linear_kernel

sklearn.metrics.pairwise.linear_kernel(X, Y=None, dense_output=True)[source]

Compute the linear kernel between X and Y.

Read more in the User Guide.

Parameters:

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.

dense_outputbool, default=True

Whether to return dense output even when the input is sparse. If False, the output is sparse if both input arrays are sparse.

Added in version 0.20.

Returns:

kernelndarray of shape (n_samples_X, n_samples_Y)

The Gram matrix of the linear kernel, i.e. X @ Y.T.

Examples

>>> from sklearn.metrics.pairwise import linear_kernel
>>> X = [[0, 0, 0], [1, 1, 1]]
>>> Y = [[1, 0, 0], [1, 1, 0]]
>>> linear_kernel(X, Y)
array([[0., 0.],
       [1., 2.]])