On characteristic rank for matrix and tensor completion

2020/09/03 by Alexander Shapiro, Yao Xie, Shapiro, Alexander +3
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2009.01893

openalex publication_date 2020/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Tensor Decompositions and Applications
• Tensor Decomposition for Signal Processing and Machine Learning
• Rank one tensor completion problem

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• Tensor network ranks
• Tensor Low Rank Modeling and Its Applications in Signal Processing
• On the equivalence between low rank matrix completion and tensor rank
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