%
%  Take Home Exam:  Problem 1
%

load MenAndWomen2;  %This loads the data into matrix Y

%
%  Separate the data into training and testing sets.
%
Women=Y(:,1:13);
Men=Y(:,14:26);

%
% Randomly select 7 columns from Women, 7 columns from Men for training,
% and the remaining 6 in each class for testing (4 sets in all).
% 


%
% Compute the mean "face" for women, men separately, then mean-subtract
% (like you did in the movie data).
%
% Find the SVD of each, and keep the first three columns of the appropriate
% matrix for your basis vectors.
%


% Test the classifier:
misclassW=0; misclassM=0;
for j=1:6
    %Testing the 6 columns of women (one at a time)
    x=       %Mean subtract the women's mean.
    xhat=    %Projection to the col space for women
    d1=norm(x-xhat);  
    
    x=       %Mean subtract the men's mean
    xhat=    %Projection to the col space for men
    d2=norm(x-xhat);
    if d1>d2
        misclassW=misclassW+1;
    end
    
    %Testing the 6 columns of men (one at a time)
    x=        %Mean subtract the women's mean
    xhat=     %Projection to the col space for women
    d1=norm(x-xhat);
    
    x=        %Mean subtract the men's mean
    xhat=     %Projection to the col space for men
    d2=norm(x-xhat);
    if d1<d2
        misclassM=misclassM+1;
    end    
end
%The percentage misclassified (will print to the command window)
misclass=(misclassM+misclassW)/12