Completely Positive Binary Tensors

• 成果类型: Article
• 署名作者: Fan, Jinyan; Nie, Jiawang; Zhou, Anwa
• 署名单位: Shanghai Jiao Tong University; Shanghai Jiao Tong University; University of California System; University of California San Diego; Shanghai University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0963
• 发表日期: 2019
• 页码: 1087-1100
• 关键词: hankel tensors

摘要

A symmetric tensor is completely positive (CP) if it is a sum of tensor powers of nonnegative vectors. This paper characterizes completely positive binary tensors. We show that a binary tensor is completely positive if and only if it satisfies two linear matrix inequalities. This result can be used to determine whether a binary tensor is completely positive or not. When it is, we give an algorithm for computing its cp-rank and the decomposition. When the order is odd, we show that the cp-rank decomposition is unique. When the order is even, we completely characterize when the cp-rank decomposition is unique. We also discuss how to compute the nearest cp-approximation when a binary tensor is not completely positive.