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% this is main function comes from my AAAI 2017 paper. I will upload the whole package after the journal version is finished
function [W,history]=admm_shoe(X,Y,M,alpha,beta,rho,label_size)
%W=inv(X'*X+beta*eye(size(X,2)))*X'*Y;
W=zeros(size(X,2),size(Y,2));
%V=W*M;
V=zeros(size(W*M));
u=zeros(size(X,2),size(M,2));
[nInstance,nFeat]=size(X);
MAXITER =100;
iter = 1;
groups=label_size;
nTags=size(Y,2);
alpha_ij=alpha;
%U_2=data.U2;
%Lambda_2=data.Lambda2;
while(iter <= MAXITER)
fprintf('ITERATION %d\n',iter);
tic;
%%%% update W
[U_1,Lambda_1]=eig(X'*X);
[U_2,Lambda_2]=eig(rho/2*M*M'+beta*eye(size(M,1)));
Q=U_1'*(X'*Y+rho/2*(V+u./rho)*M')*U_2;
for i=1:size(Q,1)
for j=1:size(Q,2)
W_tild(i,j)=Q(i,j)/(Lambda_1(i,i)+Lambda_2(j,j));
end
end
W=U_1*W_tild*U_2';
time=toc;
fprintf('Time taken for W Update %f \n',time);
old_V=V;
Z=W*M-u./rho;
%%% update V
tic;
for i=1:nFeat
for k=1:groups
index_start=nTags*(k-1)+1;
index_end=nTags*k;
group_V{k}=updateV(alpha_ij,rho,Z(i,index_start:index_end));
end
V(i,:)=cell2mat(group_V(1:groups));
end
time=toc;
fprintf('Time taken for V Update %f \n',time);
% assert(~isequal(V,old_V));
u = u + rho*(V-W*M);
iter = iter + 1;
r = V-W*M;
s = rho*(V-old_V)*M';
history.obj(iter) = calcObj(X,Y,V,W,M,beta,alpha_ij,rho,u,nFeat,nTags,groups);
if iter==MAXITER
history.W{iter}=W;
history.V{iter}=V;
history.u{iter}=u;
end
fprintf('the objective function error is %f \n', history.obj(iter));
rho=min(rho*1.1,1e9);
if iter>2
if history.obj(iter-1)-history.obj(iter)<0.0001
break;
end
end
% eps_primal = RELTOL*max([norm(W*M,'fro'),norm(V,'fro')]);
% eps_dual = RELTOL*max([norm(W*M,'fro'),norm(V,'fro')]);
%
% %
% if norm(r) < eps_primal && norm(s) < eps_dual
% fprintf('FINISHED\n');
% break
% elseif norm(r) > SCALETOL*norm(s,'fro')
% rho=INC_FACTOR*rho;
% fprintf('Rho changed to %f\n',rho);
% elseif norm(s) > SCALETOL*norm(r,'fro')
% rho=rho/DEC_FACTOR;
% fprintf('Rho changed to %f\n',rho);
% end
%
end
function obj=calcObj(X,Y,V,W,M,beta,alpha_ij,rho,u,nFeat,nTags,nGroup)
loss=norm(X*W-Y,'fro')^2+beta*norm(W,'fro')^2+rho/2*norm((V-W*M),'fro')^2+trace(u'*(V-W*M));
tmp=0;
for i=nFeat
for j=1:nGroup
tmp=tmp+alpha_ij*norm(V(i,(nTags*(j-1)+1):(nTags*j)));
end
end
obj=loss+tmp;
function v=updateV(alpha_ij,rho,Z)
if norm(Z) <= alpha_ij/rho
v=zeros(size(Z));
else
v=Z*(norm(Z) - (alpha_ij/rho))/norm(Z);
end