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Title: Multilinear operators for higher-order decompositions.

Multilinear operators for higher-order decompositions. We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties of the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.
Authors:
Publication Date:
OSTI Identifier:923081
Report Number(s):SAND2006-2081
TRN: US200806%%270
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; MATRICES; MATHEMATICAL OPERATORS; DIMENSIONLESS NUMBERS; P CODES Matrix logic.; Tensor algebra.