Non-Negative Matrix Factorization, Convexity and Isometry
| dc.creator | Vasiloglou, Nikolaos | |
| dc.creator | Gray, Alexander G. | |
| dc.creator | Anderson, David V. | |
| dc.date | 2008-10-13 | |
| dc.date | 2009-04-22 | |
| dc.date.accessioned | 2026-07-07T13:06:36Z | |
| dc.date.available | 2026-07-07T13:06:36Z | |
| dc.description | 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. | |
| dc.description | accpepted in SIAM Data Mining 2009, 12 pages | |
| dc.identifier | https://arxiv.org/abs/0810.2311 | |
| dc.identifier | http://arxiv.org/abs/0810.2311 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227829 | |
| dc.subject | Artificial Intelligence | |
| dc.subject | Computer Vision and Pattern Recognition | |
| dc.title | Non-Negative Matrix Factorization, Convexity and Isometry | |
| dc.type | text |