Big data blind separation

Data or signal separation is one of the critical areas of data analysis. In this work, the problem of non-negative data separation is considered. The problem can be briefly described as follows: given X ∈ R^m×N, find A ∈ R^m×n and S ∈ R₊ ^n×N such that X = AS. Specifically, the problem with sparse locally dominant sources is addressed in this work. Although the problem is well studied in the literature, a test to validate the locally dominant assumption is not yet available. In addition to that, the typical approaches available in the literature sequentially extract the elements of the mixing matrix. In this work, a mathematical modeling-based approach is presented that can simultaneously validate the assumption, and separate the given mixture data. In addition to that, a correntropy-based measure is proposed to reduce the model size. The approach presented in this paper is suitable for big data separation. Numerical experiments are conducted to illustrate the performance and validity of the proposed approach.