Symmetric nonnegative matrix trifactorization

Abstract

The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of an n×n nonnegative symmetric matrix A of the form BCBT, where C is a k×k symmetric matrix, and both B and C are required to be nonnegative. This work introduces the SNT-rank of A, as the minimal k, for which such factorization exists. After a list of basic properties and an exploration of SNT-rank of low rank matrices, the class of nonnegative symmetric matrices with SNT-rank equal to rank is studied. The paper concludes with a completion problem, that asks for matrices with the smallest possible SNT-rank among all nonnegative symmetric matrices with given diagonal blocks.