Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme

By Mariya Ishteva, Pierre-Antoine Absil, S. Van Huffel, Lieven De Lathauwer. 2011

137 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Examples include nonlinear conjugate gradient or Newton-like methods on manifolds of low-rank matrices [35,191,198,257,258] or low-rank tensors [52,53,131,132,255], see also Section 3.4.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, methodology): “…(also called the differential geometric optimization) has been successfully applied to the computation of the best Tucker approximation [Ishteva et al., 2009, 2011, Steinlechner, 2016a], whereby the Tucker manifold structure can be formulated through a set of Tucker tensors of fixed…”
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, background): “Optimization-based algorithms exploiting second-order information have also been proposed [71], [72].”
First-order Methods for Geodesically Convex Optimization (2016, background): “…nonconvex problems where Riemannian optimization has proved quite useful, e.g., low-rank matrix and tensor factorization (Vandereycken, 2013; Ishteva et al., 2011; Mishra et al., 2013); dictionary learning (Sun et al., 2015; Harandi et al., 2012); optimization under orthog-onality…”
Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors (2009, background): “…three Stiefel manifolds and a Euclidean space O( l, p ) × O( m, q ) × O( n, r ) × R p × q × r , to a maximization problem over a product of three Grassmannians Gr( l, p ) × Gr( m, q ) × Gr( n, r ); and likewise we reduce (1.2) from O( n, r ) × S 3 ( R r ) to a maximization problem over Gr( n, r ).”
Krylov-Type Methods for Tensor Computations (2010, unknown): “One of the main theoretical and algorithmic problems researchers have addressed is the computation of low rank approximation of a given tensor [9, 14, 16, 23, 26].”
Tensor Decomposition for Signal Processing and Machine Learning (2016, background): “Variants for low multilinear rank approximation are discussed in [92], [93] and references therein.”
Variational calculus with sums of elementary tensors of fixed rank (2012, unknown): “It suggests that the approach might be competitive with optimization algorithms for alternative tensor formats as the Tucker Format [30] or the HT [17] format (with the TT format [26–28] as special case), for which the development is also still in progress: For the Tucker format, one obtains an opti”