Nonnegative low rank matrix approximation for nonnegative matrices

On Reduced Rank Nonnegative Matrix Factorization for Symmetric Nonnegative Matrices

Let V ∈ R be a nonnegative matrix. The nonnegative matrix factorization (NNMF) problem consists of finding nonnegative matrix factors W ∈ R and H ∈ R such that V ≈ WH. Lee and Seung proposed two algorithms which find nonnegative W and H such that ‖V −WH‖F is minimized. After examining the case in which r = 1 about which a complete characterization of the solution is possible, we consider the ca...

A Nonnegative Projection Based Algorithm for Low-Rank Nonnegative Matrix Approximation

SymNMF: nonnegative low-rank approximation of a similarity matrix for graph clustering

Nonnegative matrix factorization (NMF) provides a lower rank approximation of a matrix by a product of two nonnegative factors. NMF has been shown to produce clustering results that are often superior to those by other methods such as K-means. In this paper, we provide further interpretation of NMF as a clustering method and study an extended formulation for graph clustering called Symmetric NM...

Small Polynomial Matrix Presentations of Nonnegative Matrices

We investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior.

Nonnegative Matrices

For a loopless, acyclic, transitive directed graph S, we study the relations between the predecessor property and the well structured property on S. These properties assure the existence of nonnegativ€ Jordan bases for any nonnegative matrix with singular graph S.