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polynomial_kernel — scikit-learn 1.7.0 documentation

sklearn.metrics.pairwise.polynomial_kernel(X, Y=None, degree=3, gamma=None, coef0=1)[source]#

Compute the polynomial kernel between X and Y.

K(X, Y) = (gamma <X, Y> + coef0) ^ degree

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.

degreefloat, default=3

Kernel degree.

gammafloat, default=None

Coefficient of the vector inner product. If None, defaults to 1.0 / n_features.

coef0float, default=1

Constant offset added to scaled inner product.

Returns:

kernelndarray of shape (n_samples_X, n_samples_Y)

The polynomial kernel.

Examples

>>> from sklearn.metrics.pairwise import polynomial_kernel
>>> X = [[0, 0, 0], [1, 1, 1]]
>>> Y = [[1, 0, 0], [1, 1, 0]]
>>> polynomial_kernel(X, Y, degree=2)
array([[1.     , 1.     ],
       [1.77, 2.77]])

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