The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
Tensor-Train Decomposition
Abstract
A simple nonrecursive form of the tensor decomposition in d dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number of parameters as the canonical decomposition, but it is stable and its computation is based on low-rank approximation of auxiliary unfolding matrices. The new form gives a clear and convenient way to implement all basic operations efficiently. A fast rounding procedure is presented, as well as basic linear algebra operations. Examples showing the benefits of the decomposition are given, and the efficiency is demonstrated by the computation of the smallest eigenvalue of a 19-dimensional operator.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Tensor Decompositions and Applications
Kolda, T. G., & Bader, B. W. (2009) · SIAM Review · doi:10.1137/07070111x · Cited by 10,301
Carroll, J. D., & Chang, J.-J. (1970) · Psychometrika · doi:10.1007/bf02310791 · Cited by 4,678
A Multilinear Singular Value Decomposition
De Lathauwer, L., De Moor, B., & Vandewalle, J. (2000) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479896305696 · Cited by 4,106
Some Mathematical Notes on Three-Mode Factor Analysis
Tucker, L. R. (1966) · Psychometrika · doi:10.1007/bf02289464 · Cited by 3,492
PARAFAC. Tutorial and applications
Bro, R. (1997) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(97)00032-4 · Cited by 2,814
Harshman, R. A. (1970) · Cited by 2,255
On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
De Lathauwer, L., De Moor, B., & Vandewalle, J. (2000) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479898346995 · Cited by 1,567
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
Babuska, I. M., Nobile, F., & Tempone, R. F. (2007) · SIAM Journal on Numerical Analysis · doi:10.1137/050645142 · Cited by 1,458
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
de Silva, V., & Lim, L.-H. (2008) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/06066518x · Cited by 927
Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
Babuska, I. M., Tempone, R. F., & Zouraris, G. E. (2004) · SIAM Journal on Numerical Analysis · doi:10.1137/s0036142902418680 · Cited by 877
Cited by
Recent advances in convolutional neural networks
Gu, J., Wang, Z., Kuen, J., Ma, L., Shahroudy, A., Shuai, B., Liu, T., Wang, X., Wang, G., Cai, J., et al. (2018) · Pattern Recognition · doi:10.1016/j.patcog.2017.10.013 · Cited by 6,576
Deep Convolutional Neural Networks for Image Classification: A Comprehensive Review
Rawat, W., & Wang, Z. (2017) · Neural Computation · doi:10.1162/neco_a_00990 · Cited by 3,503
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
Benner, P., Gugercin, S., & Willcox, K. (2015) · SIAM Review · doi:10.1137/130932715 · Cited by 1,916
Tensor Decomposition for Signal Processing and Machine Learning
Sidiropoulos, N. D., De Lathauwer, L., Fu, X., Huang, K., Papalexakis, E. E., & Faloutsos, C. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2017.2690524 · Cited by 1,617
Deep learning enables rapid identification of potent DDR1 kinase inhibitors
Zhavoronkov, A., Ivanenkov, Y. A., Aliper, A., Veselov, M. S., Aladinskiy, V. A., Aladinskaya, A. V., Terentiev, V. A., Polykovskiy, D. A., Kuznetsov, M. D., Asadulaev, A., et al. (2019) · Nature Biotechnology · doi:10.1038/s41587-019-0224-x · Cited by 1,573
Metadata
- Authors
- Oseledets, I. V.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2011-01
- Volume
- 33
- Issue
- 5
- Pages
- 2295-2317
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W1993482030
- Cited by
- 2,636
- References
- 31
- FWCI
- 12.34
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Tensor-Train Decomposition. https://app.cochat.ai/papers/10.1137/090752286
- The paper
- Oseledets, I. V. (2011). Tensor-Train Decomposition. SIAM Journal on Scientific Computing. https://doi.org/10.1137/090752286
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
