RBFKernel.java

/*
 * 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 static rapaio.sys.WS.formatFlex;

/**
 * The GaussianPdf kernel is an example of radial basis function kernel.
 * <p>
 * k(x, y) = \exp\left(-\frac{ \lVert x-y \rVert ^2}{2\sigma^2}\right)
 * <p>
 * Alternatively, it could also be implemented using
 * <p>
 * k(x, y) = \exp\left(- \gamma \lVert x-y \rVert ^2 )
 * <p>
 * The adjustable parameter sigma plays a major role in the performance of
 * the kernel, and should be carefully tuned to the problem at hand. If
 * overestimated, the exponential will behave almost linearly and the
 * higher-dimensional projection will start to lose its non-linear power.
 * In the other hand, if underestimated, the function will lack regularization
 * and the decision boundary will be highly sensitive to noise in training data.
 * <p>
 * Created by <a href="mailto:padreati@yahoo.com">Aurelian Tutuianu</a> at 1/16/15.
 */
public class RBFKernel extends AbstractKernel {

    private static final long serialVersionUID = -2105174939802643460L;

    private final double sigma;
    private final double factor;

    public RBFKernel(double sigma) {
        this.sigma = sigma;
        this.factor = 1.0 / (2.0 * sigma * sigma);
    }

    @Override
    public double eval(Frame df1, int row1, Frame df2, int row2) {
        double value = deltaDotProd(df1, row1, df2, row2);
        return 1.0 / Math.pow(Math.E, factor * value * value);
    }

    @Override
    public Kernel newInstance() {
        return new RBFKernel(sigma);
    }

    @Override
    public String name() {
        return "RBF(sigma=" + formatFlex(sigma) + ")";
    }
}