Orthogonal nonnegative matrix t factorizations for clustering
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.
KDD '06