On characteristic rank for matrix and tensor completion
Statistics Theory
2020-11-12 v2 Statistics Theory
Abstract
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing. Below, we illustrate this framework using two examples: matrix and three-way tensor completion problems, and consider basic properties include identifiability of a matrix or tensor, given partial observations. In this note, we consider cases without observation noise to illustrate the principle.
Cite
@article{arxiv.2009.01893,
title = {On characteristic rank for matrix and tensor completion},
author = {Alexander Shapiro and Yao Xie and Rui Zhang},
journal= {arXiv preprint arXiv:2009.01893},
year = {2020}
}