Collaborative Representation Classifier with Training and Validation Data

With CRC I can simplify the equation to

I have training data, validation data and test data. How do I go about implementing this. This is what I have done so far. I just need to implement CRC but I am losts as to how to do it with training data and validation data.

load AR_DAT.mat

figure; imagesc(reshape(NewTrain_DAT(:,1),60,43)); colormap(gray)

NewTrain_DAT = double(NewTrain_DAT);

NewTest_DAT = double(NewTest_DAT);

% cross-validation

nfold = 5; % k-fold cross-validation

C = length(unique(trainlabels));

%% Use leave-one-out to tune regularization parameter

lambda = [0.005, 0.05, 0.01, 0.1, 0.5, 1, 2, 5]; % please set/tune the range yourself

Acc = zeros(1,length(lambda)); % record the accuracy for each lambda

nfoldAcc = zeros(1,nfold);

for k = 1:length(Acc)

for i = 1:nfold

XTrain = []; % new training set, for the next fold this will be cleared and construct a new one

XVal = []; % valiation set

LTrain = []; % lables

LVal = [];

for j = 1:C

data = NewTrain_DAT(:, trainlabels==j); % class j samples

XVal = [XVal, data(:,i)]; % leave the ith sample out for validation

LVal = [LVal, j];

data(:,i) = []; % the rest for training

XTrain = [XTrain, data];

LTrain = [LTrain, j*ones(1,size(data,2))];

end

%nfoldAcc(i) = CRC(XTrain, XVal, LTrain, LVal, lambda(k)); %need to create this function

end

Acc(k) = mean(nfoldAcc); % the average accuracy for lambda(k)

end

I do not want the answer. I just want some assistance on how to go from here. I am mostly confused about the training data and validation data.

Answer 1

[Shashank Gupta]

Hey Shay,

You can probably first start with attacking a simpler problem by just taking training set and test set and omitting validation data for now, things become slightly easy to understand when there are less complication from validation sets. The equation of CRC have "X" and "y", first you need to understand, here "X" will be Xtrain(taking notation from your code) and "y" will be "Ltest", use the equation and find out "P" (rho cap) and use this for further processing. So in simple terms the equation will look something like,

% Projection matrix
H = inv((Xtrain' * Xtrain + lambda * eye(size(Xtrain,2)))) * Xtrain';
% finding P
rho_hat = H * Ltest;

I hope this clear some confusion about the data classificaiton.

Cheers