.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/mixture/plot_concentration_prior.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:here  to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_mixture_plot_concentration_prior.py: ======================================================================== Concentration Prior Type Analysis of Variation Bayesian Gaussian Mixture ======================================================================== This example plots the ellipsoids obtained from a toy dataset (mixture of three Gaussians) fitted by the BayesianGaussianMixture class models with a Dirichlet distribution prior (weight_concentration_prior_type='dirichlet_distribution') and a Dirichlet process prior (weight_concentration_prior_type='dirichlet_process'). On each figure, we plot the results for three different values of the weight concentration prior. The BayesianGaussianMixture class can adapt its number of mixture components automatically. The parameter weight_concentration_prior has a direct link with the resulting number of components with non-zero weights. Specifying a low value for the concentration prior will make the model put most of the weight on few components set the remaining components weights very close to zero. High values of the concentration prior will allow a larger number of components to be active in the mixture. The Dirichlet process prior allows to define an infinite number of components and automatically selects the correct number of components: it activates a component only if it is necessary. On the contrary the classical finite mixture model with a Dirichlet distribution prior will favor more uniformly weighted components and therefore tends to divide natural clusters into unnecessary sub-components. .. GENERATED FROM PYTHON SOURCE LINES 31-165 .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/mixture/images/sphx_glr_plot_concentration_prior_001.png :alt: Finite mixture with a Dirichlet distribution prior and $\gamma_0=$$1.0e-03, Finite mixture with a Dirichlet distribution prior and \gamma_0=$$1.0e+00$, Finite mixture with a Dirichlet distribution prior and $\gamma_0=$$1.0e+03 :srcset: /auto_examples/mixture/images/sphx_glr_plot_concentration_prior_001.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/mixture/images/sphx_glr_plot_concentration_prior_002.png :alt: Infinite mixture with a Dirichlet process prior and\gamma_0=$$1.0e+00$, Infinite mixture with a Dirichlet process prior and$\gamma_0=$$1.0e+03, Infinite mixture with a Dirichlet process prior and\gamma_0=$$1.0e+05$ :srcset: /auto_examples/mixture/images/sphx_glr_plot_concentration_prior_002.png :class: sphx-glr-multi-img .. code-block:: default # Author: Thierry Guillemot # 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 def plot_ellipses(ax, weights, means, covars): for n in range(means.shape[0]): eig_vals, eig_vecs = np.linalg.eigh(covars[n]) unit_eig_vec = eig_vecs[0] / np.linalg.norm(eig_vecs[0]) angle = np.arctan2(unit_eig_vec[1], unit_eig_vec[0]) # Ellipse needs degrees angle = 180 * angle / np.pi # eigenvector normalization eig_vals = 2 * np.sqrt(2) * np.sqrt(eig_vals) ell = mpl.patches.Ellipse( means[n], eig_vals[0], eig_vals[1], 180 + angle, edgecolor="black" ) ell.set_clip_box(ax.bbox) ell.set_alpha(weights[n]) ell.set_facecolor("#56B4E9") ax.add_artist(ell) def plot_results(ax1, ax2, estimator, X, y, title, plot_title=False): ax1.set_title(title) ax1.scatter(X[:, 0], X[:, 1], s=5, marker="o", color=colors[y], alpha=0.8) ax1.set_xlim(-2.0, 2.0) ax1.set_ylim(-3.0, 3.0) 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, w, width=0.9, color="#56B4E9", zorder=3, align="center", edgecolor="black", ) ax2.text(k, w + 0.007, "%.1f%%" % (w * 100.0), horizontalalignment="center") ax2.set_xlim(-0.6, 2 * n_components - 0.4) ax2.set_ylim(0.0, 1.1) ax2.tick_params(axis="y", which="both", left=False, right=False, labelleft=False) ax2.tick_params(axis="x", which="both", top=False) if plot_title: ax1.set_ylabel("Estimated Mixtures") ax2.set_ylabel("Weight of each component") # Parameters of the dataset random_state, n_components, n_features = 2, 3, 2 colors = np.array(["#0072B2", "#F0E442", "#D55E00"]) covars = np.array( [[[0.7, 0.0], [0.0, 0.1]], [[0.5, 0.0], [0.0, 0.1]], [[0.5, 0.0], [0.0, 0.1]]] ) samples = np.array([200, 500, 200]) means = np.array([[0.0, -0.70], [0.0, 0.0], [0.0, 0.70]]) # mean_precision_prior= 0.8 to minimize the influence of the prior estimators = [ ( "Finite mixture with a Dirichlet distribution\nprior and " r"$\gamma_0=$", BayesianGaussianMixture( weight_concentration_prior_type="dirichlet_distribution", n_components=2 * n_components, reg_covar=0, init_params="random", max_iter=1500, mean_precision_prior=0.8, random_state=random_state, ), [0.001, 1, 1000], ), ( "Infinite mixture with a Dirichlet process\n prior and" r"$\gamma_0=$", BayesianGaussianMixture( weight_concentration_prior_type="dirichlet_process", n_components=2 * n_components, reg_covar=0, init_params="random", max_iter=1500, mean_precision_prior=0.8, random_state=random_state, ), [1, 1000, 100000], ), ] # 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([np.full(samples[j], j, dtype=int) for j in range(n_components)]) # Plot results in two different figures for title, estimator, concentrations_prior in estimators: plt.figure(figsize=(4.7 * 3, 8)) plt.subplots_adjust( bottom=0.04, top=0.90, hspace=0.05, wspace=0.05, left=0.03, right=0.99 ) gs = gridspec.GridSpec(3, len(concentrations_prior)) for k, concentration in enumerate(concentrations_prior): estimator.weight_concentration_prior = concentration estimator.fit(X) plot_results( plt.subplot(gs[0:2, k]), plt.subplot(gs[2, k]), estimator, X, y, r"%s$%.1e$" % (title, concentration), plot_title=k == 0, ) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 9.450 seconds) .. _sphx_glr_download_auto_examples_mixture_plot_concentration_prior.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/mixture/plot_concentration_prior.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:Download Python source code: plot_concentration_prior.py  .. container:: sphx-glr-download sphx-glr-download-jupyter :download:Download Jupyter notebook: plot_concentration_prior.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery _