How to label the training projections obtained by PCA to use for training SVM for classification? MATLAB

Question

I have a "training set" of images. I have formed the 'Eigenspace'. Now i need to label the projections to train the SVM. The projections of "face 1" to the Eigenspace has to be labelled +1 and the projections of all the other faces to the Eigenspace has to be labelled -1.

I don't know how to do this.Any suggestions would be really helpful!

I formed the eigenspace using the following :

    function [signals,V] = pca2(data)
    [M,N] = size(data); 
    data = reshape(data, M*N,1); % subtract off the mean for each dimension 
    mn = mean(data,2); 
    data = bsxfun(@minus, data, mean(data,1)); 
    % construct the matrix Y 
    Y = data'*data / (M*N-1); 
    [V D] = eigs(Y, 10); % reduce to 10 dimension 
    % project the original data 
    signals = data * V; 

Answer 1

If you are trying to recognize more than one person, you have to create one separate data file for each person, and one sepparate SVM for each person. This is because SVM are focused on two-class separation.

This is an example using libsvm for Matlab (here is the full code), supposing you have the data in a file:

[person1_label, person1_inst] = libsvmread('../person1');
[person2_label, person2_inst] = libsvmread('../person2');
[person3_label, person3_inst] = libsvmread('../person3');

model1 = svmtrain(person1_label, person1_inst, '-c 1 -g 0.07 -b 1');
model2 = svmtrain(person2_label, person2_inst, '-c 1 -g 0.07 -b 1');
model3 = svmtrain(person3_label, person3_inst, '-c 1 -g 0.07 -b 1');

To test one face, you need to apply all the models and get the max output (when using svmpredict you have to use '-b 1' to obtain the probability estimates.

Additionally, in Matlab you don't need to use svmread or svmwrite, you can pass directly the data:

training_data = [];%Your matrix that contains 4 feature vectors
person1_label =[1,1,-1,-1];
person2_label = [-1,-1,1,-1];
person3_label = [-1,-1,-1,1];

model1 = svmtrain(person1_label, person_inst, '-c 1 -g 0.07 -b 1');
model2 = svmtrain(person2_label, person_inst, '-c 1 -g 0.07 -b 1');
model3 = svmtrain(person3_label, person_inst, '-c 1 -g 0.07 -b 1');

Answer 2

label = ones(N,1);% N samples in total, +1 represents face 1
for i=1:N 
    % For each face image, you run
    [signals,V] = pca2(data); % ith data
    if ....  % other faces than face 1
        label(i) = -1;
    end
    face(i,:) = reshape(signals,1,[]);
end
model = svmtrain(label,face);

Answer 3

It seems that you cannot train the SVM... This is an example on how you can train a Matlab SVM:

%Generate 100 positive points (the data is a circle)
r = sqrt(rand(100,1)); % radius
t = 2*pi*rand(100,1); % angle
dataP = [r.*cos(t), r.*sin(t)]; % points

%Generate 100 negative points (the data is a circle)
r2 = sqrt(3*rand(100,1)+1); % radius
t2 = 2*pi*rand(100,1); % angle
dataN = [r2.*cos(t2), r2.*sin(t2)]; % points

data3 = [dataN;dataP];
theclass = ones(200,1);
theclass(1:100) = -1; %First 100 points are negative

%Train the SVM
cl = svmtrain(data3,theclass,'Kernel_Function','rbf');