Nonnegative matrix factorization via rank-one downdate

Authors:
Michael Biggs;Ali Ghodsi;Stephen Vavasis
Affiliations:
University of Waterloo, Waterloo, ON;University of Waterloo, Waterloo, ON;University of Waterloo, Waterloo, ON
Venue:
Proceedings of the 25th international conference on Machine learning
Year:
2008

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Abstract

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 sub-matrices 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.