An Axiomatic Approach to Tensor Rank Functions

2020/12/08 by Wayne W. Wheeler, Wheeler, Wayne W.
Mathematics · Engineering · Computer Science · #Tensor decomposition and applications #Sparse and Compressive Sensing Techniques #Error Correcting Code Techniques

paper · pdf · doi:10.48550/arxiv.2012.04730

Abstract

Recent work of Qi et al. arXiv:2004.11240v7 proposes a set of axioms for tensor rank functions. The current paper presents examples showing that their axioms allow rank functions to have some undesirable properties, and a stronger set of axioms is suggested that eliminates these properties. Two questions raised by Qi et al. involving the submax rank function are also answered.

Citations

• Some Mathematical Notes on Three-Mode Factor Analysis
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Tensor Decompositions and Applications
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics

Related

• A Tensor Rank Theory and Maximum Full Rank Subtensors
• Tensor network ranks
• Bounds on the tensor rank
• A comparison of different notions of ranks of symmetric tensors
• Notions of Tensor Rank