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lowRankKernelSubspaceClustering.m
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lowRankKernelSubspaceClustering.m
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function [missrate, A, grps, obj, resid] = lowRankKernelSubspaceClustering(X, s, lambda1, lambda2, lambda3, kType, affine, outlier, param)
% Author: Pan Ji, University of Adelaide
% All rights reserved!
if(nargin<8)
outlier = false;
end
if(nargin<7)
affine = false;
end
if(nargin<6)
kType = 'pol';
end
if(nargin<5)
lambda3 = 1;
end
if(nargin<4)
lambda2 = 1;
end
if(nargin<3)
lambda1 = 1;
end
% normalize data to lie in [-1 1]
if(max(X(:)) <= 1 && min(X(:)) >= -1)
else
X = X - min(X(:));
X = X/(max(X(:))+1);
X = 2*(X - 0.5);
end
[~, N] = size(X);
alpha = param.alpha;
if(strcmpi(kType,'pol'))
a = param.a;
b = param.b;
KG = polynKernelMatrix(X,a,b); % hopkins 2.2 3 %two frames 3.4 2 % yale face 12 2
elseif(strcmpi(kType,'lin'))
KG = polynKernelMatrix(X,0,1);
elseif(strcmpi(kType,'rbf'))
sig = std(sqrt(sum(X.^2)));
KG = rbfKernelMatrix(X, 1*sig);
else
disp(['Select the kernel types: pol, lin, or rbf! Pol is used by default.']);
KG = polynKernelMatrix(X,1.4,3);
end
% ADMM parameters
epsilon = 1e-6; rho = 1e-8; maxIter = 1e3; eta = param.eta; max_rho = 1e10;
% Initializations
[U,S,V] = svd(KG);
B = U*sqrt(S)*V';
K = KG;
obj = [];
resid = [];
if(~outlier)
if(~affine)
Y2 = zeros(N, N);
A = zeros(N,N);
iter= 0;
while(iter<maxIter)
iter = iter+1;
% Update C
tmp = A + Y2/rho;
C = max(0, abs(tmp)-lambda1/rho) .* sign(tmp);
C = C - diag(diag(C));
% Update A
K = B'*B;
lhs = lambda2*K + rho*eye(N);
rhs = lambda2*K - Y2 + rho*(C-diag(diag(C)));
A = lhs\rhs;
% Update B
tmp = KG-lambda2*(eye(N)-2*A'+A*A')/(2*lambda3);
B = solveB(tmp, lambda3);
leq2 = A - (C - diag(diag(C)));
stpC = max(abs(leq2(:)));
if(iter == 1 || mod(iter,50)==0 || stpC<epsilon)
disp(['iter ' num2str(iter) ',rho=' num2str(rho,'%2.1e') ',stopALM=' num2str(stpC,'%2.3e')]);
end
if(stpC<epsilon)
break;
else
Y2 = Y2 + rho*leq2;
rho = min(max_rho,rho*eta);
end
end
else %affine
Y2 = zeros(N, N);
y3 = zeros(1,N);
A = zeros(N,N);
iter= 0;
while(iter<maxIter)
iter = iter+1;
% Update C
tmp = A + Y2/rho;
C = max(0, abs(tmp)-lambda1/rho) .* sign(tmp);
C = C - diag(diag(C));
% Update A
K = B'*B;
lhs = lambda2*K + rho*eye(N) + rho*ones(N,N);
rhs = lambda2*K - Y2 - ones(N,1)*y3 + rho*(C-diag(diag(C))+ones(N,N));
A = lhs\rhs;
% Update B
tmp = KG-lambda2*(eye(N)-2*A'+A*A')/(2*lambda3);
B = solveB(tmp, lambda3);
leq2 = A - (C - diag(diag(C)));
leq3 = sum(A) - ones(1,N);
obj(iter) = sum(svd(B)) + lambda1*sum(abs(C(:))) + ...
0.5*lambda2*trace((eye(N)-2*A+A*A')*(B'*B)) + ...
0.5*lambda3*norm(KG-B'*B,'fro')^2;
resid(iter) = max(norm(leq2,'fro'),norm(leq3));
stpC = max(abs(leq2(:)));
stpC2 = max(abs(leq3));
stpC = max(stpC, stpC2);
if(iter == 1 || mod(iter,50)==0 || stpC<epsilon)
disp(['iter ' num2str(iter) ',rho=' num2str(rho,'%2.1e') ',stopALM=' num2str(stpC,'%2.3e')]);
end
if(stpC<epsilon)
break;
else
Y2 = Y2 + rho*leq2;
y3 = y3 + rho*leq3;
rho = min(max_rho,rho*eta);
end
end
end
else% outliers
if(~affine)
%Y1 = zeros(N, N);
Y2 = zeros(N, N);
Y4 = zeros(N, N);
A = zeros(N,N);
E = zeros(N,N);
iter= 0;
while(iter<maxIter)
iter = iter+1;
% Update C
tmp = A + Y2/rho;
C = max(0, abs(tmp)-lambda1/rho) .* sign(tmp);
C = C - diag(diag(C));
% Update A
K = B'*B;
lhs = lambda2*K + rho*eye(N);
rhs = lambda2*K - Y2 + rho*(C-diag(diag(C)));
A = lhs\rhs;
% Update B
tmp = KG - E - (0.5*lambda2*(eye(N)-2*A'+A*A')-Y4)/rho;
B = solveB(tmp, rho);
% Update E
tmp = KG - B'*B + Y4/rho;
E = max(0,tmp - lambda3/rho)+min(0,tmp + lambda3/rho);
%E = solve_l1l2(tmp,lambda3/rho);
leq2 = A - (C - diag(diag(C)));
leq4 = KG - B'*B - E;
stpC = max(abs(leq2(:)));
stpC2 = max(abs(leq4(:)));
stpC = max(stpC, stpC2);
if(iter == 1 || mod(iter,50)==0 || stpC<epsilon)
disp(['iter ' num2str(iter) ',rho=' num2str(rho,'%2.1e') ',stopALM=' num2str(stpC,'%2.3e')]);
end
if(stpC<epsilon)
break;
else
Y2 = Y2 + rho*leq2;
Y4 = Y4 + rho*leq4;
rho = min(max_rho,rho*eta);
end
end
else
%Y1 = zeros(N, N);
Y2 = zeros(N, N);
y3 = zeros(1, N);
Y4 = zeros(N, N);
A = zeros(N, N);
E = zeros(N, N);
iter= 0;
while(iter<maxIter)
iter = iter+1;
% Update C
tmp = A + Y2/rho;
C = max(0, abs(tmp)-lambda1/rho) .* sign(tmp);
C = C - diag(diag(C));
% Update A
K = B'*B;
lhs = lambda2*K + rho*eye(N) + rho*ones(N,N);
rhs = lambda2*K - Y2 - ones(N,1)*y3 + rho*(C-diag(diag(C))+ones(N,N));
A = lhs\rhs;
% Update B
%tmp = 0.5*(K - E + KG + (Y1+Y4)/rho);
tmp = KG - E - (0.5*lambda2*(eye(N)-2*A'+A*A')-Y4)/rho;
B = solveB(tmp, rho);
% Update E
tmp = KG - B'*B + Y4/rho;
E = max(0,tmp - lambda3/rho)+min(0,tmp + lambda3/rho);
%E = solve_l1l2(tmp,lambda3/rho);
leq2 = A - (C - diag(diag(C)));
leq3 = sum(A) - ones(1,N);
leq4 = KG - B'*B - E;
obj(iter) = sum(svd(B)) + lambda1*sum(abs(C(:))) + ...
0.5*lambda2*trace((eye(N)-2*A+A*A')*(B'*B)) + ...
lambda3*sum(abs(E(:)));
resid(iter) = max(max(norm(leq2,'fro'),norm(leq3)), norm(leq4,'fro'));
stpC = max(abs(leq2(:)));
stpC2 = max(max(abs(leq3)), max(abs(leq4(:))));
stpC = max(stpC, stpC2);
if(iter == 1 || mod(iter,50)==0 || stpC<epsilon)
disp(['iter ' num2str(iter) ',rho=' num2str(rho,'%2.1e') ',stopALM=' num2str(stpC,'%2.3e')]);
end
if(stpC<epsilon)
break;
else
%Y1 = Y1 + rho*leq1;
Y2 = Y2 + rho*leq2;
y3 = y3 + rho*leq3;
Y4 = Y4 + rho*leq4;
rho = min(max_rho,rho*eta);
end
end
end
end
A = BuildAdjacency(thrC(C,alpha));
grp = SpectralClustering(A, max(s));
grps = bestMap(s,grp);
missrate = sum(s(:) ~= grps(:)) / length(s);
end
function [E] = solve_l1l2(W,lambda)
n = size(W,2);
E = W;
for i=1:n
E(:,i) = solve_l2(W(:,i),lambda);
end
end
function [x] = solve_l2(w,lambda)
% min lambda |x|_2 + |x-w|_2^2
nw = norm(w);
if nw>lambda
x = (nw-lambda)*w/nw;
else
x = zeros(length(w),1);
end
end