% Computer the nonlinear map based on SRF.

clear all;

%% kernel parameter

a = 4;

b = 7;

num_gaussians = 10;

%% data

load('usps.mat');

num_train = size(data_train, 1);

num_test = size(data_test,1);

X = [data_train; data_test];

%% normalization

for i = 1:size(X,1)

X(i,:) = X(i,:)./norm(X(i,:),2);

end

%% kernel apprximation and evaluation

N_sample = 10000;

mapdim_all = 2.^[9, 10, 11, 12, 13, 14];

if (size(X,1) > N_sample)

rand_r = randperm(size(X,1));

X = X(rand_r(1:N_sample), :);

end

kernelfunc = @(normz) (1 - (normz/a).^2 ).^b;

MSE = zeros(1, length(mapdim_all));

for ii = 1:length(mapdim_all)

mapdim = mapdim_all(ii);

fea = gen_RFF(X, a, b, num_gaussians, mapdim);

kernel_gt = kernelfunc(sqrt(2 - X*X'*2));

kernel_diff = (kernel_gt - fea * fea').^2;

MSE(ii) = mean(kernel_diff(:));

end

close all;

figure;

hold on;

plot(log(mapdim_all)/log(2), MSE);

xlabel('log(mapped dimensionality)');

ylabel('MSE')