On Characteristic Rank for Matrix and Tensor Completion [Lecture Notes]

被引：0
|
作者：
Shapiro, Alexander [1 ]
Xie, Yao [1 ,2 ]
Zhang, Rui [1 ]
机构：
[1] Georgia Inst Technol, H Milton Stewart Sch Ind & Syst Engn, Atlanta, GA 30332 USA
[2] Machine Learning Ctr, Los Angeles, CA USA
来源：
IEEE SIGNAL PROCESSING MAGAZINE | 2021年 / 38卷 / 02期
基金：
美国国家科学基金会;
关键词：
Tensors; Signal processing;
D O I：
10.1109/MSP.2020.3046233
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
In this lecture note, we discuss a fundamental concept, referred to as the characteristic rank, that suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing. We illustrate this framework through two examples-matrix and three-way tensor completion problems-and consider basic properties, including the identifiability of matrices and tensors, given partial observations. We consider cases without observation noise to illustrate the principle.
引用
收藏
页码：125 / 129
页数：5
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