Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems

Algorithm 4

% Barzilai-Borwein gradient projection (GPSR-BB) algorithm

%

function [X] = nmf_gpsr_bb(A,Y,X,no_iter)

%

% [X] = nmf_gpsr_bb(A,Y,X,no_iter) finds such matrix X that solves

% the equation AX = Y subject to nonnegativity constraints.

%

% INPUTS:

% A - system matrix of dimension [I by J]

% Y - matrix of observations [I by T]

% X - matrix of initial guess [J by T]

% no_iter - maximum number of iterations

%

% OUTPUTS:

% X - matrix of estimated sources [J by T]

%

% #########################################################################

% Parameters

alpha_min = 1E-8; alpha_max = 1;

alpha = .1*ones(1,size(Y,2));

B = A’*A; Yt = A’*Y;

for k=1:no_iter

 G = B*X - Yt;

 delta = max(eps, X - repmat(alpha,size(G,1),1).*G) - X;

 deltaB = B*delta;

 lambda = max(0, min(1, -sum(delta.*G,1)./(sum(delta.*deltaB,1) + eps)));

 X = max(eps,X + delta.*repmat(lambda,size(delta,1),1));

 gamma = sum(delta.*deltaB,1) + eps;

 if gamma

   alpha = min(alpha_max, max(alpha_min, sum(delta.̂‌2,1)./gamma ));

 else

   alpha = alpha_max;

 end

end