A Multilinear Singular Value Decomposition

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

4,389 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mathematics, Signal Processing

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Another consequence of the relation (4) is the higher-order SVD (HOSVD) introduced in [54, 55] for approximating a tensor by a Tucker decomposition (3) of lower multilinear rank.”
Deeper, Broader and Artier Domain Generalization (2017, background): “ensional dense vector that guides how to linearly combine the shared factors, which weighted sum. Given a tensor Wthe Tucker problem can be solved via high-order singular value decomposition (HO-SVD) [15]. G= W 1 UT M UT (6) where U n is the Umatrix from the SVD of the the mode-n ﬂattening of W. How”
Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications (2015, methodology): “Two of the most popular tensor decomposition models are CANDECOMP/PARAFAC model (Carroll & Chang, 1970; Harshman & Lundy, 1994; Shashua & Hazan, 2005) and Tucker model (Tucker, 1966; De Lathauwer et al., 2000; Kim & Choi, 2007).”
mTrust: discerning multi-faceted trust in a connected world (2012, background): “A tensor, also known as multidimensional matrix [3], is a higher order generalization of a vector (first order tensor) and a matrix (second order tensor).”
Fast truncation of mode ranks for bilinear tensor operations (2010, positive): “They can be computed by SVD of the unfoldings of F , as proposed in [5], but this method requires evaluation of all elements of tensor and is not feasible for large mode sizes.”
Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time (2008, background): “Let us recall some basic facts about tensors [10, 11].”
Collaborative Filtering Meets Mobile Recommendation: A User-Centered Approach (2010, methodology): “In contrast, we model the three-party relations in a tensor; and beyond standard tensor decomposition (Lathauwer, Moor, and Vandewalle 2000), we will further exploit additional matrix inputs for a regularized decomposition solution.”
Model Compression and Hardware Acceleration for Neural Networks: A Comprehensive Survey (2020, background): “It is also called multilinear SVD (MLSVD) [113], because it is a special form of Tucker decomposition that all the factor matrices F ( i ) in (19) are orthogonal and thus the kernel tensor K is called all-orthogonal.”
Geometry of Quantum States: Index (2007, background): “Turning to the mathematical literature in order to standardise the tensor ijk in some way, we learn many interesting things [251, 552, 696], but there is no magical recipe that solves our problem.”
Non incremental strategies based on separated representations: applications in computational rheology (2010, methodology): “In particular the Hartree-Fock (that involves a single product of functions) and post-Hartree-Fock approaches (as the MCSCF that involves a finite number of sums) made use of a separated representation of the wavefunction.”
Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme (2011, background): “The HOSVD [12, 46, 47] is a generalization of SVD to higher-order tensors.”
Black Box Low Tensor-Rank Approximation Using Fiber-Crosses (2009, background): “They are in general not the left dominant singular vectors of the matrix of fibers from W(T , μ). By choosing the dominant singular vectors in each direction μ = 1 ,...,d and discarding the singular values σ (μ) i , i = k � + 1 ,...,k μ, one introduces an error of the size [ 5 ]”
Jacobi Algorithm for the Best Low Multilinear Rank Approximation of Symmetric Tensors (2013, background): “However, due to the properties of the core tensor, truncation of HOSVD leads to a good approximation that can be used as a starting point of iterative algorithms.”