sklearn.metrics.pairwise.laplacian_kernel(X, Y=None, gamma=None)[source]#

Compute the laplacian kernel between X and Y.

The laplacian kernel is defined as:

K(x, y) = exp(-gamma ||x-y||_1)

for each pair of rows x in X and y in Y. Read more in the User Guide.

Added in version 0.17.

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

A feature array.

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

An optional second feature array. If None, uses Y=X.

gammafloat, default=None

If None, defaults to 1.0 / n_features. Otherwise it should be strictly positive.

kernelndarray of shape (n_samples_X, n_samples_Y)

The kernel matrix.


>>> from sklearn.metrics.pairwise import laplacian_kernel
>>> X = [[0, 0, 0], [1, 1, 1]]
>>> Y = [[1, 0, 0], [1, 1, 0]]
>>> laplacian_kernel(X, Y)
array([[0.71..., 0.51...],
       [0.51..., 0.71...]])