About: Low Complexity Damped Gauss-Newton algorithms for CANDECOMP/PARAFAC

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of factors and different magnitudes of factors; nevertheless, for factorization of an order-N tensor of size I_1I_2 I_N with rank R, the algorithm is computationally demanding due to construction of large approximate Hessian of size (RT RT) and its inversion where T= sum_n I_n. In this paper, we propose a fast implementation of the dGN algorithm which is based on novel expressions of the inverse approximate Hessian in block form. The new implementation has lower computational complexity, besides computation of the gradient, requiring the inversion of a matrix of size NR^2xNR^2, which is smaller than the whole approximate Hessian, if T>NR. In addition, neither the Hessian nor its inverse never needs to be stored in its entirety. A variant of the algorithm working with complex-valued data is proposed as well. The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of factors and different magnitudes of factors; nevertheless, for factorization of an order-N tensor of size I_1I_2 I_N with rank R, the algorithm is computationally demanding due to construction of large approximate Hessian of size (RT RT) and its inversion where T= sum_n I_n. In this paper, we propose a fast implementation of the dGN algorithm which is based on novel expressions of the inverse approximate Hessian in block form. The new implementation has lower computational complexity, besides computation of the gradient, requiring the inversion of a matrix of size NR^2xNR^2, which is smaller than the whole approximate Hessian, if T>NR. In addition, neither the Hessian nor its inverse never needs to be stored in its entirety. A variant of the algorithm working with complex-valued data is proposed as well. (en)
Title	Low Complexity Damped Gauss-Newton algorithms for CANDECOMP/PARAFAC Low Complexity Damped Gauss-Newton algorithms for CANDECOMP/PARAFAC (en)
skos:prefLabel	Low Complexity Damped Gauss-Newton algorithms for CANDECOMP/PARAFAC Low Complexity Damped Gauss-Newton algorithms for CANDECOMP/PARAFAC (en)
skos:notation	RIV/67985556:_____/13:00391019!RIV14-MSM-67985556
http://linked.open...avai/predkladatel	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(1M0572), P(GA102/09/1278)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Tichavský, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	85459
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/13:00391019
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	tensor factorization; canonical polyadic decomposition; alternating least squares (en)
http://linked.open.../riv/klicoveSlovo	tensor factorization alternating least squares canonical polyadic decomposition
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[BFC37CFE944A]
http://linked.open...i/riv/nazevZdroje	SIAM Journal on Matrix Analysis and Applications
http://linked.open...in/vavai/riv/obor	BB
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Advanced methods of blind source separation and blind deconvolution Data, algorithms, decision making
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	34
http://linked.open...iv/tvurceVysledku	Tichavský, Petr Cichocki, A. Phan, A. H.
http://linked.open...ain/vavai/riv/wos	000316855600007
issn	0895-4798
number of pages	22 (xsd:int)
http://bibframe.org/vocab/doi	10.1137/100808034

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