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

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Title: Non-negative Matrix and Tensor Approximations: Algorithms, Software and ApplicationsApplications as diverse as data mining, chemometrics, and bioinformaticslead to the need for analysis of co-occurrence and count data.These data sets are intrinsically composed of non-negative numbers, andoften can be represented as multi-dimensional matrices. Analysis of suchdata is a major contemporary scientific challenge.This research studies approximations of non-negative matrices andtensors that reveal an easily interpretable parts-based representationof the data. Fast, numerical algorithms are developed that incorporatestate-of-the-art techniques from numerical optimization. A softwaretoolbox is made available to the public after being tested onapplications in web data mining, bioinformatics and computer vision.An emphasis of the project is to train graduate and undergraduatestudents in mathematics and computer science, and make the softwareavailable via a public web site.