Non-negative Matrix-Set Factorization

Non-negative matrix factorization (NMF) is a recently developed, biologically inspired method for nonlinearly finding purely additive, sparse, linear, low-dimension representations of non-negative multivariate data to consequently make latent structure, feature or pattern in the data clear. Although it has been successfully applied in several research fields, it is confronted with three main problems, unsatisfactory accuracy, bad generality and high computational load, while the processed data appear as matrices. In this paper, a new method coined non-negative matrix-set factorization (NMSF) is developed to overcome the problems and an efficient, strictly monotonically convergent algorithm of NMSF is put forward. As opposed to NMF, NMSF directly processes original data matrices rather than vectorization results of them. Theoretical analysis and experimental results show that NMSF has higher accuracy, better generality and lower computational load than NMF.