Class BaseL2Kernel

JSAT/src/jsat/distributions/kernels/BaseL2Kernel.java:20–138

Many Kernels can be described in terms the L2 norm with some operations performed on it. For example, the RBFKernel and RationalQuadraticKernel can both be expressed in terms of the L 2 norm of the two inputs. To simplify the addition of other kernels based on the same norm

 * @author Edward Raff
 */
public abstract class BaseL2Kernel implements KernelTrick
{

    private static final long serialVersionUID = 2917497058710848085L;

    @Override
    abstract public double eval(Vec a, Vec b);

    @Override
    abstract public KernelTrick clone();

    @Override
    public boolean supportsAcceleration()
    {
        return true;
    }
    
    /**
     * Returns the squared L<sup>2</sup> norm between two points from the cache values. 
     * @param i the first index in the vector list
     * @param j the second index in the vector list
     * @param vecs the list of vectors that make the collection
     * @param cache the cache of values for each vector in the collection
     * @return the squared norm ||x<sub>i</sub>-x<sub>j</sub>||<sup>2</sup>
     */
    protected double getSqrdNorm(int i, int j, List<? extends Vec> vecs, List<Double> cache)
    {
        if(cache == null)
            return Math.pow(vecs.get(i).pNormDist(2.0, vecs.get(j)), 2);
        return cache.get(i)+cache.get(j)-2*vecs.get(i).dot(vecs.get(j));
    }
    
    /**
     * Returns the squared L<sup>2</sup> norm of the given point from the cache
     * @param i the index in the vector list to get the squared norm from
     * @param vecs the list of vectors that make the collection
     * @param cache the cache of values for each vector in the collection
     * @return the squared norm ||x<sub>i</sub>||<sup>2</sup>
     */
    protected double getSqrdNorm(int i, List<? extends Vec> vecs, List<Double> cache)
    {
        return cache.get(i);
    }
    
    /**
     * Returns the squared L<sup>2</sup> norm between a point in the cache and one with a provided qi value
     * @param i the index in the vector list
     * @param y the other vector 
     * @param qi the acceleration values for the other vector
     * @param vecs the list of vectors to make the collection
     * @param cache the cache of values for each vector in the collection
     * @return the squared norm ||x<sub>i</sub>-y||<sup>2</sup>
     */
    protected double getSqrdNorm(int i, Vec y, List<Double> qi, List<? extends Vec> vecs, List<Double> cache)
    {
        if(cache == null)
            return Math.pow(vecs.get(i).pNormDist(2.0, y), 2);
        return cache.get(i)+qi.get(0)-2*vecs.get(i).dot(y);