subgradient3.m

function w=subgradient3(x,y,u,maxIter)
% This function is to find the optimal weights w.
% set bias b to be zero.
dim=size(x,2);
w=zeros(dim,1); % initial weights
N=size(x,1);
x=zscore(x);% standardization
C=0.01; % trade-off coeff.
% C=15
%% Training (Using Pegasos):
for iter1=1:maxIter
    % pick one data point in one iteration until MaxIter
    iter2=randi(N);
    if y(iter2)*w' * x(iter2,:)' <=1
       w=(1-u)*w + u*C*N*y(iter2)* x(iter2,:)'; 
    else
       w=(1-u)*w;
    end
end 
%% Training (Using mini-batch Pegasos):
a=1; % if a=0.01, is the same as Pegasos
k=a*N;
for iter1=1:maxIter
    S=randperm(N); % Shuffle the set
    S=S([1:k]);
    xx=x(S,:); % new data set
    yy=y(S);
    temp=zeros(dim,length(S));
    for iter2=1:length(S)
        % sub-gradient: iter for each data point in the subset for every
        % iteration
        if yy(iter2)*w' * xx(iter2,:)' <=1
           temp(:,iter2)=u*C*N*yy(iter2)* xx(iter2,:)';     
        else
           temp(:,iter2)=zeros(dim,1);
        end        
    end
    w=(1-u)*w + mean(temp,2);
end

end