sklearn.metrics
.silhouette_score¶

sklearn.metrics.
silhouette_score
(X, labels, metric=’euclidean’, sample_size=None, random_state=None, **kwds)[source]¶ Compute the mean Silhouette Coefficient of all samples.
The Silhouette Coefficient is calculated using the mean intracluster distance (
a
) and the mean nearestcluster distance (b
) for each sample. The Silhouette Coefficient for a sample is(b  a) / max(a, b)
. To clarify,b
is the distance between a sample and the nearest cluster that the sample is not a part of. Note that Silhouette Coefficient is only defined if number of labels is 2 <= n_labels <= n_samples  1.This function returns the mean Silhouette 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.
Read more in the User Guide.
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]
Predicted labels 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, usemetric="precomputed"
. sample_size : int or None
The size of the sample to use when computing the Silhouette Coefficient on a random subset of the data. If
sample_size is None
, no sampling is used. random_state : int, RandomState instance or None, optional (default=None)
The generator used to randomly select a subset of samples. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by
np.random
. Used whensample_size is not None
. **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
[1] Peter J. Rousseeuw (1987). “Silhouettes: a Graphical Aid to the Interpretation and Validation of Cluster Analysis”. Computational and Applied Mathematics 20: 5365. [2] Wikipedia entry on the Silhouette Coefficient