smile.math.kernel.Gaussian Maven / Gradle / Ivy

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 * Copyright (c) 2010-2020 Haifeng Li. All rights reserved.
 *
 * Smile is free software: you can redistribute it and/or modify
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 *
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 * along with Smile.  If not, see .
 ******************************************************************************/

package smile.math.kernel;

import smile.math.MathEx;

/**
 * Gaussian kernel, also referred as RBF kernel or squared exponential kernel.
 * 
 * 
 *     k(u, v) = e^{-||u-v||² / (2 * σ²)}
 * 
 * where σ > 0 is the scale parameter of the kernel.
 * 
 * The Gaussian kernel is a good choice for a great deal of applications,
 * although sometimes it is remarked as being overused.
 *
 * @author Haifeng Li
 */
public class Gaussian implements IsotropicKernel {
    private static final long serialVersionUID = 2L;

    /** The length scale of the kernel. */
    final double sigma;
    /** The lower bound of length scale for hyperparameter tuning. */
    final double lo;
    /** The upper bound of length scale for hyperparameter tuning. */
    final double hi;

    /**
     * Constructor.
     * @param sigma The length scale of kernel.
     * @param lo The lower bound of length scale for hyperparameter tuning.
     * @param hi The upper bound of length scale for hyperparameter tuning.
     */
    public Gaussian(double sigma, double lo, double hi) {
        if (sigma <= 0) {
            throw new IllegalArgumentException("sigma is not positive: " + sigma);
        }

        this.sigma = sigma;
        this.lo = lo;
        this.hi = hi;
    }

    /** Returns the length scale of kernel. */
    public double scale() {
        return sigma;
    }

    @Override
    public String toString() {
        return String.format("GaussianKernel(%.4f)", sigma);
    }

    @Override
    public double k(double dist) {
        double d = dist / sigma;
        return Math.exp(-0.5 * d * d);
    }

    @Override
    public double[] kg(double dist) {
        double[] g = new double[2];
        double d = dist / sigma;
        double k = Math.exp(-0.5 * d * d);
        g[0] = k;
        g[1] = k * d * d / sigma;
        return g;
    }
}