Nonnegative Matrix Factorizations for Clustering: A Survey

Abstract

This chapter introduces the basic formulations of nonnegative matrix factorization (NMF) and outlines the theoretical foundations on NMF for clustering and presents the equivalence results between NMF and various clustering methodologies. It demonstrates the NMF clustering capabilities and analyzes the advantages of NMF in clustering analysis. The chapter provides an outline on the NMF algorithm development and discusses several practical issues in NMF algorithms. The intrinsic alternating minimization in NMF algorithms is nonconvex, even though the objective function is convex with respect to one set of variables. The chapter also provides an overview of many different NMF variants and examines the advances on using NMF-based methods for solving many other clustering problems including co-clustering, semisupervised clustering, and consensus clustering and discusses future research directions. Co-clustering algorithms aim at clustering different types of data simultaneously by making use of the dual relationship information such as the term-document matrix and the gene-sample matrix.