.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/mixture/plot_gmm_init.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code or to run this example in your browser via JupyterLite or Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_mixture_plot_gmm_init.py: ========================== GMM Initialization Methods ========================== Examples of the different methods of initialization in Gaussian Mixture Models See :ref:`gmm` for more information on the estimator. Here we generate some sample data with four easy to identify clusters. The purpose of this example is to show the four different methods for the initialization parameter *init_param*. The four initializations are *kmeans* (default), *random*, *random_from_data* and *k-means++*. Orange diamonds represent the initialization centers for the gmm generated by the *init_param*. The rest of the data is represented as crosses and the colouring represents the eventual associated classification after the GMM has finished. The numbers in the top right of each subplot represent the number of iterations taken for the GaussianMixture to converge and the relative time taken for the initialization part of the algorithm to run. The shorter initialization times tend to have a greater number of iterations to converge. The initialization time is the ratio of the time taken for that method versus the time taken for the default *kmeans* method. As you can see all three alternative methods take less time to initialize when compared to *kmeans*. In this example, when initialized with *random_from_data* or *random* the model takes more iterations to converge. Here *k-means++* does a good job of both low time to initialize and low number of GaussianMixture iterations to converge. .. GENERATED FROM PYTHON SOURCE LINES 35-111 .. image-sg:: /auto_examples/mixture/images/sphx_glr_plot_gmm_init_001.png :alt: GMM iterations and relative time taken to initialize, kmeans, Iter 8 | Init Time 1.00x, random_from_data, Iter 137 | Init Time 0.54x, k-means++, Iter 11 | Init Time 0.89x, random, Iter 47 | Init Time 0.55x :srcset: /auto_examples/mixture/images/sphx_glr_plot_gmm_init_001.png :class: sphx-glr-single-img .. code-block:: Python # Author: Gordon Walsh # Data generation code from Jake Vanderplas from timeit import default_timer as timer import matplotlib.pyplot as plt import numpy as np from sklearn.datasets._samples_generator import make_blobs from sklearn.mixture import GaussianMixture from sklearn.utils.extmath import row_norms print(__doc__) # Generate some data X, y_true = make_blobs(n_samples=4000, centers=4, cluster_std=0.60, random_state=0) X = X[:, ::-1] n_samples = 4000 n_components = 4 x_squared_norms = row_norms(X, squared=True) def get_initial_means(X, init_params, r): # Run a GaussianMixture with max_iter=0 to output the initialization means gmm = GaussianMixture( n_components=4, init_params=init_params, tol=1e-9, max_iter=0, random_state=r ).fit(X) return gmm.means_ methods = ["kmeans", "random_from_data", "k-means++", "random"] colors = ["navy", "turquoise", "cornflowerblue", "darkorange"] times_init = {} relative_times = {} plt.figure(figsize=(4 * len(methods) // 2, 6)) plt.subplots_adjust( bottom=0.1, top=0.9, hspace=0.15, wspace=0.05, left=0.05, right=0.95 ) for n, method in enumerate(methods): r = np.random.RandomState(seed=1234) plt.subplot(2, len(methods) // 2, n + 1) start = timer() ini = get_initial_means(X, method, r) end = timer() init_time = end - start gmm = GaussianMixture( n_components=4, means_init=ini, tol=1e-9, max_iter=2000, random_state=r ).fit(X) times_init[method] = init_time for i, color in enumerate(colors): data = X[gmm.predict(X) == i] plt.scatter(data[:, 0], data[:, 1], color=color, marker="x") plt.scatter( ini[:, 0], ini[:, 1], s=75, marker="D", c="orange", lw=1.5, edgecolors="black" ) relative_times[method] = times_init[method] / times_init[methods[0]] plt.xticks(()) plt.yticks(()) plt.title(method, loc="left", fontsize=12) plt.title( "Iter %i | Init Time %.2fx" % (gmm.n_iter_, relative_times[method]), loc="right", fontsize=10, ) plt.suptitle("GMM iterations and relative time taken to initialize") plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.677 seconds) .. _sphx_glr_download_auto_examples_mixture_plot_gmm_init.py: .. only:: html .. container:: sphx-glr-footer 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_gmm_init.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/?path=auto_examples/mixture/plot_gmm_init.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_gmm_init.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_gmm_init.py ` .. include:: plot_gmm_init.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_