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polymicro.m
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function [W,X,M,beta,nits] = polymicro(Y,K,draw)
%[W,Mu,M,beta] = multi_garrote(Y,K,Nits,alpha,draW)
%
[J,T]=size(Y);
[~,~,U]=svd(Y',0);
W=U(:,1:K);
M=(1/K)*ones(K,T); %M=0.45 + 0.1*rand(K,T);
%%% Pass true M
% s = zeros(K,T);
% s(1,:) = sin((1:T)/10)>0.8;
% %s(2,:) = sin((1:T)/100)>0.5;
% s(3,:) = sin((1:T)/1000)>0.2;
% s(2,find(sum(s,1) == 0)) = 1;
% M = s;
% oldM = M;
X = rand(K,T);
%%% Pass true X
% X = 0.1*bsxfun(@times,sin(bsxfun(@plus,bsxfun(@times,repmat(1:T,K,1),[1,2,3]'/10^2),[5,10,15]')) ...
% + cos(bsxfun(@plus,bsxfun(@times,repmat(1:T,K,1),[3,2,1]'/10^2),[2,4,19]')),[17,4,5]');
% oldX = X;
beta=1/mean(mean(Y.*Y));
gamma = -0.52;
count=1;
Nits = 3000;
if draw==1,
t_arr=zeros(1,ceil(Nits/10));
beta_arr=zeros(1,ceil(Nits/10));
mact=zeros(K,ceil(Nits/10));
err=zeros(1,ceil(Nits/10));
no_X=zeros(K,ceil(Nits/10));
no_W=zeros(K,ceil(Nits/10));
figure(1)
end
converged = 0;
nits = 0;
logistic = @(x)1/(exp(-x)+1);
while ~converged
%%% W
% tmp = zeros(K,1);
% for k = 1:K
% for t = 1:T
% tmp(k) = tmp(k) + X(k,t)^2*(M(k,t) - M(k,t)^2);
% end
% end
MoX = M.*X;
oldW = W;
% % W = Y*MoX'/((MoX*MoX') + MoX*((1-M).*X)');
% for t = 1:size(X,2)
% W(:,t) = Y(:,t)*MoX/((MoX*MoX') + diag(MoX*((1-M).*x)')));
% end
if rcond(MoX*MoX') < 10e-10
keyboard
end
%W = 0.95*W + 0.05*(Y*MoX'/(MoX*MoX' + diag(sum(X.^2.*(M - M.^2),2))));
%%% dropout
% D = abs(randi(2,J,K)-1);
% W = D.*W + (1-D).*(Y*MoX'/(MoX*MoX' + diag(sum(X.^2.*(M - M.^2),2))));
%%% soft dropout
D = abs(rand(J,K));
% for i=1:K
% most_correlated_maps = abs(corr(W(:,1),Y))>0.5;
% W(:,i) = Y(:,most_correlated_maps)*MoX(i,most_correlated_maps)'/(MoX(i,most_correlated_maps)*MoX(i,most_correlated_maps)' + diag(sum(X.^2.*(M - M.^2),2)));
% W(:,i) = D.*oldW(:,i) + (1-D).*W(:,i);
% end
W = D.*W + (1-D).*(Y*MoX'/(MoX*MoX' + diag(sum(X.^2.*(M - M.^2),2))));
%%% X
% led1 = zeros(K,T);
% led2 = zeros(K,T);
% for t = 1:T
% wsq = zeros(K,1);
% for l = 1:K
% for j = 1:J
% for k = 1:K
% led1(l,t) = led1(l,t) + W(j,k)*W(j,l)*M(k,t)*X(k,t);
% end
% wsq(l) = wsq(l) + W(j,l)^2;
% end
% led2(l,t) = X(l,t)*(1-M(l,t))*wsq(l);
% end
% end
%
Wsq = W'*W;
diagww = diag(Wsq);
WY = W'*Y;
oldX = X;
for t = 1:size(X,2)
tmp = (Wsq*diag(M(:,t)) + diag((1-M(:,t)).*diagww));
if rcond(tmp) < 10e-10
keyboard
end
%D = abs(randi(2,K,1)-1);
D = abs(rand(K,1));
X(:,t) = D.*X(:,t) + (1-D).*(tmp\(WY(:,t)));
end
%%% M
yrec = W*(M.*X);
oldM = M;
% for l=1:K
% for t=1:T
% led1 = 0;
% led2 = 0;
% for j=1:J
% led1 = led1 + (Y(j,t)-yrec(j,t))*W(j,l)*X(l,t);
% led2 = led2 + W(j,l)^2*X(l,t)^2*(1-2*M(l,t));
% end
% M(l,t) = 0.95*M(l,t) + 0.05*logistic(gamma+beta*led1-beta/2*led2);
% end
% end
%M = 0.95*M + 0.05*arrayfun(logistic,gamma + beta*X.*(bsxfun(@times,X.*(M-.5),diagww) + W'*(Y-yrec)));
%D = abs(randi(2,K,T)-1);
D = abs(rand(K,T));
M = D.*M + (1-D).*arrayfun(logistic,gamma + beta*X.*(bsxfun(@times,X.*(M-.5),diagww) + W'*(Y-yrec)));
%%% beta
%
% led1 = 0;
% led2 = 0;
% for t = 1:T
% for j = 1:J
% yrec = 0;
% for k = 1:K
% yrec = yrec + M(k,t)*W(j,k)*X(k,t);
% led1 = led1 + W(j,k)^2*X(k,t)^2*M(k,t)^2-M(k,t);
% end
% led2 = led2 + (Y(j,t)-yrec);
% end
% end
%yrec = W*(M.*X);
%D = abs(randi(2,J,T)-1);
D = abs(rand(J,T));
yrec = D.*(W*(M.*X)) + (1-D).*yrec;
beta = 0.95*beta + 0.05*J*T/(sum(sum((Y-yrec).^2)) - sum(sum(W.^2*(X.^2.*(M.^2-M)))));
sumsumM = sum(sum(M));
gamma = 0.95*gamma - 0.05*log(sumsumM/(K*T-sumsumM));
if (draw==1)&&(rem(nits,10)==1),
Ms=M>0.5;
t_arr(count)=nits;
no_W(count)=norm(W);
no_X(count)=norm(X);
beta_arr(count)=beta;
gamma_arr(count)=gamma;
err(count)=norm(Y-yrec)/norm(Y);
mact(:,count)=sum(Ms,2);
subplot(3,2,1),plot(t_arr(1:count),no_W(1:count)),title('||W||')
subplot(3,2,2),plot(t_arr(1:count),err(1:count)),title('Rel Rec Error')
subplot(3,2,3),plot(t_arr(1:count),no_X(1:count)), title('||Mu||')
%subplot(3,2,5),plot3(U(:,1)'*Y,U(:,2)'*Y,U(:,3)'*Y,'.')
subplot(3,2,5),plot(t_arr(1:count),gamma_arr(1:count)), title('\gamma')
grid
subplot(3,2,4),plot(mact(:,1:count)')
subplot(3,2,6), plot(t_arr(1:count),beta_arr(1:count)),title('\beta')
drawnow
count=count+1;
end
tol = 10^(-4);
converged1 = norm(M - oldM)/norm(oldM) < tol;
converged2 = norm(W - oldW)/norm(oldW) < tol;
converged3 = norm(X - oldX)/norm(oldX) < tol;
converged = converged1*converged2*converged3;
nits = nits +1;
if nits>1500
converged = 1;
end
end