pairwise_LRSSC_1view.m

%
% One step of ADMM for one view of pairwise multi-view LRSSC.
%
% -------------------------------------------------------
% Input:
%   X: mxn data matrix for one view; columns are samples
%   K: nxn kernel matrix current view
%   num_views: number of views
%   C1: nxn low-rank coefficient matrix for current view
%   C2: nxn sparse coefficient matrix for current view
%   C3: nxn consensus coefficient matrix for current view
%   C_sum: sum of nxn coefficient matrices for all views except current
%   Lambda1, Lambda2, Lambda3, Lambda4:  Lagrange multipliers
%   lambda: coefficients for low-rank, sparsity and consensus constraint
%   mu: penalty parameters in augmented Lagrangian
%   noisy: if true then use noisy variant
%
% Output:
%   C1: updated low-rank coefficient matrix for current view
%   C2: updated sparse coefficient matrix for current view
%   C3: updated consensus coefficient matrix for current view
%   Lambda1, Lambda2, Lambda3, Lambda4:  updated Lagrange multipliers
%
function [C1, C2, C3, Lambda1, Lambda2, Lambda3, Lambda4, A] = pairwise_LRSSC_1view(X, K, num_views, C1, C2, C3, C_sum, ...
    Lambda1, Lambda2, Lambda3, Lambda4, lambda, mu, noisy)

n = size(X,2);

% updating A
if ~noisy
    inv_A = inv(mu(1)*K+(mu(2)+mu(3)+mu(4))*eye(n));
    A = inv_A*(mu(1)*K+mu(2)*(C2-Lambda2/mu(2))+mu(3)*(C1-Lambda3/mu(3))+mu(4)*(C3-Lambda4/mu(4))+X'*Lambda1);
else
    inv_A = inv(K+(mu(2)+mu(3)+mu(4))*eye(n));
    A = inv_A*(K+mu(2)*(C2-Lambda2/mu(2))+mu(3)*(C1-Lambda3/mu(3))+mu(4)*(C3-Lambda4/mu(4)));
end

% updating C1,C2 and C3
C2 = soft_thresh(A+Lambda2/mu(2),lambda(2)/mu(2));
C2 = C2-diag(diag(C2));
C1 = sigma_soft_thresh(A+Lambda3/mu(3),lambda(1)/mu(3));
C3 = 1/(2*lambda(3)*(num_views-1)+mu(4))*(2*lambda(3)*C_sum+mu(4)*A+Lambda4);

% updating Lagrange multipliers
if ~noisy
    Lambda1 = Lambda1 + mu(1)*(X-X*A);
end
Lambda2 = Lambda2+mu(2)*(A-C2);
Lambda3 = Lambda3+mu(3)*(A-C1);
Lambda4 = Lambda4+mu(4)*(A-C3);

end