Fundamental tensor operations for large-scale data analysis using tensor network formats

DOI10.1007/s11045-017-0481-0zbMath1448.94107arXiv1405.7786OpenAlexW2593392256MaRDI QIDQ784596

Namgil Lee, Andrzej Cichocki

Publication date: 3 August 2020

Published in: Multidimensional Systems and Signal Processing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.7786

zbMATH Keywords

multilinear operatortensor calculusbig datatensor networksmatrix product statecontracted productgeneralized Tucker modelmatrix product operatorstrong Kronecker producttensor train

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Quadratic and bilinear forms, inner products (15A63) Multilinear algebra, tensor calculus (15A69) Orthogonalization in numerical linear algebra (65F25) Informational aspects of data analysis and big data (94A16)

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Uses Software

• TT Toolbox
• GitHub

Cites Work

• Unnamed Item
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• Tensor-Train Decomposition
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• Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity
• A literature survey of low-rank tensor approximation techniques
• The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
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• Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
• Tensor Spaces and Numerical Tensor Calculus
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• Ideal spatial adaptation by wavelet shrinkage
• A Multilinear Singular Value Decomposition
• Low-Rank Explicit QTT Representation of the Laplace Operator and Its Inverse
• Solution of Linear Systems and Matrix Inversion in the TT-Format
• Estimating a Few Extreme Singular Values and Vectors for Large-Scale Matrices in Tensor Train Format
• Sparse grids

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