Nonnegative Matrix Factorization via Rank-One Downdate
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 a NMF that is partly motivated by 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 dataset 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.
Cite
@article{arxiv.0805.0120,
title = {Nonnegative Matrix Factorization via Rank-One Downdate},
author = {Michael Biggs and Ali Ghodsi and Stephen Vavasis},
journal= {arXiv preprint arXiv:0805.0120},
year = {2008}
}