research-article

Static and Streaming Tucker Decomposition for Dense Tensors

Authors:

U KangAuthors Info & Claims

ACM Transactions on Knowledge Discovery from Data, Volume 17, Issue 5

Article No.: 66, Pages 1 - 34

https://doi.org/10.1145/3568682

Published: 27 February 2023 Publication History

Abstract

Given a dense tensor, how can we efficiently discover hidden relations and patterns in static and online streaming settings? Tucker decomposition is a fundamental tool to analyze multidimensional arrays in the form of tensors. However, existing Tucker decomposition methods in both static and online streaming settings have limitations of efficiency since they directly deal with large dense tensors for the result of Tucker decomposition. In a static setting, although few static methods have tried to reduce their time cost by sampling tensors, sketching tensors, and efficient matrix operations, there remains a need for an efficient method. Moreover, streaming versions of Tucker decomposition are still time-consuming to deal with newly arrived tensors.

We propose D-Tucker and D-TuckerO, efficient Tucker decomposition methods for large dense tensors in static and online streaming settings, respectively. By decomposing a given large dense tensor with randomized singular value decomposition, avoiding the reconstruction from SVD results, and carefully determining the order of operations, D-Tucker and D-TuckerO efficiently obtain factor matrices and core tensor. Experimental results show that D-Tucker achieves up to 38.4 × faster running times, and requires up to 17.2 × less space than existing methods while having similar accuracy. Furthermore, D-TuckerO is up to 6.1× faster than existing streaming methods for each newly arrived tensor while its running time is proportional to the size of the newly arrived tensor, not the accumulated tensor.

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Cited By

Kim JPark KJang JKang UBaeza-Yates RBonchi F(2024)Fast and Accurate Domain Adaptation for Irregular Tensor DecompositionProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671670(1383-1394)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671670
Jang JPark YKang USerra ESpezzano F(2024)Fast and Accurate PARAFAC2 Decomposition for Time Range Queries on Irregular TensorsProceedings of the 33rd ACM International Conference on Information and Knowledge Management10.1145/3627673.3679735(962-972)Online publication date: 21-Oct-2024
https://dl.acm.org/doi/10.1145/3627673.3679735
Liu HHe QDong HLiu ZHu X(2024)Sparse Geomagnetic Time-Series Sensing Data Completion Leveraging Improved Tensor Correlated Total VariationIEEE Sensors Journal10.1109/JSEN.2024.348631324:24(41484-41495)Online publication date: 15-Dec-2024
https://doi.org/10.1109/JSEN.2024.3486313
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Index Terms

Static and Streaming Tucker Decomposition for Dense Tensors
1. Computing methodologies
  1. Machine learning
    1. Machine learning approaches
      1. Factorization methods
2. Information systems
  1. Information systems applications
    1. Data mining

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cover image ACM Transactions on Knowledge Discovery from Data

ACM Transactions on Knowledge Discovery from Data Volume 17, Issue 5

June 2023

386 pages

ISSN:1556-4681

EISSN:1556-472X

DOI:10.1145/3583066

Editor:
Charu Aggarwal
IBM T. J. Watson Research, USA

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Publication History

Published: 27 February 2023

Online AM: 20 October 2022

Accepted: 23 September 2022

Revised: 01 August 2022

Received: 09 December 2021

Published in TKDD Volume 17, Issue 5

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National Research Foundation of Korea (NRF) funded by MSIT
Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by MSIT
Artificial Intelligence Graduate School Program (Seoul National University)
Artificial Intelligence Innovation Hub (Artificial Intelligence Institute, Seoul National University)

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Cited By

Kim JPark KJang JKang UBaeza-Yates RBonchi F(2024)Fast and Accurate Domain Adaptation for Irregular Tensor DecompositionProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671670(1383-1394)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671670
Jang JPark YKang USerra ESpezzano F(2024)Fast and Accurate PARAFAC2 Decomposition for Time Range Queries on Irregular TensorsProceedings of the 33rd ACM International Conference on Information and Knowledge Management10.1145/3627673.3679735(962-972)Online publication date: 21-Oct-2024
https://dl.acm.org/doi/10.1145/3627673.3679735
Liu HHe QDong HLiu ZHu X(2024)Sparse Geomagnetic Time-Series Sensing Data Completion Leveraging Improved Tensor Correlated Total VariationIEEE Sensors Journal10.1109/JSEN.2024.348631324:24(41484-41495)Online publication date: 15-Dec-2024
https://doi.org/10.1109/JSEN.2024.3486313
Lee SPark YKang U(2024)Accurate Coupled Tensor Factorization with Knowledge Graph2024 IEEE International Conference on Big Data (BigData)10.1109/BigData62323.2024.10825614(1009-1018)Online publication date: 15-Dec-2024
https://doi.org/10.1109/BigData62323.2024.10825614
Wei STang YGao TWang YWang FChen D(2024)Scale-variant structural feature construction of EEG stream via component-increased Dynamic Tensor DecompositionKnowledge-Based Systems10.1016/j.knosys.2024.111747294(111747)Online publication date: Jul-2024
https://doi.org/10.1016/j.knosys.2024.111747
Gillet ALeclercq ÉSautot L(2023)A Guide to the Tucker Tensor Decomposition for Data Mining: Exploratory Analysis, Clustering and ClassificationTransactions on Large-Scale Data- and Knowledge-Centered Systems LIV10.1007/978-3-662-68014-8_3(56-88)Online publication date: 22-Sep-2023
https://doi.org/10.1007/978-3-662-68014-8_3
Jang JLee JPark JKang U(2022)Accurate PARAFAC2 Decomposition for Temporal Irregular Tensors with Missing Values2022 IEEE International Conference on Big Data (Big Data)10.1109/BigData55660.2022.10020667(982-991)Online publication date: 17-Dec-2022
https://doi.org/10.1109/BigData55660.2022.10020667

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