mssvdd.m

% Input:  Traindata = Contains training data for each modality as a cell Traindata{data1},Traindata{data2}
%         Trainlabel = Contains training labels for each modality as a cell Trainlabel{data1},Trainlabel{data1}
%         maxIter = Maximum number of iterations
%         numofmodes = Total number of modalities
%         Cval = Value of hyperparameter C
%         omega = Regularizaterm term
%         Bta = Controling the importance of the regularization term
%         eta = Used as step size for gradient
%         D = dimensionality of data in original feature space
%         d = dimensionality of data in lower dimension
% Output: Model = Trained model
%         Q = Contains projection matrices for each modality, Q{modality1},Q{modality2}

function [Model,Q]=mssvdd(Traindata,Trainlabel,maxIter,numofmodes,Cval,omega,Bta,eta,D,d)
D{1}=size(Traindata{1},1);
D{2}=size(Traindata{2},1);
%Initialize the Q{i} for each modality
for i=1:numofmodes
    tempQ = pca(Traindata{i}');
    Q{i}=tempQ(:,1:d)';
    reducedData{i} = Q{i} * Traindata{i};
end

for ii=1:maxIter
    ReducedcombinedTraindata=[];
    combinedTrainLabel=[];
    for i=1: numofmodes
        ReducedcombinedTraindata=[ReducedcombinedTraindata reducedData{i}];
        combinedTrainLabel=[combinedTrainLabel; Trainlabel];
    end
    
    Model = svmtrain(combinedTrainLabel, ReducedcombinedTraindata', ['-s 5 -t 0 -c ',num2str(Cval)]);
    
    %Get the bigAlphaVector which is vector of all alphas for all concatenated data
    Alphaindex=Model.sv_indices; %Indices where alpha is non-zero
    AlphaValue=Model.sv_coef; %values of Alpha
    BigAlphavector=zeros(size(ReducedcombinedTraindata,2),1); %Generate a vector of zeros
    for qq=1:size(Alphaindex,1)
        BigAlphavector(Alphaindex(qq))=AlphaValue(qq);
    end
    %Here get the Alphavector{i} for corresponding modality
    j=0; i=1;
    while(j<size(BigAlphavector,1))
        Alphavector{i}= BigAlphavector(j+1:j+size(reducedData{i},2));
        j=j+size(reducedData{i},2);
        i=i+1;
    end
    
    const_d= constraintmssvdd(omega,Cval,Q,Traindata,Alphavector,numofmodes); %Type of regularization term used
    
    for M_num=1:numofmodes %M_num = mode number
        %compute the gradient and update the matrix Q{i}
        Sum1=2*Q{M_num}*Traindata{M_num}*diag(Alphavector{M_num})*Traindata{M_num}';
        
        loopsum2j=zeros(d,D{M_num});
        for j=1:numofmodes
            sum=Q{j}*Traindata{j}*Alphavector{j};
            loopsum2j=loopsum2j+sum;
        end
        Sum2=2*loopsum2j*diag(Alphavector{M_num}'*Traindata{M_num}');
        
        Grad{M_num} = Sum1-Sum2+(Bta*const_d{M_num});
        Q{M_num} = Q{M_num} - eta*Grad{M_num}; % I
        %orthogonalize and normalize Q{i}
        Q{M_num} = OandN_Q(Q{M_num});
        reducedData{M_num} = Q{M_num} * Traindata{M_num};
    end
end
end