# Copyright 1999-2020 Alibaba Group Holding Ltd. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. from .... import tensor as mt from .core import PairwiseDistances from .euclidean import euclidean_distances [docs]def rbf_kernel(X, Y=None, gamma=None): """ Compute the rbf (gaussian) kernel between X and Y:: K(x, y) = exp(-gamma ||x-y||^2) for each pair of rows x in X and y in Y. Read more in the :ref:`User Guide <rbf_kernel>`. Parameters ---------- X : tensor of shape (n_samples_X, n_features) Y : tensor of shape (n_samples_Y, n_features) gamma : float, default None If None, defaults to 1.0 / n_features Returns ------- kernel_matrix : tensor of shape (n_samples_X, n_samples_Y) """ X, Y = PairwiseDistances.check_pairwise_arrays(X, Y) if gamma is None: gamma = 1.0 / X.shape[1] K = euclidean_distances(X, Y, squared=True) K *= -gamma K = mt.exp(K) return K