.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/cluster/plot_kmeans_stability_low_dim_dense.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 Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_cluster_plot_kmeans_stability_low_dim_dense.py: ============================================================ Empirical evaluation of the impact of k-means initialization ============================================================ Evaluate the ability of k-means initializations strategies to make the algorithm convergence robust, as measured by the relative standard deviation of the inertia of the clustering (i.e. the sum of squared distances to the nearest cluster center). The first plot shows the best inertia reached for each combination of the model (``KMeans`` or ``MiniBatchKMeans``), and the init method (``init="random"`` or ``init="k-means++"``) for increasing values of the ``n_init`` parameter that controls the number of initializations. The second plot demonstrates one single run of the ``MiniBatchKMeans`` estimator using a ``init="random"`` and ``n_init=1``. This run leads to a bad convergence (local optimum), with estimated centers stuck between ground truth clusters. The dataset used for evaluation is a 2D grid of isotropic Gaussian clusters widely spaced. .. GENERATED FROM PYTHON SOURCE LINES 25-133 .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_stability_low_dim_dense_001.png :alt: Mean inertia for various k-means init across 5 runs :srcset: /auto_examples/cluster/images/sphx_glr_plot_kmeans_stability_low_dim_dense_001.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_stability_low_dim_dense_002.png :alt: Example cluster allocation with a single random init with MiniBatchKMeans :srcset: /auto_examples/cluster/images/sphx_glr_plot_kmeans_stability_low_dim_dense_002.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none Evaluation of KMeans with k-means++ init Evaluation of KMeans with random init Evaluation of MiniBatchKMeans with k-means++ init Evaluation of MiniBatchKMeans with random init | .. code-block:: Python # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import matplotlib.cm as cm import matplotlib.pyplot as plt import numpy as np from sklearn.cluster import KMeans, MiniBatchKMeans from sklearn.utils import check_random_state, shuffle random_state = np.random.RandomState(0) # Number of run (with randomly generated dataset) for each strategy so as # to be able to compute an estimate of the standard deviation n_runs = 5 # k-means models can do several random inits so as to be able to trade # CPU time for convergence robustness n_init_range = np.array([1, 5, 10, 15, 20]) # Datasets generation parameters n_samples_per_center = 100 grid_size = 3 scale = 0.1 n_clusters = grid_size**2 def make_data(random_state, n_samples_per_center, grid_size, scale): random_state = check_random_state(random_state) centers = np.array([[i, j] for i in range(grid_size) for j in range(grid_size)]) n_clusters_true, n_features = centers.shape noise = random_state.normal( scale=scale, size=(n_samples_per_center, centers.shape[1]) ) X = np.concatenate([c + noise for c in centers]) y = np.concatenate([[i] * n_samples_per_center for i in range(n_clusters_true)]) return shuffle(X, y, random_state=random_state) # Part 1: Quantitative evaluation of various init methods plt.figure() plots = [] legends = [] cases = [ (KMeans, "k-means++", {}, "^-"), (KMeans, "random", {}, "o-"), (MiniBatchKMeans, "k-means++", {"max_no_improvement": 3}, "x-"), (MiniBatchKMeans, "random", {"max_no_improvement": 3, "init_size": 500}, "d-"), ] for factory, init, params, format in cases: print("Evaluation of %s with %s init" % (factory.__name__, init)) inertia = np.empty((len(n_init_range), n_runs)) for run_id in range(n_runs): X, y = make_data(run_id, n_samples_per_center, grid_size, scale) for i, n_init in enumerate(n_init_range): km = factory( n_clusters=n_clusters, init=init, random_state=run_id, n_init=n_init, **params, ).fit(X) inertia[i, run_id] = km.inertia_ p = plt.errorbar( n_init_range, inertia.mean(axis=1), inertia.std(axis=1), fmt=format ) plots.append(p[0]) legends.append("%s with %s init" % (factory.__name__, init)) plt.xlabel("n_init") plt.ylabel("inertia") plt.legend(plots, legends) plt.title("Mean inertia for various k-means init across %d runs" % n_runs) # Part 2: Qualitative visual inspection of the convergence X, y = make_data(random_state, n_samples_per_center, grid_size, scale) km = MiniBatchKMeans( n_clusters=n_clusters, init="random", n_init=1, random_state=random_state ).fit(X) plt.figure() for k in range(n_clusters): my_members = km.labels_ == k color = cm.nipy_spectral(float(k) / n_clusters, 1) plt.plot(X[my_members, 0], X[my_members, 1], ".", c=color) cluster_center = km.cluster_centers_[k] plt.plot( cluster_center[0], cluster_center[1], "o", markerfacecolor=color, markeredgecolor="k", markersize=6, ) plt.title( "Example cluster allocation with a single random init\nwith MiniBatchKMeans" ) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.112 seconds) .. _sphx_glr_download_auto_examples_cluster_plot_kmeans_stability_low_dim_dense.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/cluster/plot_kmeans_stability_low_dim_dense.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_kmeans_stability_low_dim_dense.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_kmeans_stability_low_dim_dense.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_kmeans_stability_low_dim_dense.zip ` .. include:: plot_kmeans_stability_low_dim_dense.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_