smile.math.kernel.SparseHyperbolicTangentKernel Maven / Gradle / Ivy
/*******************************************************************************
* Copyright (c) 2010 Haifeng Li
*
* 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.
*******************************************************************************/
package smile.math.kernel;
import smile.math.Math;
import smile.math.SparseArray;
/**
* The hyperbolic tangent kernel.
* k(u, v) = tanh(γ uTv - λ), where γ is the scale
* of the used inner product and λ is the offset of the used inner
* product. If the offset is negative the likelihood of obtaining a kernel
* matrix that is not positive definite is much higher (since then even some
* diagonal elements may be negative), hence if this kernel has to be used,
* the offset should always be positive. Note, however, that this is no
* guarantee that the kernel will be positive.
*
* The hyperbolic tangent kernel was quite popular for support vector machines
* due to its origin from neural networks. However, it should be used carefully
* since the kernel matrix may not be positive semi-definite. Besides, it was
* reported the hyperbolic tangent kernel is not better than the Gaussian kernel
* in general..
*
* @author Haifeng Li
*/
public class SparseHyperbolicTangentKernel implements MercerKernel {
private double scale;
private double offset;
/**
* Constructor with scale 1.0 and offset 0.0.
*/
public SparseHyperbolicTangentKernel() {
this(1.0, 0.0);
}
/**
* Constructor.
*/
public SparseHyperbolicTangentKernel(double scale, double offset) {
this.scale = scale;
this.offset = offset;
}
@Override
public String toString() {
return String.format("Sparse Hyperbolic Tangent Kernel (scale = %.4f, offset = %.4f)", scale, offset);
}
@Override
public double k(SparseArray x, SparseArray y) {
double dot = Math.dot(x, y);
return Math.tanh(scale * dot + offset);
}
}