PolyKernel.m

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namespace kernels{


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class PolyKernel
  :public kernels.BaseKernel {
    public: /* ( setObservable ) */

        Degree = 2;
    public: /* ( setObservable ) */


        PolyKernel(deg) {
            if nargin == 1
                /*  \todo validity checks */
                this.Degree= deg;
            end
            this.IsScProd= true;
        }


        function copy = clone() {
            copy = clone@kernels.BaseKernel(this, kernels.PolyKernel);
            copy.Degree= this.Degree;
        }


        function c = getGlobalLipschitz() {
            error(" Not implemented yet! ");
        }
        function Nabla = getNabla(colvec<double> x,matrix<double> y) {
            Nabla = this.Degree*bsxfun(@times, y, x^t*y.^(this.Degree-1));
        }
        function K = evaluate(colvec<double> x,matrix<double> y) {
            if ~isempty(this.fP)
                x = x(this.fP,:);
            end
            if nargin == 2 || isempty(y)
                y = x;
            else
                if ~isempty(this.fP)
                    y = y(this.fP,:);
                end
            end
            K = (x^t*(this.fG*y)).^this.Degree;
/*              sx = this.fG*x;
 *             n1sq = sum(x.*sx,1);
 *             n1 = size(x,2);
 *             if nargin == 2 || isempty(y)
 *                 y = x;
 *                 n2sq = n1sq;
 *                 n2 = n1;
 *             else
 *                 if ~isempty(this.fP)
 *                     y = y(this.fP,:);
 *                 end
 *                 n2sq = sum(y.*(this.fG*y),1);
 *                 n2 = size(y,2);
 *             end
 *             no = sqrt(repmat(n1sq',1,n2) .* repmat(n2sq,n1,1));
 *             a = (sx'*y);
 *             b = a ./ no;
 *             K = b.^this.Degree;
 *             %K = ((sx'*y) ./ no).^this.Degree; */
        }

    
    public: /* ( Static ) */ /* ( setObservable ) */

        static function res = test_PolyKernel(pm) {
            if nargin < 1
                pm = PlotManager(false,3,3);
                pm.LeaveOpen= true;
            end
            c = 1;
            x = (-1.2:.01:1.2)+c;

            k = kernels.PolyKernel;
            kexp = kernels.KernelExpansion;
            kexp.Kernel= k;
            kexp.Centers.xi= c;
            kexp.Ma= 1;
            conf = [.1 .4 .8 1 2 3 4];
            for n = 1:length(conf)
                k.Degree= conf(n);
                tag = sprintf(" poly_1d_deg%g ",k.Degree);
                h = pm.nextPlot(tag,sprintf(" Polynomial kernel with deg=%g on 1D data ",k.Degree));
                z = kexp.evaluate(x);
                plot(h,x,[real(z); imag(z)]);
            end
            kexp.Centers.xi= [c; 1.6*c];
            [X,Y] = meshgrid(x);
            x2 = [X(:)" ; Y(:) "];
            for n = 1:length(conf)
                k.Degree= conf(n);
                tag = sprintf(" poly_2d_deg%g ",k.Degree);
                h = pm.nextPlot(tag,sprintf(" Polynomial kernel with deg=%g on 2D data ",k.Degree));
                Z = real(reshape(kexp.evaluate(x2),length(x),[]));
                surf(h,X,Y,Z," EdgeColor "," none ");
            end
            if nargin < 1
                pm.done;
            end
            res = true;
        }

    

};
}