Effect of step-by-step estimation technique on uniqueness of solution in nonnegative matrix factorization minimizing quasi-L1 norm

Abstract

Nonnegative matrix factorization (NMF) is a linear nonnegative approximate data representation technique. NMF is often used to solve blind signal separation (BSS) problem. We had used a basic NMF algorithm named ISRA and our original algorithm named QL1-NMF to analyze the environmental electromagnetic data in extremely low frequency (ELF) band. In previous research, we found that QL1-NMF works more robust than ISRA when our data includes many outliers. However, both algorithms have a problem that their solutions are not unique. In this paper, we try to estimate signals step-by-step. We research the effect which this technique has on the uniqueness of solutions.