摘要: Nonnegative tensors arise in a wide range of applications, including hyperspectral imaging, spectroscopy, statistics, phylogenetics, data mining, pattern recognition, among other areas. In these applications, one frequently needs to find (i) the nonnegative rank, (ii) a nonnegative rank decomposition, and (iii) a best low nonnegative rank approximation, of a nonnegative tensor. Such problems also arise for instance in chemometrics and hyperspectral imaging, where quantities like concentration and intensity can only take on nonnegative values. In this talk we address these questions by studying the semialgebraic structure of the set of nonnegative tensors of nonnegative rank less or equal to r. More precisely, we will talk about the relation among the nonnegative rank, the real rank and the complex rank of a nonnegative tensor, give conditions such that a nonnegative rank decomposition is unique, and discuss the uniqueness of low nonnegative rank approximations.

报告人简介:  Yang Qi博士，2013年在德克萨斯农工(A&M)大学获得数学专业博士学位，其后在Universite Grenoble Alpes和University of Chicago从事博士后研究工作。研究方向为用几何方法研究信号处理、统计和计算科学中的问题, 在《SIAM Journal on Matrix Analysis and Applications》等期刊发表多篇论文。