An Algebraic Method for Approximate Rank One Factorization of Rank Deficient Matrices

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Abstract

In this paper we consider the problem of finding approximate common rank one factors for a set of matrices. Instead of jointly diagonalizing the matrices, we perform calculations directly in the problem intrinsic domain: we present an algorithm, AROFAC, which searches the approximate linear span of the matrices using an indicator function for the rank one factors, finding specific single sources. We evaluate the feasibility of this approach by discussing simulations on generated data and a neurophysiological dataset. Note however that our contribution is intended to be mainly conceptual in nature.