.. _sphx_glr_auto_examples_cluster_plot_kmeans_assumptions.py:


====================================
Demonstration of k-means assumptions
====================================

This example is meant to illustrate situations where k-means will produce
unintuitive and possibly unexpected clusters. In the first three plots, the
input data does not conform to some implicit assumption that k-means makes and
undesirable clusters are produced as a result. In the last plot, k-means
returns intuitive clusters despite unevenly sized blobs.



.. image:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_assumptions_001.png
    :align: center





.. code-block:: python

    print(__doc__)

    # Author: Phil Roth <mr.phil.roth@gmail.com>
    # License: BSD 3 clause

    import numpy as np
    import matplotlib.pyplot as plt

    from sklearn.cluster import KMeans
    from sklearn.datasets import make_blobs

    plt.figure(figsize=(12, 12))

    n_samples = 1500
    random_state = 170
    X, y = make_blobs(n_samples=n_samples, random_state=random_state)

    # Incorrect number of clusters
    y_pred = KMeans(n_clusters=2, random_state=random_state).fit_predict(X)

    plt.subplot(221)
    plt.scatter(X[:, 0], X[:, 1], c=y_pred)
    plt.title("Incorrect Number of Blobs")

    # Anisotropicly distributed data
    transformation = [[ 0.60834549, -0.63667341], [-0.40887718, 0.85253229]]
    X_aniso = np.dot(X, transformation)
    y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_aniso)

    plt.subplot(222)
    plt.scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred)
    plt.title("Anisotropicly Distributed Blobs")

    # Different variance
    X_varied, y_varied = make_blobs(n_samples=n_samples,
                                    cluster_std=[1.0, 2.5, 0.5],
                                    random_state=random_state)
    y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_varied)

    plt.subplot(223)
    plt.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred)
    plt.title("Unequal Variance")

    # Unevenly sized blobs
    X_filtered = np.vstack((X[y == 0][:500], X[y == 1][:100], X[y == 2][:10]))
    y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_filtered)

    plt.subplot(224)
    plt.scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_pred)
    plt.title("Unevenly Sized Blobs")

    plt.show()

**Total running time of the script:**
(0 minutes 0.364 seconds)



.. container:: sphx-glr-download

    **Download Python source code:** :download:`plot_kmeans_assumptions.py <plot_kmeans_assumptions.py>`


.. container:: sphx-glr-download

    **Download IPython notebook:** :download:`plot_kmeans_assumptions.ipynb <plot_kmeans_assumptions.ipynb>`