Optimizing the Order of Modes in Tensor Train Decomposition
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F25%3A00618543" target="_blank" >RIV/67985556:_____/25:00618543 - isvavai.cz</a>
Alternative codes found
RIV/49777513:23520/25:43976695
Result on the web
<a href="https://ieeexplore.ieee.org/document/10930561" target="_blank" >https://ieeexplore.ieee.org/document/10930561</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/LSP.2025.3552005" target="_blank" >10.1109/LSP.2025.3552005</a>
Alternative languages
Result language
angličtina
Original language name
Optimizing the Order of Modes in Tensor Train Decomposition
Original language description
The tensor train (TT) is a popular way of representing high-dimensional hyper-rectangular data structures called tensors. It is widely used, for example, in quantum chemistry under the name „matrix product state“. The complexity of the TT model mainly depends on the bond dimensions that connect TT cores, constituting the model. Unlike canonical polyadic decomposition, the TT model complexity may depend on the order of the modes/indices in the data structures or the order of the core tensors in the TT, in general. This paper aims to provide methods for optimizing the order of the modes to reduce the bond dimensions. Since the number of possible orderings of the cores is exponentially high, we propose a greedy algorithm that provides a suboptimal solution. We consider three problem setups, i.e., specifications of the tensor: tensor given by a list of all its elements, tensor described by a TT model with some default order of the modes, and tensor obtained by sampling a multivariate function.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA22-11101S" target="_blank" >GA22-11101S: Tensor Decomposition in Active Fault Diagnosis for Stochastic Large Scale Systems</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Signal Processing Letters
ISSN
1070-9908
e-ISSN
1558-2361
Volume of the periodical
32
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
5
Pages from-to
1361-1365
UT code for WoS article
001455423000004
EID of the result in the Scopus database
2-s2.0-105001657523