/*
* Apache License
* Version 2.0, January 2004
* http://www.apache.org/licenses/
*
* Copyright 2013 Aurelian Tutuianu
* Copyright 2014 Aurelian Tutuianu
* Copyright 2015 Aurelian Tutuianu
* Copyright 2016 Aurelian Tutuianu
*
* 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 rapaio.ml.classifier.svm.kernel;
import rapaio.data.Frame;
import rapaio.sys.WS;
/**
* The Cauchy kernel comes from the Cauchy distribution (Basak, 2008).
* It is a long-tailed kernel and can be used to give long-range influence
* and sensitivity over the high dimension space.
* <p>
* k(x, y) = \frac{1}{1 + \frac{\lVert x-y \rVert^2}{\sigma^2} }
* <p>
* Created by <a href="mailto:padreati@yahoo.com">Aurelian Tutuianu</a> at 1/21/15.
*/
public class CauchyKernel extends AbstractKernel {
private static final long serialVersionUID = -5631098319904454645L;
private final double sigma;
/**
* The Cauchy kernel comes from the Cauchy distribution (Basak, 2008).
* It is a long-tailed kernel and can be used to give long-range influence
* and sensitivity over the high dimension space.
* <p>
* k(x, y) = \frac{1}{1 + \frac{\lVert x-y \rVert^2}{\sigma^2} }
*
* @param sigma sigma value
*/
public CauchyKernel(double sigma) {
this.sigma = sigma;
}
@Override
public double eval(Frame df1, int row1, Frame df2, int row2) {
double dot = deltaDotProd(df1, row1, df2, row2);
return 1.0 / (1.0 + Math.pow(dot / sigma, 2));
}
@Override
public Kernel newInstance() {
return new CauchyKernel(sigma);
}
@Override
public String name() {
return "Cauchy(" + WS.formatFlex(sigma) + ")";
}
}