364 lines
14 KiB
Python
364 lines
14 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 functools
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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 ...utils import _safe_indexing
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from ..pairwise import pairwise_distances_chunked
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from ..pairwise import pairwise_distances
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from ...preprocessing import LabelEncoder
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from ...utils.validation import _deprecate_positional_args
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def check_number_of_labels(n_labels, n_samples):
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"""Check that number of labels are valid.
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Parameters
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----------
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n_labels : int
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Number of labels
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n_samples : int
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Number of samples
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"""
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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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@_deprecate_positional_args
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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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Determines random number generation for selecting a subset of samples.
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Used when ``sample_size is not None``.
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Pass an int for reproducible results across multiple function calls.
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See :term:`Glossary <random_state>`.
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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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<https://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_reduce(D_chunk, start, labels, label_freqs):
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"""Accumulate silhouette statistics for vertical chunk of X
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Parameters
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----------
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D_chunk : shape (n_chunk_samples, n_samples)
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precomputed distances for a chunk
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start : int
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first index in chunk
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labels : array, shape (n_samples,)
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corresponding cluster labels, encoded as {0, ..., n_clusters-1}
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label_freqs : array
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distribution of cluster labels in ``labels``
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"""
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# accumulate distances from each sample to each cluster
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clust_dists = np.zeros((len(D_chunk), len(label_freqs)),
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dtype=D_chunk.dtype)
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for i in range(len(D_chunk)):
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clust_dists[i] += np.bincount(labels, weights=D_chunk[i],
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minlength=len(label_freqs))
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# intra_index selects intra-cluster distances within clust_dists
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intra_index = (np.arange(len(D_chunk)), labels[start:start + len(D_chunk)])
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# intra_clust_dists are averaged over cluster size outside this function
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intra_clust_dists = clust_dists[intra_index]
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# of the remaining distances we normalise and extract the minimum
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clust_dists[intra_index] = np.inf
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clust_dists /= label_freqs
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inter_clust_dists = clust_dists.min(axis=1)
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return intra_clust_dists, inter_clust_dists
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@_deprecate_positional_args
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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. Precomputed
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distance matrices must have 0 along the diagonal.
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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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<https://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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# Check for non-zero diagonal entries in precomputed distance matrix
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if metric == 'precomputed':
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atol = np.finfo(X.dtype).eps * 100
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if np.any(np.abs(np.diagonal(X)) > atol):
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raise ValueError(
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'The precomputed distance matrix contains non-zero '
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'elements on the diagonal. Use np.fill_diagonal(X, 0).'
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)
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le = LabelEncoder()
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labels = le.fit_transform(labels)
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n_samples = len(labels)
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label_freqs = np.bincount(labels)
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check_number_of_labels(len(le.classes_), n_samples)
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kwds['metric'] = metric
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reduce_func = functools.partial(_silhouette_reduce,
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labels=labels, label_freqs=label_freqs)
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results = zip(*pairwise_distances_chunked(X, reduce_func=reduce_func,
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**kwds))
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intra_clust_dists, inter_clust_dists = results
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intra_clust_dists = np.concatenate(intra_clust_dists)
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inter_clust_dists = np.concatenate(inter_clust_dists)
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denom = (label_freqs - 1).take(labels, mode='clip')
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with np.errstate(divide="ignore", invalid="ignore"):
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intra_clust_dists /= denom
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sil_samples = inter_clust_dists - intra_clust_dists
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with np.errstate(divide="ignore", invalid="ignore"):
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sil_samples /= np.maximum(intra_clust_dists, inter_clust_dists)
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# nan values are for clusters of size 1, and should be 0
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return np.nan_to_num(sil_samples)
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def calinski_harabasz_score(X, labels):
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"""Compute the Calinski and Harabasz score.
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It is also known as the Variance Ratio Criterion.
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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_harabasz_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-Harabasz 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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<https://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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def davies_bouldin_score(X, labels):
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"""Computes the Davies-Bouldin score.
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The score is defined as the average similarity measure of each cluster with
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its most similar cluster, where similarity is the ratio of within-cluster
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distances to between-cluster distances. Thus, clusters which are farther
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apart and less dispersed will result in a better score.
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The minimum score is zero, with lower values indicating better clustering.
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Read more in the :ref:`User Guide <davies-bouldin_index>`.
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.. versionadded:: 0.20
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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 Davies-Bouldin score.
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References
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----------
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.. [1] Davies, David L.; Bouldin, Donald W. (1979).
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`"A Cluster Separation Measure"
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<https://ieeexplore.ieee.org/document/4766909>`__.
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IEEE Transactions on Pattern Analysis and Machine Intelligence.
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PAMI-1 (2): 224-227
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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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intra_dists = np.zeros(n_labels)
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centroids = np.zeros((n_labels, len(X[0])), dtype=np.float)
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for k in range(n_labels):
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cluster_k = _safe_indexing(X, labels == k)
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centroid = cluster_k.mean(axis=0)
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centroids[k] = centroid
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intra_dists[k] = np.average(pairwise_distances(
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cluster_k, [centroid]))
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centroid_distances = pairwise_distances(centroids)
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|
|
if np.allclose(intra_dists, 0) or np.allclose(centroid_distances, 0):
|
||
|
|
return 0.0
|
||
|
|
|
||
|
|
centroid_distances[centroid_distances == 0] = np.inf
|
||
|
|
combined_intra_dists = intra_dists[:, None] + intra_dists
|
||
|
|
scores = np.max(combined_intra_dists / centroid_distances, axis=1)
|
||
|
|
return np.mean(scores)
|