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

标题：非负矩阵和张量近似：算法、软件和应用数据挖掘、化学计量学和生物信息学等各种应用导致需要分析共现和计数数据。这些数据集本质上是由非负数组成的，并且通常可以表示为多维矩阵。对这些数据的分析是当代科学的一大挑战。本研究研究了非负矩阵和张量的近似值，揭示了数据的易于解释的基于部分的表示。快速，数值算法的发展，结合了最先进的技术，从数值优化。在对网络数据挖掘、生物信息学和计算机视觉的应用进行测试后，一个软件工具箱向公众开放。该项目的重点是培养数学和计算机科学方面的研究生和本科生，并通过公共网站提供软件。

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.