%--------------------------------------------------------------------------
% This function takes the D x N matrix of N data points and write every
% point as a sparse linear combination of other points.
% Xp: D x N matrix of N data points
% cst: 1 if using the affine constraint sum(c)=1, else 0
% Opt: type of optimization, {'L1Perfect','L1Noisy','Lasso','L1ED'}
% lambda: regularizartion parameter of LASSO, typically between 0.001 and
% 0.1 or the noise level for 'L1Noise'
% CMat: N x N matrix of coefficients, column i correspond to the sparse
% coefficients of data point in column i of Xp
%--------------------------------------------------------------------------
% Copyright @ Ehsan Elhamifar, 2010
%--------------------------------------------------------------------------
function CMat = SparseCoefRecovery(Xp,cst,Opt,lambda)
if (nargin < 2)
cst = 0;
end
if (nargin < 3)
Opt = 'Lasso';
end
if (nargin < 4)
lambda = 0.001;
end
D = size(Xp,1);
N = size(Xp,2);
for i = 1:N
y = Xp(:,i);
if i == 1
Y = Xp(:,i+1:end);
elseif ( (i > 1) && (i < N) )
Y = [Xp(:,1:i-1) Xp(:,i+1:N)];
else
Y = Xp(:,1:N-1);
end
% L1 optimization using CVX
if cst == 1
if ( strcmp(Opt , 'Lasso') )
cvx_begin;
cvx_precision high
variable c(N-1,1);
minimize( norm(c,1) + lambda * norm(Y * c - y) );
subject to
sum(c) == 1;
cvx_end;
elseif ( strcmp(Opt , 'L1Perfect') )
cvx_begin;
cvx_precision high
variable c(N-1,1);
minimize( norm(c,1) );
subject to
Y * c == y;
sum(c) == 1;
cvx_end;
elseif ( strcmp(Opt , 'L1Noisy') )
cvx_begin;
cvx_precision high
variable c(N-1,1);
minimize( norm(c,1) );
subject to
norm( Y * c - y ) <= lambda;
sum(c) == 1;
cvx_end;
elseif ( strcmp(Opt , 'L1ED') )
cvx_begin;
cvx_precision high
variable c(N-1+D,1);
minimize( norm(c,1) );
subject to
[Y eye(D)] * c == y;
sum(c(1:N-1)) == 1;
cvx_end;
end
else
if ( strcmp(Opt , 'Lasso') )
cvx_begin;
cvx_precision high
variable c(N-1,1);
minimize( norm(c,1) + lambda * norm(Y * c - y) );
cvx_end;
elseif ( strcmp(Opt , 'L1Perfect') )
cvx_begin;
cvx_precision high
variable c(N-1,1);
minimize( norm(c,1) );
subject to
Y * c == y;
cvx_end;
elseif ( strcmp(Opt , 'L1Noisy') )
cvx_begin;
cvx_precision high
variable c(N-1,1);
minimize( norm(c,1) );
subject to
norm( Y * c - y ) <= lambda;
cvx_end;
elseif ( strcmp(Opt , 'L1ED') )
cvx_begin;
cvx_precision high
variable c(N-1+D,1);
minimize( norm(c,1) );
subject to
[Y eye(D)] * c == y;
cvx_end;
end
end
% place 0's in the diagonals of the coefficient matrix
if i == 1
CMat(1,1) = 0;
CMat(2:N,1) = c(1:N-1);
elseif ( (i > 1) && (i < N) )
CMat(1:i-1,i) = c(1:i-1);
CMat(i,i) = 0;
CMat(i+1:N,i) = c(i:N-1);
else
CMat(1:N-1,N) = c(1:N-1);
CMat(N,N) = 0;
end
end
SSC_2a.rar （15个子文件） 
SSC_1.0 
OutlierDetection.m 1KB missclassGroups.m 1KB Misclassification.m 734B DataProjection.m 1KB Lasso_001.mat 830KB 2a.mat 5KB SSC3c.asv 1KB SparseCoefRecovery.m 4KB SSC.m 3KB SpectralClustering.m 2KB BuildAdjacency.m 1KB SSC2a.asv 3KB Readme.tex 120B SSC3c.m 1KB SSC2a.m 3KB
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