_,
+                  estimator.covariances_)
+
+    ax2.get_xaxis().set_tick_params(direction='out')
+    ax2.yaxis.grid(True, alpha=0.7)
+    for k, w in enumerate(estimator.weights_):
+        ax2.bar(k - .45, w, width=0.9, color='royalblue', zorder=3)
+        ax2.text(k, w + 0.007, "%.1f%%" % (w * 100.),
+                 horizontalalignment='center')
+    ax2.set_xlim(-.6, 2 * n_components - .4)
+    ax2.set_ylim(0., 1.1)
+    ax2.tick_params(axis='y', which='both', left='off',
+                    right='off', labelleft='off')
+    ax2.tick_params(axis='x', which='both', top='off')
+
+    if plot_title:
+        ax1.set_ylabel('Estimated Mixtures')
+        ax2.set_ylabel('Weight of each component')
+
+# Parameters
+random_state = 2
+n_components, n_features = 3, 2
+colors = np.array(['mediumseagreen', 'royalblue', 'r', 'gold',
+                   'orchid', 'indigo', 'darkcyan', 'tomato'])
+dirichlet_concentration_prior = np.logspace(-3, 3, 3)
+covars = np.array([[[.7, .0], [.0, .1]],
+                   [[.5, .0], [.0, .1]],
+                   [[.5, .0], [.0, .1]]])
+samples = np.array([200, 500, 200])
+means = np.array([[.0, -.70],
+                  [.0, .0],
+                  [.0, .70]])
+
+
+# Here we put beta_prior to 0.8 to minimize the influence of the prior for this
+# dataset
+estimator = BayesianGaussianMixture(n_components=2 * n_components,
+                                    init_params='random', max_iter=1500,
+                                    mean_precision_prior=.8, tol=1e-9,
+                                    random_state=random_state)
+
+# Generate data
+rng = np.random.RandomState(random_state)
+X = np.vstack([
+    rng.multivariate_normal(means[j], covars[j], samples[j])
+    for j in range(n_components)])
+y = np.concatenate([j * np.ones(samples[j], dtype=int)
+                    for j in range(n_components)])
+
+# Plot Results
+plt.figure(figsize=(4.7 * 3, 8))
+plt.subplots_adjust(bottom=.04, top=0.95, hspace=.05, wspace=.05,
+                    left=.03, right=.97)
+
+gs = gridspec.GridSpec(3, len(dirichlet_concentration_prior))
+for k, dc in enumerate(dirichlet_concentration_prior):
+    plot_results(plt.subplot(gs[0:2, k]), plt.subplot(gs[2, k]),
+                 estimator, dc, X, y, plot_title=k == 0)
+
+plt.show()