feature_sign.zip_battle_feature sign _sparse coding_稀疏_稀疏编码

% Feature sign search % code by Wang Jinjun @ NEC Research Lab America % reference % Efficient sparse coding algorithms % Honglak Lee Alexis Battle Rajat Raina Andrew Y. Ng % Computer Science Department % Stanford University % Stanford, CA 94305 %=================HOW TO================= % B, your feature matrix % y, observation vector % lambda, a Lagrange multiplier. You can set to 0.00001, try to tune it to optimize the results. % init_x is the guessed value of x. You can set it to all zero. Also, try to optimize it. function [x]=feature_sign(B,y,lambda,init_x) %%%%%%min_x 0.5\|y-Bx\|_2^2+lambda\|x\|_1 nbases=size(B,2); OptTol = 1e-5; if nargin < 4, x=zeros(nbases, 1); else x = init_x; end; theta=sign(x); %sign flag a=(x~=0); %active set optc=0; By=B'*y; B_h=B(:,a); x_h=x(a); Bx_h=B_h*x_h; all_d=2*(B'*Bx_h-By); [ma mi]=max(abs(all_d).*(~a)); while optc==0, optc=1; if all_d(mi)>lambda+1e-10, theta(mi)=-1; a(mi)=1; b=B(:,mi); x(mi)=(lambda-all_d(mi))/(b'*b*2); elseif all_d(mi)<-lambda-1e-10, theta(mi)=1; a(mi)=1; b=B(:,mi); x(mi)=(-lambda-all_d(mi))/(b'*b*2); else if sum(a)==0, lambda=ma-2*1e-10; optc=0; b=B(:,mi); x(mi)=By(mi)/(b'*b); break; end end opts=0; B_h=B(:,a); x_h=x(a); theta_h=theta(a); while opts==0, opts=1; if size(B_h,2)<=length(y), BB=B_h'*B_h; x_new=BB\(B_h'*y-lambda*theta_h/2); o_new=L1_cost(y,B_h,x_new,lambda); %cost based on changing sign s=find(sign(x_new)~=theta_h); x_min=x_new; o_min=o_new; for j=1:length(s), zd=s(j); x_s=x_h-x_h(zd)*(x_new-x_h)/(x_new(zd)-x_h(zd)); x_s(zd)=0; %make sure it's zero o_s=L1_cost(y,B_h,x_s,lambda); if o_s<o_min, x_min=x_s; o_min=o_s; end end else d=x_h-B_h'*((B_h*B_h')\(B_h*x_h)); q=x_h./(d+eps); x_min=x_h; o_min=L1_cost(y,B_h,x_h,lambda); for j=1:length(q), zd=q(j); x_s=x_h-zd*d; x_s(j)=0; %make sure it's zero o_s=L1_cost(y,B_h,x_s,lambda); if o_s<o_min, x_min=x_s; o_min=o_s; end end end x(a)=x_min; a=(x~=0); theta=sign(x); B_h=B(:,a); x_h=x(a); theta_h=theta(a); Bx_h=B_h*x_h; active_d=2*(B_h'*(Bx_h-y))+lambda*theta_h; if ~isempty(find(abs(active_d)>OptTol)), opts=0; end end all_d=2*(B'*Bx_h-By); [ma mi]=max(abs(all_d).*(~a)); if ma>lambda+OptTol, optc=0; end end return; function cost=L1_cost(y,B,x,lambda) tmp = y-B*x; cost = tmp'*tmp+lambda*norm(x,1); return