% An example of RBF regression using built-in k-means.
%   We will need the edm from the folder.

%% Step 1:  Create the data
numpts=150;
X = rand([numpts,1]);
X = sort(X);
noise = 0.1*randn(numpts,1);
y = sin(3*pi*X)+noise;
clear noise

% Split into training and test sets.  We'll do it manually here:
idx=randperm(numpts);
N1=round(0.3*numpts); N2=numpts-N1;
Xtrain=X(idx(1:N2),:); Xtest=X(idx(N2+1:end),:);
ytrain=y(idx(1:N2),:); ytest=y(idx(N2+1:end),:);
clear idx N1 N2

%% Step 2:  k-means on the training input data to get the centers.
k=4;
[~,C]=kmeans(X,k);

%% Step 3:  Build the RBF matrices and solve for weights and biases
spr=sqrt(-log(0.5));  % This is Matlab's default
D=edm(C,Xtrain);
Phi=exp(-spr*(D.^2));
[nc,nr]=size(Phi);   % Phi should be numcenters x num data point 
% Add a row of ones
Phi_hat=[Phi;ones(1,nr)];
W_hat=ytrain'*pinv(Phi_hat);

%% Step 4: Construct the RBF output on the testing data:
spr=sqrt(-log(0.5));  % This is Matlab's default
D=edm(C,Xtest);
Phi=exp(-spr*(D.^2));
[nc,nr]=size(Phi);   % Phi should be numcenters x num data point 
% Add a row of ones
Phi_hat=[Phi;ones(1,nr)];

y_out=W_hat*Phi_hat;

plot(X,y,'b.-',Xtest,y_out','ro',C,zeros(size(C)),'k*');
legend('Orig Data','RBF Output on Test set','Center Location')