# Source code for mars.learn.metrics.pairwise.rbf_kernel

# Copyright 1999-2021 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