Convex Nonnegative Matrix Factorization with Rank-1 Update for Clustering

Abstract

In convex nonnegative matrix factorization, the feature vectors are modeled by convex combinations of observation vectors. In the paper, we propose to express the factorization model in terms of the sum of rank-1 matrices. Then the sparse factors can be easily estimated by applying the concept of the Hierarchical Alternating Least Squares (HALS) algorithm which is still regarded as one of the most effective algorithms for solving many nonnegative matrix factorization problems. The proposed algorithm has been applied to find partially overlapping clusters in various datasets, including textual documents. The experiments demonstrate the high performance of the proposed approach.