dataset3Params.m

function [C, sigma] = dataset3Params(X, y, Xval, yval)
%DATASET3PARAMS returns your choice of C and sigma for Part 3 of the exercise
%where you select the optimal (C, sigma) learning parameters to use for SVM
%with RBF kernel
%   [C, sigma] = DATASET3PARAMS(X, y, Xval, yval) returns your choice of C and 
%   sigma. You should complete this function to return the optimal C and 
%   sigma based on a cross-validation set.
%

% You need to return the following variables correctly.
C = 1;
sigma = 0.3;

% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return the optimal C and sigma
%               learning parameters found using the cross validation set.
%               You can use svmPredict to predict the labels on the cross
%               validation set. For example, 
%                   predictions = svmPredict(model, Xval);
%               will return the predictions on the cross validation set.
%
%  Note: You can compute the prediction error using 
%        mean(double(predictions ~= yval))
%


Ctemp=[0.01; 0.03; 0.1; 0.3; 1; 3; 10; 30];
sigtemp=[0.01; 0.03; 0.1; 0.3; 1; 3; 10; 30];
rowsn=numel(Ctemp)*numel(sigtemp);
errmat=zeros(rowsn,3);
r=1;
for i=1:numel(Ctemp)

for j=1:numel(sigtemp)

model= svmTrain(X, y, Ctemp(i), @(x1, x2) gaussianKernel(x1, x2, sigtemp(j))); 
predictions = svmPredict(model, Xval);
errmat(r,1)=mean(double(predictions ~= yval));
errmat(r,2)=Ctemp(i);
errmat(r,3)=sigtemp(j);
r=r+1;
end
end

%display(errmat);
errvals=errmat(:,1);
[minerr,index]=min(errvals);
%display(index);
C=errmat(index,2);
sigma=errmat(index,3);

% =========================================================================

end