Algebraic Methods for Tensor Data
Abstract
We develop algebraic methods for computations with tensor data. We give three applications: extracting features that are invariant under the orthogonal symmetries in each of the modes, approximation of the tensor spectral norm, and amplification of low rank tensor structure. We introduce colored Brauer diagrams, which are used for algebraic computations and in analyzing their computational complexity. We present numerical experiments whose results show that the performance of the alternating least squares algorithm for rank 1 approximations for tensors can be improved using tensor amplification.
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Information & Authors
Information
Published In
SIAM Journal on Applied Algebra and Geometry
Pages: 1 - 27
DOI: 10.1137/19M1272494
ISSN (online): 2470-6566
Copyright
© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 5 July 2019
Accepted: 29 September 2020
Published online: 4 January 2021
Keywords
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Funding Information
National Science Foundation https://doi.org/10.13039/100000001 : 1837985
U.S. Department of Defense https://doi.org/10.13039/100000005 : BA150235
University of Michigan https://doi.org/10.13039/100007270 : U063159
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