Orthogonal nonnegative matrix t-factorizations for clustering

Abstract

Currently, most research on nonnegative matrix factorization (NMF)focus on 2-factor $X=FG^T$ factorization. We provide a systematicanalysis of 3-factor $X=FSG^T$ NMF. While it unconstrained 3-factor NMF is equivalent to it unconstrained 2-factor NMF, itconstrained 3-factor NMF brings new features to it constrained 2-factor NMF. We study the orthogonality constraint because it leadsto rigorous clustering interpretation. We provide new rules for updating $F,S, G$ and prove the convergenceof these algorithms. Experiments on 5 datasets and a real world casestudy are performed to show the capability of bi-orthogonal 3-factorNMF on simultaneously clustering rows and columns of the input datamatrix. We provide a new approach of evaluating the quality ofclustering on words using class aggregate distribution andmulti-peak distribution. We also provide an overview of various NMF extensions andexamine their relationships.