sklearn.metrics.pairwise
.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 vector array X and Y.
For efficiency reasons, the euclidean distance between a pair of row vector 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, then
dot(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 exactly symmetric as required by, e.g.,
scipy.spatial.distance
functions.Read more in the User 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. If
None
, 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 of
X
and 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 be unused if they are passed asnp.float32
.Examples
>>> from sklearn.metrics.pairwise import euclidean_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]])