Completely Positive Binary Tensors
Optimization and Control
2018-08-08 v1
Abstract
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.
Cite
@article{arxiv.1808.02211,
title = {Completely Positive Binary Tensors},
author = {Jinyan Fan and Jiawang Nie and Anwa Zhou},
journal= {arXiv preprint arXiv:1808.02211},
year = {2018}
}