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))
%
gap = [ 0.01 0.03 0.1 0.3 1 3 10 30]
optim_C = 0.01;
optim_sigma = 0.01;

model = svmTrain(X,y,C,@(x1,x2)gaussianKernel(x1,x2,sigma));
predictions = svmPredict(model,Xval);
minError = mean(double(predictions ~= yval));

for C = gap
    for sigma = gap
        model = svmTrain(X,y,C,@(x1,x2)gaussianKernel(x1,x2,sigma));
        predictions = svmPredict(model,Xval);
        error = mean(double(predictions ~= yval));
        
        if error < minError
            minError = error;
            optim_C = C;
            optim_sigma = sigma;
        end;
    end;
end;
C = optim_C;
sigma = optim_sigma;


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

end