259 lines
10 KiB
Python
259 lines
10 KiB
Python
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"""Unsupervised evaluation metrics."""
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# Authors: Robert Layton <robertlayton@gmail.com>
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# Arnaud Fouchet <foucheta@gmail.com>
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# Thierry Guillemot <thierry.guillemot.work@gmail.com>
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# License: BSD 3 clause
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import numpy as np
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from ...utils import check_random_state
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from ...utils import check_X_y
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from ..pairwise import pairwise_distances
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from ...preprocessing import LabelEncoder
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def check_number_of_labels(n_labels, n_samples):
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if not 1 < n_labels < n_samples:
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raise ValueError("Number of labels is %d. Valid values are 2 "
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"to n_samples - 1 (inclusive)" % n_labels)
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def silhouette_score(X, labels, metric='euclidean', sample_size=None,
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random_state=None, **kwds):
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"""Compute the mean Silhouette Coefficient of all samples.
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The Silhouette Coefficient is calculated using the mean intra-cluster
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distance (``a``) and the mean nearest-cluster distance (``b``) for each
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sample. The Silhouette Coefficient for a sample is ``(b - a) / max(a,
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b)``. To clarify, ``b`` is the distance between a sample and the nearest
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cluster that the sample is not a part of.
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Note that Silhouette Coefficient is only defined if number of labels
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is 2 <= n_labels <= n_samples - 1.
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This function returns the mean Silhouette Coefficient over all samples.
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To obtain the values for each sample, use :func:`silhouette_samples`.
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The best value is 1 and the worst value is -1. Values near 0 indicate
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overlapping clusters. Negative values generally indicate that a sample has
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been assigned to the wrong cluster, as a different cluster is more similar.
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Read more in the :ref:`User Guide <silhouette_coefficient>`.
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Parameters
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----------
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X : array [n_samples_a, n_samples_a] if metric == "precomputed", or, \
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[n_samples_a, n_features] otherwise
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Array of pairwise distances between samples, or a feature array.
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labels : array, shape = [n_samples]
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Predicted labels for each sample.
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metric : string, or callable
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The metric to use when calculating distance between instances in a
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feature array. If metric is a string, it must be one of the options
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allowed by :func:`metrics.pairwise.pairwise_distances
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<sklearn.metrics.pairwise.pairwise_distances>`. If X is the distance
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array itself, use ``metric="precomputed"``.
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sample_size : int or None
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The size of the sample to use when computing the Silhouette Coefficient
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on a random subset of the data.
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If ``sample_size is None``, no sampling is used.
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random_state : int, RandomState instance or None, optional (default=None)
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The generator used to randomly select a subset of samples. If int,
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random_state is the seed used by the random number generator; If
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RandomState instance, random_state is the random number generator; If
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None, the random number generator is the RandomState instance used by
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`np.random`. Used when ``sample_size is not None``.
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**kwds : optional keyword parameters
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Any further parameters are passed directly to the distance function.
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If using a scipy.spatial.distance metric, the parameters are still
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metric dependent. See the scipy docs for usage examples.
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Returns
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-------
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silhouette : float
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Mean Silhouette Coefficient for all samples.
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References
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----------
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.. [1] `Peter J. Rousseeuw (1987). "Silhouettes: a Graphical Aid to the
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Interpretation and Validation of Cluster Analysis". Computational
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and Applied Mathematics 20: 53-65.
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<http://www.sciencedirect.com/science/article/pii/0377042787901257>`_
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.. [2] `Wikipedia entry on the Silhouette Coefficient
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<https://en.wikipedia.org/wiki/Silhouette_(clustering)>`_
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"""
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if sample_size is not None:
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X, labels = check_X_y(X, labels, accept_sparse=['csc', 'csr'])
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random_state = check_random_state(random_state)
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indices = random_state.permutation(X.shape[0])[:sample_size]
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if metric == "precomputed":
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X, labels = X[indices].T[indices].T, labels[indices]
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else:
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X, labels = X[indices], labels[indices]
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return np.mean(silhouette_samples(X, labels, metric=metric, **kwds))
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def silhouette_samples(X, labels, metric='euclidean', **kwds):
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"""Compute the Silhouette Coefficient for each sample.
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The Silhouette Coefficient is a measure of how well samples are clustered
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with samples that are similar to themselves. Clustering models with a high
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Silhouette Coefficient are said to be dense, where samples in the same
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cluster are similar to each other, and well separated, where samples in
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different clusters are not very similar to each other.
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The Silhouette Coefficient is calculated using the mean intra-cluster
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distance (``a``) and the mean nearest-cluster distance (``b``) for each
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sample. The Silhouette Coefficient for a sample is ``(b - a) / max(a,
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b)``.
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Note that Silhouette Coefficient is only defined if number of labels
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is 2 <= n_labels <= n_samples - 1.
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This function returns the Silhouette Coefficient for each sample.
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The best value is 1 and the worst value is -1. Values near 0 indicate
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overlapping clusters.
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Read more in the :ref:`User Guide <silhouette_coefficient>`.
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Parameters
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----------
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X : array [n_samples_a, n_samples_a] if metric == "precomputed", or, \
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[n_samples_a, n_features] otherwise
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Array of pairwise distances between samples, or a feature array.
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labels : array, shape = [n_samples]
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label values for each sample
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metric : string, or callable
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The metric to use when calculating distance between instances in a
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feature array. If metric is a string, it must be one of the options
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allowed by :func:`sklearn.metrics.pairwise.pairwise_distances`. If X is
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the distance array itself, use "precomputed" as the metric.
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**kwds : optional keyword parameters
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Any further parameters are passed directly to the distance function.
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If using a ``scipy.spatial.distance`` metric, the parameters are still
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metric dependent. See the scipy docs for usage examples.
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Returns
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-------
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silhouette : array, shape = [n_samples]
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Silhouette Coefficient for each samples.
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References
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----------
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.. [1] `Peter J. Rousseeuw (1987). "Silhouettes: a Graphical Aid to the
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Interpretation and Validation of Cluster Analysis". Computational
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and Applied Mathematics 20: 53-65.
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<http://www.sciencedirect.com/science/article/pii/0377042787901257>`_
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.. [2] `Wikipedia entry on the Silhouette Coefficient
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<https://en.wikipedia.org/wiki/Silhouette_(clustering)>`_
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"""
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X, labels = check_X_y(X, labels, accept_sparse=['csc', 'csr'])
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le = LabelEncoder()
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labels = le.fit_transform(labels)
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check_number_of_labels(len(le.classes_), X.shape[0])
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distances = pairwise_distances(X, metric=metric, **kwds)
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unique_labels = le.classes_
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n_samples_per_label = np.bincount(labels, minlength=len(unique_labels))
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# For sample i, store the mean distance of the cluster to which
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# it belongs in intra_clust_dists[i]
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intra_clust_dists = np.zeros(distances.shape[0], dtype=distances.dtype)
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# For sample i, store the mean distance of the second closest
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# cluster in inter_clust_dists[i]
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inter_clust_dists = np.inf + intra_clust_dists
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for curr_label in range(len(unique_labels)):
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# Find inter_clust_dist for all samples belonging to the same
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# label.
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mask = labels == curr_label
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current_distances = distances[mask]
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# Leave out current sample.
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n_samples_curr_lab = n_samples_per_label[curr_label] - 1
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if n_samples_curr_lab != 0:
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intra_clust_dists[mask] = np.sum(
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current_distances[:, mask], axis=1) / n_samples_curr_lab
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# Now iterate over all other labels, finding the mean
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# cluster distance that is closest to every sample.
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for other_label in range(len(unique_labels)):
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if other_label != curr_label:
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other_mask = labels == other_label
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other_distances = np.mean(
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current_distances[:, other_mask], axis=1)
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inter_clust_dists[mask] = np.minimum(
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inter_clust_dists[mask], other_distances)
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sil_samples = inter_clust_dists - intra_clust_dists
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sil_samples /= np.maximum(intra_clust_dists, inter_clust_dists)
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# score 0 for clusters of size 1, according to the paper
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sil_samples[n_samples_per_label.take(labels) == 1] = 0
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return sil_samples
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def calinski_harabaz_score(X, labels):
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"""Compute the Calinski and Harabaz score.
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The score is defined as ratio between the within-cluster dispersion and
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the between-cluster dispersion.
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Read more in the :ref:`User Guide <calinski_harabaz_index>`.
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Parameters
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----------
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X : array-like, shape (``n_samples``, ``n_features``)
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List of ``n_features``-dimensional data points. Each row corresponds
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to a single data point.
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labels : array-like, shape (``n_samples``,)
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Predicted labels for each sample.
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Returns
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-------
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score : float
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The resulting Calinski-Harabaz score.
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References
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----------
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.. [1] `T. Calinski and J. Harabasz, 1974. "A dendrite method for cluster
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analysis". Communications in Statistics
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<http://www.tandfonline.com/doi/abs/10.1080/03610927408827101>`_
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"""
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X, labels = check_X_y(X, labels)
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le = LabelEncoder()
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labels = le.fit_transform(labels)
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n_samples, _ = X.shape
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n_labels = len(le.classes_)
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check_number_of_labels(n_labels, n_samples)
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extra_disp, intra_disp = 0., 0.
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mean = np.mean(X, axis=0)
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for k in range(n_labels):
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cluster_k = X[labels == k]
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mean_k = np.mean(cluster_k, axis=0)
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extra_disp += len(cluster_k) * np.sum((mean_k - mean) ** 2)
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intra_disp += np.sum((cluster_k - mean_k) ** 2)
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return (1. if intra_disp == 0. else
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extra_disp * (n_samples - n_labels) /
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(intra_disp * (n_labels - 1.)))
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