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

Algorithm 1

(OPL).

Set  A, X, % Initialization

   𝜂^𝑗(𝑋)=2(𝐀^𝑇𝐀𝟏_𝐽)_𝑗,

For  𝑘=1,2,…, % Inner iterations for X

   𝐆_𝑋=𝐀^𝑇(𝐀𝐗−𝐘), % Gradient with respect to X

   𝐗←𝑃_Ω[𝐗−diag{𝜂_𝑗}𝐆_𝑋], % Updating

End