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))
%

param = [0.01 0.03 0.1 0.3 1 3 10 30] 
error = realmax();
for i=1:size(param,2)
    for j=1:size(param,2)
        C_i = param(i);
        sigma_j = param(j);
        
        model = svmTrain(X,y,C_i, @(x1, x2) gaussianKernel(x1, x2, sigma_j));
        predictions = svmPredict(model,Xval);
        temp = mean(double(predictions ~= yval));
        
        if temp < error
            error = temp;
            C = C_i;
            sigma = sigma_j;
        end
    end
end

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

end