Enhanced Line Search: A novel method to accelerate Parafac

By Myriam Rajih, Pierre Comon. 2005

243 citations recorded by the source corpus.

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…robustness of gradient-based and Newton-like methods [2,72,74,140,223,224], modifying and improving ALS (alternating least squares) [41, 57, 58, 90, 225], studying the convergence of ALS [51, 194, 253] and reducing the cost of the unfolding operations required during the approximation [222,269].”
A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition (2011, methodology): “All initial guesses are determined uniformly randomly, as in [14], and when we compare diﬀerent methods they are given the same random initial guess.”
CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping (2012, methodology): “In addition, line search extrapolation methods [1], [4], [5], [23], [24], [36 ] become more complicated, and demand high computational cost to build up and solve (2 N − 1)- order polynomials.”
Computations in quantum tensor networks (2012, methodology): “One possibility to accelerate the als -based optimization procedure is to apply the Enhanced Linesearch method [59], which is not considered here.”
An Adaptive Algebraic Multigrid Algorithm for Low-Rank Canonical Tensor Decomposition (2011, unknown): “It would also be interesting to consider other ALS-type methods for the relaxations, for example, ALS accelerated by line search [32], as well as to apply our method to the regularized optimization formulation of CP as described in [1].”
On Fast Computation of Gradients for CANDECOMP/PARAFAC Algorithms (2012, methodology): “, there have been intensive research eﬀorts to improveperformanceand accelerate convergencerate of CP algorithms. A numberof particulartechniquesare developedsuch as line search extrapolation methods [2, 16, 27, 33], compression [19], or simply adding a small diagonal matrix [10]. Instead of alterna”
Local Convergence of the Alternating Least Squares Algorithm for Canonical Tensor Approximation (2012, background): “The great majority of the literature focuses on global properties of the iteration, like the existence of convergent subsequences and critical points, or the occurrence of swamps [3, 6, 7, 15, 17, 21, 22].”
New ALS Methods With Extrapolating Search Directions and Optimal Step Size for Complex-Valued Tensor Decompositions (2011, methodology): “This method is called “enhanced line search” (ELS) [6], [29], [30].”
Tensors : A brief introduction (2014, unknown): “General-purpose optimization algorithms will generally sufﬁce to solve the problem, e.g. [77], [65], [46], [21], [84]; they are widely used but their convergence towards a minimum is not guaranteed, because the objective function may have only an inﬁmum.”