On the Best Rank-1 and Rank-(

By Lieven De Lathauwer, B. De Moor, Joos Vandewalle. 2004

194 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8526f7d58b58294521636d4709a08272e6f1f3c8

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Citations in the corpus

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 rank1 approximation of a tensor under the Frobenius norm obtained in [3, 4].”
Subtracting a best rank-1 approximation may increase tensor rank (2009, background): “It is shown in [11] that the stationary points of the 2 × ×2 symmetric best rank-1 approximation problem are obtained as the roots of a 3rd degree polynomial.”
Contrastive Learning Using Spectral Methods (2013, methodology): “The following proposition shows that one of the vectors ai (and its associated λi) can be obtained from M2 and M3 using a simple power method similar to that from [5, 18] (note that which of the K components is obtained depends on the initialization of the procedure).”
Tensor decompositions for learning latent variable models (2012, methodology): “When using the excess kurtosis (i.e., fourth-order cumulant) as the contrast function, this method reduces to a generalization of the power method for symmetric tensors [LMV00, ZG01, KR02].”
A Newton-Grassmann Method for Computing the Best Multilinear Rank-(r1, r2, r3) Approximation of a Tensor (2009, methodology): “As initial approximation a random tensor was chosen and 10 HOOI iterations were performed before the Newton method was started.”
Robust Low-Rank Tensor Recovery: Models and Algorithms (2013, methodology): “A widely-used approach for computing the factor matrices is called the higher-order orthogonal iteration (HOOI) [12], which is essentially an ALS method based on computing the dominant left singular vectors of each X ( n ) .”
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, methodology): “When it comes to finding the best approximation, the ALS-type algorithms exhibit similar advantages and drawbacks to those used for CPD [8], [70].”
Tensor-Product Approximation to Multidimensional Integral Operators and Green's Functions (2008, unknown): “We refer to [4] concerning orthogonal rank-(r1, .”
Product Form Approximations for Communicating Markov Processes (2008, methodology): “The whole approach is motivated by the computation of tensor approximations for matrices where similar problems arise and similar approaches are used [21] and which have several applications in statistics and computer vision [23].”
Multilinear image analysis for facial recognition (2002, background): “According to [3], a useful generalization to tensors involves an optimal rank(R1; R2; : : : ; RN ) approximation which iteratively optimizes each of the modes of the given tensor, where each optimization step involves a best reduced-rank approximation of a positive semi-definite symmetric matrix.”
Tensor-Train Decomposition (2011, background): “Multilinear algebra, tensor analysis, and the theory of tensor approximations play increasingly important roles in computational mathematics and numerical analysis [8, 7, 9, 5, 14]; see also the review [26].”