Non-negative matrix factorization: Ill-posedness and a geometric algorithm

Authors:
Bradley Klingenberg;James Curry;Anne Dougherty
Affiliations:
Department of Applied Mathematics, University of Colorado, UCB 526, Boulder, CO 80309-0526, USA;Department of Applied Mathematics, University of Colorado, UCB 526, Boulder, CO 80309-0526, USA;Department of Applied Mathematics, University of Colorado, UCB 526, Boulder, CO 80309-0526, USA
Venue:
Pattern Recognition
Year:
2009

Citing 3
Cited 3

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Projected Gradient Methods for Nonnegative Matrix Factorization

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On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization

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Nonlinear nonnegative matrix factorization based on Mercer kernel construction

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Underdetermined Sparse Blind Source Separation of Nonnegative and Partially Overlapped Data

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Sparse and unique nonnegative matrix factorization through data preprocessing

The Journal of Machine Learning Research

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Abstract

Non-negative matrix factorization (NMF) has been proposed as a mathematical tool for identifying the components of a dataset. However, popular NMF algorithms tend to operate slowly and do not always identify the components which are most representative of the data. In this paper, an alternative algorithm for performing NMF is developed using the geometry of the problem. The computational costs of the algorithm are explored, and it is shown to successfully identify the components of a simulated dataset. The development of the geometric algorithm framework illustrates the ill-posedness of the NMF problem and suggests that NMF is not sufficiently constrained to be applied successfully outside of a particular class of problems.