Symmetric Nonnegative Matrix Trifactorization

Abstract

The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of an $n\times n$ nonnegative symmetric matrix $A$ of the form $BC{B}^T$, where $C$ is a $k\times k$ 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 listing basic properties and exploring 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.

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