pairwise_distances#

sklearn.metrics.pairwise_distances(X, Y=None, metric='euclidean', *, n_jobs=None, force_all_finite='deprecated', ensure_all_finite=None, **kwds)[source]#

Compute the distance matrix from a feature array X and optional Y.

This function takes one or two feature arrays or a distance matrix, and returns a distance matrix.

  • If X is a feature array, of shape (n_samples_X, n_features), and:

    • Y is None and metric is not ‘precomputed’, the pairwise distances between X and itself are returned.

    • Y is a feature array of shape (n_samples_Y, n_features), the pairwise distances between X and Y is returned.

  • If X is a distance matrix, of shape (n_samples_X, n_samples_X), metric should be ‘precomputed’. Y is thus ignored and X is returned as is.

If the input is a collection of non-numeric data (e.g. a list of strings or a boolean array), a custom metric must be passed.

This method provides a safe way to take a distance matrix as input, while preserving compatibility with many other algorithms that take a vector array.

Valid values for metric are:

  • From scikit-learn: [‘cityblock’, ‘cosine’, ‘euclidean’, ‘l1’, ‘l2’, ‘manhattan’, ‘nan_euclidean’]. All metrics support sparse matrix inputs except ‘nan_euclidean’.

  • From scipy.spatial.distance: [‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘correlation’, ‘dice’, ‘hamming’, ‘jaccard’, ‘kulsinski’, ‘mahalanobis’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘yule’] See the documentation for scipy.spatial.distance for details on these metrics. These metrics do not support sparse matrix inputs.

Note

'kulsinski' is deprecated from SciPy 1.9 and will be removed in SciPy 1.11.

Note

'matching' has been removed in SciPy 1.9 (use 'hamming' instead).

Note that in the case of ‘cityblock’, ‘cosine’ and ‘euclidean’ (which are valid scipy.spatial.distance metrics), the scikit-learn implementation will be used, which is faster and has support for sparse matrices (except for ‘cityblock’). For a verbose description of the metrics from scikit-learn, see sklearn.metrics.pairwise.distance_metrics function.

Read more in the User Guide.

Parameters:
X{array-like, sparse matrix} of shape (n_samples_X, n_samples_X) or (n_samples_X, n_features)

Array of pairwise distances between samples, or a feature array. The shape of the array should be (n_samples_X, n_samples_X) if metric == “precomputed” and (n_samples_X, n_features) otherwise.

Y{array-like, sparse matrix} of shape (n_samples_Y, n_features), default=None

An optional second feature array. Only allowed if metric != “precomputed”.

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 scipy.spatial.distance.pdist for its metric parameter, or a metric listed in pairwise.PAIRWISE_DISTANCE_FUNCTIONS. If metric is “precomputed”, X is assumed to be a distance matrix. Alternatively, if metric is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two arrays from X as input and return a value indicating the distance between them.

n_jobsint, default=None

The number of jobs to use for the computation. This works by breaking down the pairwise matrix into n_jobs even slices and computing them using multithreading.

None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

The “euclidean” and “cosine” metrics rely heavily on BLAS which is already multithreaded. So, increasing n_jobs would likely cause oversubscription and quickly degrade performance.

force_all_finitebool or ‘allow-nan’, default=True

Whether to raise an error on np.inf, np.nan, pd.NA in array. Ignored for a metric listed in pairwise.PAIRWISE_DISTANCE_FUNCTIONS. The possibilities are:

  • True: Force all values of array to be finite.

  • False: accepts np.inf, np.nan, pd.NA in array.

  • ‘allow-nan’: accepts only np.nan and pd.NA values in array. Values cannot be infinite.

Added in version 0.22: force_all_finite accepts the string 'allow-nan'.

Changed in version 0.23: Accepts pd.NA and converts it into np.nan.

Deprecated since version 1.6: force_all_finite was renamed to ensure_all_finite and will be removed in 1.8.

ensure_all_finitebool or ‘allow-nan’, default=True

Whether to raise an error on np.inf, np.nan, pd.NA in array. Ignored for a metric listed in pairwise.PAIRWISE_DISTANCE_FUNCTIONS. The possibilities are:

  • True: Force all values of array to be finite.

  • False: accepts np.inf, np.nan, pd.NA in array.

  • ‘allow-nan’: accepts only np.nan and pd.NA values in array. Values cannot be infinite.

Added in version 1.6: force_all_finite was renamed to ensure_all_finite.

**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:
Dndarray of shape (n_samples_X, n_samples_X) or (n_samples_X, n_samples_Y)

A distance matrix D such that D_{i, j} is the distance between the ith and jth vectors of the given matrix X, if Y is None. If Y is not None, then D_{i, j} is the distance between the ith array from X and the jth array from Y.

See also

pairwise_distances_chunked

Performs the same calculation as this function, but returns a generator of chunks of the distance matrix, in order to limit memory usage.

sklearn.metrics.pairwise.paired_distances

Computes the distances between corresponding elements of two arrays.

Notes

If metric is a callable, no restrictions are placed on X and Y dimensions.

Examples

>>> from sklearn.metrics.pairwise import pairwise_distances
>>> X = [[0, 0, 0], [1, 1, 1]]
>>> Y = [[1, 0, 0], [1, 1, 0]]
>>> pairwise_distances(X, Y, metric='sqeuclidean')
array([[1., 2.],
       [2., 1.]])