1. Symmetric Nonnegative Matrix Trifactorization
- Author
-
Damjana Kokol Bukovšek and Helena Šmigoc
- Subjects
Numerical Analysis ,Algebra and Number Theory ,mathematical economy ,matematična ekonomija ,mathematics ,matrična algebra ,completely positive matrices ,nonnegative matrix factorization ,matrix algebra ,udc:330.4 ,nonnegative rank ,Mathematics - Spectral Theory ,nonnegative symmetric matrices ,matematika ,Optimization and Control (math.OC) ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,Geometry and Topology ,Mathematics - Optimization and Control ,Spectral Theory (math.SP) ,15A23, 15B48 - Abstract
The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of an $n \times n$ nonnegative symmetric matrix $A$ of the form $BCB^T$, 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.
- Published
- 2021
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