SciTech Connect

Title: Efficient MATLAB computations with sparse and factored tensors.

Efficient MATLAB computations with sparse and factored tensors. In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
Authors: ;
Publication Date:
OSTI Identifier:897641
Report Number(s):SAND2006-7592
TRN: US200705%%125
DOE Contract Number:AC04-94AL85000
Resource Type:Technical Report
Data Type:
Research Org:Sandia National Laboratories
Sponsoring Org:USDOE
Country of Publication:United States
Language:English
Subject: 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; M CODES; COMPUTER CALCULATIONS; ALGORITHMS; EFFICIENCY MATLAB.; Calculus of tensors.