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Convex and Semi-Nonnegative Matrix Factorizations (2008)
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| Citations: | 110 - 10 self |
BibTeX
@MISC{Ding08convexand,
author = {Chris Ding and Tao Li and Michael I. Jordan},
title = { Convex and Semi-Nonnegative Matrix Factorizations},
year = {2008}
}
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Abstract
We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X = F GT, we focus on algorithms in which G is restricted to contain nonnegative entries, but allow the data matrix X to have mixed signs, thus extending the applicable range of NMF methods. We also consider algorithms in which the basis vectors of F are constrained to be convex combinations of the data points. This is used for a kernel extension of NMF. We provide algorithms for computing these new factorizations and we provide supporting theoretical analysis. We also analyze the relationships between our algorithms and clustering algorithms, and consider the implications for sparseness of solutions. Finally, we present experimental results that explore the properties of these new methods.
Keyphrases
semi-nonnegative matrix factorization data point new factorization mixed sign new method several new variation applicable range form gt basis vector data matrix kernel extension nmf method convex combination nonnegative entry theoretical analysis experimental result nonnegative matrix factorization
