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arXiv · 0805.0120

Nonnegative Matrix Factorization via Rank-One Downdate

Michael Biggs·Ali Ghodsi·Stephen Vavasis
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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 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.

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Michael Biggs, Ali Ghodsi, Stephen Vavasis. 2008-05-01. Nonnegative Matrix Factorization via Rank-One Downdate. https://arxiv.org/abs/0805.0120

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