On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors

By Lieven De Lathauwer, B. De Moor, Joos Vandewalle. 2000

1,697 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Signal Processing

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Citations in the corpus

Compression of fully-connected layer in neural network by Kronecker product (2015, background): “Similarly, though there are iterative algorithms for rank-1 approximation of tensor Friedland et al. (2013), Lathauwer et al. (2000), the optimality of the approximation is lost once input data distribution is taken into consideration.”
Factorization strategies for third-order tensors (2011, background): “Algorithms for finding this (iteratively) can be found in [20, 28, 47].”
Shifted Power Method for Computing Tensor Eigenpairs (2010, methodology): “ point if ˙ˆ(J(x )) >1. 6 T. G. Kolda and J. R. Mayo 3. Symmetric higher-order power method (S-HOPM). We review the symmetric higher-order power method (S-HOPM), introduced by De Lathauwer et al. [6] and analyzed further by Kodis and Regalia [11]. The purpose of S-HOPM is to solve the optimizatio”
Decomposable-Net: Scalable Low-Rank Compression for Neural Networks (2019, methodology): “For Tucker decomposition, we apply higher-order orthogonal iteration [De Lathauwer et al., 2000] under given ranks.”
Towards an ADI iteration for Tensor Structured Equations (2014, methodology): “We use the following notation of a product of tensor T with matrix M ∈ Rnj×nj from [9]:”
Mathematik in den Naturwissenschaften Leipzig Tensor-Product Approximation to Operators and Functions in High Dimensions (2007, background): “Algebraic methods for tensor-product approximations to high-order tensors have been extensively discussed in the literature (see [25, 4, 5, 16, 21, 27] and related references).”
Singular values and eigenvalues of tensors: a variational approach (2005, methodology): “We have mentioned the relation between the l(2)-singular values/vectors and the best rank-1 approximation of a tensor under the Frobenius norm obtained in [3, 4].”
A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart–Young approach (2011, background): “The a posteriori construction of such tensor decompositions, when the function u is known, have been extensively studied over the past years in multilinear algebra community [6, 7, 13, 14, 4, 8] (essentially for finite dimensional vector spaces Vi).”
Low Complexity Damped Gauss-Newton Algorithms for CANDECOMP/PARAFAC (2012, methodology): “ ket−1k2. The algorithm should stop when µ increases to a suﬃciently large value (e.g., 1030). In practice, the factors A(n) are often initialized using the mode-n singular vectors of the data tensor [5, 7, 14], then run over ALS (3.1) after few iterations. According to the CP model (2.3), all the c”