sklearn.metrics.silhouette_score

sklearn.metrics.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 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

Xarray-like of shape (n_samples_a, n_samples_a) if metric == “precomputed” or (n_samples_a, n_features) otherwise

An array of pairwise distances between samples, or a feature array.

labelsarray-like of shape (n_samples,)

Predicted labels for each sample.

metricstr or callable, default=’euclidean’

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 metric="precomputed".

sample_sizeint, default=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_stateint, RandomState instance or None, default=None

Determines random number generation for selecting a subset of samples. Used when sample_size is not None. Pass an int for reproducible results across multiple function calls. See Glossary.

**kwdsoptional 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

silhouettefloat

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: 53-65.

2

Wikipedia entry on the Silhouette Coefficient

Examples using sklearn.metrics.silhouette_score

Demo of affinity propagation clustering algorithm

Demo of DBSCAN clustering algorithm

A demo of K-Means clustering on the handwritten digits data

Selecting the number of clusters with silhouette analysis on KMeans clustering

Clustering text documents using k-means