Tensor Deflation for CANDECOMP/PARAFAC - Part I: Alternating Subspace Update Algorithm
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F15%3A00448255" target="_blank" >RIV/67985556:_____/15:00448255 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1109/TSP.2015.2458785" target="_blank" >http://dx.doi.org/10.1109/TSP.2015.2458785</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TSP.2015.2458785" target="_blank" >10.1109/TSP.2015.2458785</a>
Alternative languages
Result language
angličtina
Original language name
Tensor Deflation for CANDECOMP/PARAFAC - Part I: Alternating Subspace Update Algorithm
Original language description
CANDECOMP/PARAFAC (CP) approximates multiway data by sum of rank-1 tensors. Unlike matrix decomposition, the procedure which estimates the best rank-tensor approximation through R sequential best rank-1 approximations does not work for tensors, because the deflation does not always reduce the tensor rank. In this paper, we propose a novel deflation method for the problem. When one factor matrix of a rank-CP decomposition is of full column rank, the decomposition can be performed through (R-1) rank-1 reductions. At each deflation stage, the residue tensor is constrained to have a reduced multilinear rank. For decomposition of order-3 tensors of size RxRxR and rank-R estimation of one rank-1 tensor has a computational cost of O(R^3) per iteration which is lower than the cost O(R^4) of the ALS algorithm for the overall CP decomposition. The method can be extended to tracking one or a few rank-one tensors of slow changes, or inspect variations of common patterns in individual datasets.
Czech name
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Czech description
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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
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Result continuities
Project
<a href="/en/project/GA14-13713S" target="_blank" >GA14-13713S: Tensor Decomposition Methods and Their Applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Signal Processing
ISSN
1053-587X
e-ISSN
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Volume of the periodical
63
Issue of the periodical within the volume
22
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
5924-5938
UT code for WoS article
000362746500004
EID of the result in the Scopus database
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