Fast rank-2 nonnegative matrix factorization for hierarchical document clustering
Da Kuang, Haesun Park · 2013
Nonnegative matrix factorization (NMF) has been successfully used as a clustering method especially for flat partitioning of documents. In this paper, we propose an efficient hierarchical document clustering method based on a new algorithm for rank-2 NMF. When the two block coordinate descent framework of nonnegative least squares is applied to computing rank-2 NMF, each subproblem requires a solution for nonnegative least squares with only two columns in the matrix. We design the algorithm for rank-2 NMF by exploiting the fact that an exhaustive search for the optimal active set can be performed extremely fast when solving these NNLS problems. In addition, we design a measure based on the results of rank-2 NMF for determining which leaf node should be further split. On a number of text data sets, our proposed method produces high-quality tree structures in significantly less time compared to other methods such as hierarchical K-means, standard NMF, and latent Dirichlet allocation.