Factorization strategies for third-order tensors
Misha E. Kilmer,Carla D. Martin +1 more
TLDR
This paper presents a new factorization of a tensor as a product of tensors, reminiscent of matrix factorizations, and introduces concepts such as tensor transpose, inverse, and identity, which lead to the notion of an orthogonal tensor.About:
This article is published in Linear Algebra and its Applications.The article was published on 2011-08-01 and is currently open access. It has received 759 citations till now. The article focuses on the topics: Invariants of tensors & Tensor product network.read more
Citations
More filters
Journal ArticleDOI
Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging
TL;DR: This paper investigates further implications including a bilinear operator on the matrices which is nearly an inner product and which leads to definitions for length ofMatrices, angle between two matrices, and orthogonality of matrices and the use of t-linear combinations to characterize the range and kernel of a mapping defined by a third-order tensor and the t-product and the quantification of the dimensions of those sets.
Proceedings ArticleDOI
Novel Methods for Multilinear Data Completion and De-noising Based on Tensor-SVD
TL;DR: In this article, a tensor-Singular Value Decomposition (t-SVD) based tensor nuclear norm penalized algorithm was proposed for video completion from missing entries.
Journal ArticleDOI
Exact Tensor Completion Using t-SVD
Zemin Zhang,Shuchin Aeron +1 more
TL;DR: In this article, a tensor singular value decomposition (t-SVD) is proposed for 3D arrays with low tubal-rank, which is similar to the SVD for matrices.
Proceedings ArticleDOI
Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization
TL;DR: This work proves that under certain suitable assumptions, it can recover both the low-rank and the sparse components exactly by simply solving a convex program whose objective is a weighted combination of the tensor nuclear norm and the l1-norm.
Posted Content
Novel methods for multilinear data completion and de-noising based on tensor-SVD
TL;DR: This paper outlines a tensor nuclear norm penalized algorithm for video completion from missing entries and shows superior performance of the method compared to the matrix robust PCA adapted to this setting as proposed in [4].
References
More filters
Journal ArticleDOI
Tensor Decompositions and Applications
Tamara G. Kolda,Brett W. Bader +1 more
TL;DR: This survey provides an overview of higher-order tensor decompositions, their applications, and available software.
Journal ArticleDOI
Analysis of individual differences in multidimensional scaling via an n-way generalization of 'eckart-young' decomposition
J. Douglas Carroll,Jih-Jie Chang +1 more
TL;DR: In this paper, an individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common "psychological space" and a corresponding method of analyzing similarities data is proposed, involving a generalization of Eckart-Young analysis to decomposition of three-way (or higher-way) tables.
Journal ArticleDOI
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
TL;DR: Numerical tests are described comparing I~QR with several other conjugate-gradient algorithms, indicating that I ~QR is the most reliable algorithm when A is ill-conditioned.
Journal ArticleDOI
A Multilinear Singular Value Decomposition
TL;DR: There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed.