euclidean_distances#

sklearn.metrics.pairwise.euclidean_distances(X,Y=None,*,Y_norm_squared=None,squared=False,X_norm_squared=None)[source]#

Compute the distance matrix between each pair from a feature array X and Y.

For efficiency reasons, the euclidean distance between a pair of rowvector x and y is computed as:

dist(x,y)=sqrt(dot(x,x)-2*dot(x,y)+dot(y,y))

This formulation has two advantages over other ways of computing distances.First, it is computationally efficient when dealing with sparse data.Second, if one argument varies but the other remains unchanged, thendot(x,x) and/ordot(y,y) can be pre-computed.

However, this is not the most precise way of doing this computation,because this equation potentially suffers from “catastrophic cancellation”.Also, the distance matrix returned by this function may not be exactlysymmetric as required by, e.g.,scipy.spatial.distance functions.

Read more in theUser Guide.

Parameters:

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

An array where each row is a sample and each column is a feature.

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

An array where each row is a sample and each column is a feature.IfNone, method usesY=X.

Y_norm_squaredarray-like of shape (n_samples_Y,) or (n_samples_Y, 1) or (1, n_samples_Y), default=None

Pre-computed dot-products of vectors in Y (e.g.,(Y**2).sum(axis=1))May be ignored in some cases, see the note below.

squaredbool, default=False

Return squared Euclidean distances.

X_norm_squaredarray-like of shape (n_samples_X,) or (n_samples_X, 1) or (1, n_samples_X), default=None

Pre-computed dot-products of vectors in X (e.g.,(X**2).sum(axis=1))May be ignored in some cases, see the note below.

Returns:

distancesndarray of shape (n_samples_X, n_samples_Y)

Returns the distances between the row vectors ofXand the row vectors ofY.

See also

paired_distances

Distances between pairs of elements of X and Y.

Notes

To achieve a better accuracy,X_norm_squared andY_norm_squared may beunused if they are passed asnp.float32.

Examples

>>>fromsklearn.metrics.pairwiseimporteuclidean_distances>>>X=[[0,1],[1,1]]>>># distance between rows of X>>>euclidean_distances(X,X)array([[0., 1.],       [1., 0.]])>>># get distance to origin>>>euclidean_distances(X,[[0,0]])array([[1.        ],       [1.41421356]])