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""" Unsupervised evaluation metrics. """
# Authors: Robert Layton <robertlayton@gmail.com>
#
# License: BSD Style.
import numpy as np
from ...utils import check_random_state
from ..pairwise import pairwise_distances
def silhouette_score(X, labels, metric='euclidean',
sample_size=None, random_state=None, **kwds):
"""Compute the mean Silhouette Coefficient of all samples.
The Silhouette Coefficient is calculated using the mean intra-cluster
distance (a) and the mean nearest-cluster distance (b) for each sample.
The Silhouette Coefficient for a sample is ``(b - a) / max(a, b)``.
To clarrify, b is the distance between a sample and the nearest cluster
that b is not a part of.
This function returns the mean Silhoeutte Coefficient over all samples.
To obtain the values for each sample, use silhouette_samples
The best value is 1 and the worst value is -1. Values near 0 indicate
overlapping clusters. Negative values generally indicate that a sample has
been assigned to the wrong cluster, as a different cluster is more similar.
Parameters
----------
X : array [n_samples_a, n_samples_a] if metric == "precomputed", or, \
[n_samples_a, n_features] otherwise
Array of pairwise distances between samples, or a feature array.
labels : array, shape = [n_samples]
label values for each sample
metric : string, or callable
The metric to use when calculating distance between instances in a
feature array. If metric is a string, it must be one of the options
allowed by metrics.pairwise.pairwise_distances. If X is the distance
array itself, use "precomputed" as the metric.
sample_size : int or None
The size of the sample to use when computing the Silhouette
Coefficient. If sample_size is None, no sampling is used.
random_state : integer or numpy.RandomState, optional
The generator used to initialize the centers. If an integer is
given, it fixes the seed. Defaults to the global numpy random
number generator.
`**kwds` : optional keyword parameters
Any further parameters are passed directly to the distance function.
If using a scipy.spatial.distance metric, the parameters are still
metric dependent. See the scipy docs for usage examples.
Returns
-------
silhouette : float
Mean Silhouette Coefficient for all samples.
References
----------
Peter J. Rousseeuw (1987). "Silhouettes: a Graphical Aid to the
Interpretation and Validation of Cluster Analysis". Computational
and Applied Mathematics 20: 53-65. doi:10.1016/0377-0427(87)90125-7.
http://en.wikipedia.org/wiki/Silhouette_(clustering)
"""
if sample_size is not None:
random_state = check_random_state(random_state)
indices = random_state.permutation(X.shape[0])[:sample_size]
if metric == "precomputed":
X, labels = X[indices].T[indices].T, labels[indices]
else:
X, labels = X[indices], labels[indices]
return np.mean(silhouette_samples(X, labels, metric=metric, **kwds))
def silhouette_samples(X, labels, metric='euclidean', **kwds):
"""Compute the Silhouette Coefficient for each sample.
The Silhoeutte Coefficient is a measure of how well samples are clustered
with samples that are similar to themselves. Clustering models with a high
Silhouette Coefficient are said to be dense, where samples in the same
cluster are similar to each other, and well separated, where samples in
different clusters are not very similar to each other.
The Silhouette Coefficient is calculated using the mean intra-cluster
distance (a) and the mean nearest-cluster distance (b) for each sample.
The Silhouette Coefficient for a sample is ``(b - a) / max(a, b)``.
This function returns the Silhoeutte Coefficient for each sample.
The best value is 1 and the worst value is -1. Values near 0 indicate
overlapping clusters.
Parameters
----------
X : array [n_samples_a, n_samples_a] if metric == "precomputed", or, \
[n_samples_a, n_features] otherwise
Array of pairwise distances between samples, or a feature array.
labels : array, shape = [n_samples]
label values for each sample
metric : string, or callable
The metric to use when calculating distance between instances in a
feature array. If metric is a string, it must be one of the options
allowed by metrics.pairwise.pairwise_distances. If X is the distance
array itself, use "precomputed" as the metric.
`**kwds` : optional keyword parameters
Any further parameters are passed directly to the distance function.
If using a scipy.spatial.distance metric, the parameters are still
metric dependent. See the scipy docs for usage examples.
Returns
-------
silhouette : array, shape = [n_samples]
Silhouette Coefficient for each samples.
References
----------
Peter J. Rousseeuw (1987). "Silhouettes: a Graphical Aid to the
Interpretation and Validation of Cluster Analysis". Computational
and Applied Mathematics 20: 53-65. doi:10.1016/0377-0427(87)90125-7.
http://en.wikipedia.org/wiki/Silhouette_(clustering)
"""
distances = pairwise_distances(X, metric=metric, **kwds)
n = labels.shape[0]
A = np.array([_intra_cluster_distance(distances[i], labels, i)
for i in range(n)])
B = np.array([_nearest_cluster_distance(distances[i], labels, i)
for i in range(n)])
return (B - A) / np.maximum(A, B)
def _intra_cluster_distance(distances_row, labels, i):
"""Calculate the mean intra-cluster distance for sample i.
Parameters
----------
distances_row : array, shape = [n_samples]
Pairwise distance matrix between sample i and each sample.
labels : array, shape = [n_samples]
label values for each sample
i : int
Sample index being calculated. It is excluded from calculation and
used to determine the current label
Returns
-------
a : float
Mean intra-cluster distance for sample i
"""
mask = labels == labels[i]
mask[i] = False
a = np.mean(distances_row[mask])
return a
def _nearest_cluster_distance(distances_row, labels, i):
"""Calculate the mean nearest-cluster distance for sample i.
Parameters
----------
distances_row : array, shape = [n_samples]
Pairwise distance matrix between sample i and each sample.
labels : array, shape = [n_samples]
label values for each sample
i : int
Sample index being calculated. It is used to determine the current
label.
Returns
-------
b : float
Mean nearest-cluster distance for sample i
"""
label = labels[i]
b = np.min([np.mean(distances_row[labels == cur_label])
for cur_label in set(labels) if not cur_label == label])
return b
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