dspca.m

关于有直接稀疏PCA的方法

function [U,X,x,F,k,dualitygap,cputime,perceigs]=DSPCA(A,rho,gapchange,maxiter,info,algo)
% Wrapper function for sparse_rank_one_mex
% DSPCA finds a sparse rank-one approximation to 
% a given symmetric matrix A, by solving the SDP
% min_U lambda_max(A+X) : X = X', abs(X(i,j)) <= rho, 1<=i,j<= n
% and its dual:
% max_X Tr(UA) - rho sum_ij |U_ij| : U=U', U \succeq 0, Tr(U)=1
% ***	inputs: ***
% A                 nxn symmetric matrix (left unchanged)
% n                 problem size
% rho              non-negative scalar 
% gapchange required change in gap from first gap (default: 1e-4) 
% MaxIter		maximum number of iterations
% info             controls verbosity: 0 silent, n>0 frequency of progress report
% k0               0 if cold start, k0 if WarmStart (total number of iterations in previous run)
% F0               Average gradient (for warm start, Fmat is updated)
% X0               symmetric matrix that solves the above SDP 
 
% ***	outputs: ***
% U                 symmetric matrix that solves the above SDP 
% X                 dual variable, solves the dual SDP 
% x                 largest eigenvector of U 
% F                 Average gradient
% k                 number of iterations run
% dualitygap  vector of duality gaps at designated iterations
% cputime      vector of cumulative cpu times at designated iterations
% perceigs     vector of percentage of eigenvalues used (in partial
%                       eigenvalue decomposition) at designated iterations

% Refer to d扐spremont, A., El Ghaoui, L., Jordan, M. & Lanckriet, G. R. G. (2005), 
% 慉 direct formulation for sparse PCA using semidefinite programming