Computer Science > Artificial Intelligence
arXiv:0810.2311 (cs)
[Submitted on 13 Oct 2008 (v1), last revised 22 Apr 2009 (this version, v2)]
Title:Non-Negative Matrix Factorization, Convexity and Isometry
View a PDF of the paper titled Non-Negative Matrix Factorization, Convexity and Isometry, by Nikolaos Vasiloglou and 2 other authors
View PDFAbstract: In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex, by using the theory of Completely Positive Factorization. We subsequently explore four novel approaches to finding globally-optimal NMF solutions using various ideas from convex optimization. We then develop a new method, isometric NMF (isoNMF), which preserves non-negativity while also providing an isometric embedding, simultaneously achieving two properties which are helpful for interpretation. Though it results in a more difficult optimization problem, we show experimentally that the resulting method is scalable and even achieves more compact spectra than standard NMF.
| Comments: | accpepted in SIAM Data Mining 2009, 12 pages |
| Subjects: | Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV) |
| Cite as: | arXiv:0810.2311 [cs.AI] |
| (orarXiv:0810.2311v2 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.0810.2311 arXiv-issued DOI via DataCite |
Submission history
From: Nikolaos Vasiloglou [view email][v1] Mon, 13 Oct 2008 20:43:24 UTC (837 KB)
[v2] Wed, 22 Apr 2009 16:05:22 UTC (837 KB)
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View a PDF of the paper titled Non-Negative Matrix Factorization, Convexity and Isometry, by Nikolaos Vasiloglou and 2 other authors
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