Multilinear operators for higher-order decompositions

By Tamara G. Kolda. 2006

460 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/5084d5c3ea15bf6c11d8c8a2dceec6162b776d71

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In Computational Mathematics

In Computational Theory and Mathematics

In Signal Processing

Citations in the corpus

Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations (2012, unknown): “Unfortunately, the number of parameters in the HOSVD is also exponential in d, and so does not appear to be a viable decomposition for general high dimensional problems.”
Distributional Memory: A General Framework for Corpus-Based Semantics (2010, background): “…use the linguistic structure of texts to compute co-occurrences, and only record whether the target occurs D ow nloaded from http://direct.m it.edu/coli/article-pdf/36/4/673/1810191/coli_a_00016.pdf by guest on 10 Septem ber 2021 in or close to the context element, without considering the type…”
Efficient MATLAB Computations with Sparse and Factored Tensors (2007, unknown): “,U from [25], but other notation can be used.”
Statistical Inference for High-Dimensional Matrix-Variate Factor Models (2020, methodology): “Tensor decomposition (Kolda and Bader, 2009; Kolda, 2006) has also been applied to matrix-variate observations.”
Scalable Tensor Decompositions for Multi-aspect Data Mining (2008, methodology): “Multiple mode-n matrix products can be performed in any order (see, e.g., [ 13 ]), i.e.,”
A scalable optimization approach for fitting canonical tensor decompositions (2011, methodology): “The premise is to iteratively optimize one factor matrix at a time, rather than solving (2) for A (1) through A ( N ) simultaneously.”
An Adaptive Algebraic Multigrid Algorithm for Low-Rank Canonical Tensor Decomposition (2011, unknown): “We note that upon completion of the ALS iterations the rank-one terms are sorted in decreasing order of the normalization factors λ r .”
Shifted Power Method for Computing Tensor Eigenpairs (2010, unknown): “ a negative shift (<0) to make it concave. We have two key results.Theorem 4.4shows that for any starting point 2Specically, A (RC ) with R = f1;:::;‘ gand C ‘+1;:::;m in matricization notation [12]. Shifted Power Method for Computing Tensor Eigenpairs 11 x 0 2, the sequence f kgproduced byAlgori”
Tensor Decompositions and Applications (2009, background): “In general, the speciﬁc permutation of columns is not important so long as it is consistent across related calculations; see [134] for further details.”
Dynamical low-rank approximation: applications and numerical experiments (2008, methodology): “[13] for a review of different decompositions) as”
Tensor Regression with Applications in Neuroimaging Data Analysis (2012, background): “The mode-( d, d (cid:48) ) matricization B ( dd (cid:48) ) ∈ IR p d p d (cid:48) × (cid:81) d (cid:48)(cid:48)(cid:54) = d , d (cid:48) p d (cid:48)(cid:48) is deﬁned in a similar fashion (Kolda, 2006).”
Factorization strategies for third-order tensors (2011, methodology): “Since we are working with third-order tensors, it is convenient to write (2.1) using Kruskal notation [23].”