Low Complexity Damped Gauss-Newton algorithms for CANDECOMP/PARAFAC
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F13%3A00391019" target="_blank" >RIV/67985556:_____/13:00391019 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/100808034" target="_blank" >http://dx.doi.org/10.1137/100808034</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/100808034" target="_blank" >10.1137/100808034</a>
Alternative languages
Result language
angličtina
Original language name
Low Complexity Damped Gauss-Newton algorithms for CANDECOMP/PARAFAC
Original language 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 algorithmis 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.
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
—
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Matrix Analysis and Applications
ISSN
0895-4798
e-ISSN
—
Volume of the periodical
34
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
22
Pages from-to
126-147
UT code for WoS article
000316855600007
EID of the result in the Scopus database
—