Nonnegative Matrix Factorization via Rank-One Downdate

Nonnegative matrix factorization (NMF) was popularized as a tool for data mining by Lee and Seung in 1999. NMF attempts to approximate a matrix with nonnegative entries by a product of two low-rank matrices, also with nonnegative entries. We propose an algorithm called rank-one downdate (R1D) for computing an NMF that is partly motivated by the singular value decomposition. This algorithm computes the dominant singular values and vectors of adaptively determined submatrices of a matrix. On each iteration, R1D extracts a rank-one submatrix from the original matrix according to an objective function. We establish a theoretical result that maximizing this objective function corresponds to correctly classifying articles in a nearly separable corpus. We also provide computational experiments showing the success of this method in identifying features in realistic datasets. The method is also much faster than other NMF routines.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Michael Biggs, Ali Ghodsi, Stephen A. Vavasis
• Keywords: CORR 2008, Education, Matrix, Nonnegative Entries, Nonnegative Matrix Factorization