Basics5_KernelsAndApprox.m

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namespace demos{


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function  Basics5_KernelsAndApprox() {


/* % Create a basic kernel expansion manually */
lw = 2;
/*  Centers */
c = [-1 .5 1.2];
/*  Coefficients */
a = [.5 -.2 .8];
/*  Get a Gaussian kernel with gamma=1 */
k = kernels.GaussKernel(1);
/*  Get the overall linear combination class and set properties */
f = kernels.KernelExpansion;
f.Kernel= k;
f.Centers.xi= c;
f.Ma= a;

/* % Plot the expansion and its centers/single elements
 * More plot functions illustrating kernels can be found at
 * kernels.Wendland.test_WendlandKernel and
 * kernels.GaussKernel.test_GaussKernel */
pm = PlotManager;
h = pm.nextPlot(" rkhs_demo "," Example kernel expansion "," x "," f(x) ");
x = -3:.01:3;
plot(h,x,f.evaluate(x)," r "," LineWidth ",lw);
hold(h," on ");
plot(h,x,0," k "," LineWidth ",lw);
for i = 1:length(c)
    f.Centers.xi= c(i);
    f.Ma= a(i);
    plot(h,x,f.evaluate(x)," r-- ");
    plot(h,c(i),0," b. "," MarkerSize ",20);
    plot(h,[c(i) c(i)+eps],[0 a(i)]," k-- ");
end
pm.done;

/* % Run a VKOGA algorithm */
fprintf(" Just ignore the following two warnings about file locations!\n ");
load(fullfile(" +demos "," spine_training_data_set.mat "));

/*  Get VKOGA instance */
alg = approx.algorithms.VKOGA;
/*  Set maximal size */
alg.MaxExpansionSize= 600;
/*  Choose variant */
alg.UsefPGreedy= false;

nG = 10;
k = [1 3];

/*  Create configuration for VKOGA */
gammas = linspace(15,70,nG);
comb = Utils.createCombinations(gammas,k);
wc = kernels.config.WendlandConfig(" G ",comb(1,:)," S ",comb(2,:));
wc.Dimension= 3;
ec = kernels.config.ExpansionConfig;
ec.StateConfig= wc;
alg.ExpConfig= ec;

/* % Execute computations */
kexp = alg.computeApproximation(atd);
kexp_dbase = kexp.toTranslateBase;
save basics5_kernelsandapprox;

/* % Plot the results */
FunVis2D(kexp, atd, [], [], lbl);

}
};