A Review of Nonnegative Matrix Factorization Methods for Clustering

Clustering, the problem of partitioning observations with high intragroup similarity, has always been one of the central themes in unsupervised learning. Although a wide variety of algorithms for clustering applications have been studied in literature, the subject still remains an active avenue for research. In fact, it is possible to formulate clustering as a matrix decomposition problem. This formulation leads to interesting interpretations as well as novel algorithms that benefit from favorable computational properties of numerical linear algebra. Popularized by Lee and Seung [11], Nonnegative Matrix Factorization (NMF) has turned into one of the primary tools for decomposing data sets into low-rank factorizing matrices in order to yield a parts-based representation.