Non-Negative Matrix and Tensor Approximations: Algorithms, Software and Applications

University Of Texas At Austin, Austin TX

Investigators

Abstract

Title: Non-negative Matrix and Tensor Approximations: Algorithms, Software and Applications Applications as diverse as data mining, chemometrics, and bioinformatics lead to the need for analysis of co-occurrence and count data. These data sets are intrinsically composed of non-negative numbers, and often can be represented as multi-dimensional matrices. Analysis of such data is a major contemporary scientific challenge. This research studies approximations of non-negative matrices and tensors that reveal an easily interpretable parts-based representation of the data. Fast, numerical algorithms are developed that incorporate state-of-the-art techniques from numerical optimization. A software toolbox is made available to the public after being tested on applications in web data mining, bioinformatics and computer vision. An emphasis of the project is to train graduate and undergraduate students in mathematics and computer science, and make the software available via a public web site.