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Article

Tensor-CUR decompositions for tensor-based data

Authors:

Michael W. Mahoney,

Mauro Maggioni,

Petros DrineasAuthors Info & Claims

KDD '06: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining

Pages 327 - 336

https://doi.org/10.1145/1150402.1150440

Published: 20 August 2006 Publication History

Abstract

Motivated by numerous applications in which the data may be modeled by a variable subscripted by three or more indices, we develop a tensor-based extension of the matrix CUR decomposition. The tensor-CUR decomposition is most relevant as a data analysis tool when the data consist of one mode that is qualitatively different than the others. In this case, the tensor-CUR decomposition approximately expresses the original data tensor in terms of a basis consisting of underlying subtensors that are actual data elements and thus that have natural interpretation in terms ofthe processes generating the data. In order to demonstrate the general applicability of this tensor decomposition, we apply it to problems in two diverse domains of data analysis: hyperspectral medical image analysis and consumer recommendation system analysis. In the hyperspectral data application, the tensor-CUR decomposition is used to compress the data, and we show that classification quality is not substantially reduced even after substantial data compression. In the recommendation system application, the tensor-CUR decomposition is used to reconstruct missing entries in a user-product-product preference tensor, and we show that high quality recommendations can be made on the basis of a small number of basis users and a small number of product-product comparisons from a new user.

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Cited By

Henneberger KQin J(2025)Hyperspectral Band Selection via Tensor Low Rankness and Generalized 3DTVRemote Sensing10.3390/rs1704056717:4(567)Online publication date: 7-Feb-2025
https://doi.org/10.3390/rs17040567
Hamlomo SAtemkeng MBrima YNunhokee CBaxter J(2025)A systematic review of low-rank and local low-rank matrix approximation in big data medical imagingNeural Computing and Applications10.1007/s00521-025-11055-2Online publication date: 4-Mar-2025
https://doi.org/10.1007/s00521-025-11055-2
Allen KLai MShen Z(2024)Maximal volume matrix cross approximation for image compression and least squares solutionAdvances in Computational Mathematics10.1007/s10444-024-10196-750:5Online publication date: 16-Sep-2024
https://doi.org/10.1007/s10444-024-10196-7
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Index Terms

Tensor-CUR decompositions for tensor-based data
1. Information systems
2. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Data types and structures

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Published In

cover image ACM Conferences

KDD '06: Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining

August 2006

986 pages

ISBN:1595933395

DOI:10.1145/1150402

Conference Chair:
Tina Eliassi-Rad
LLNL
,
General Chair:
Lyle Ungar
University of Pennsylvania
,
Program Chairs:
Mark Craven
University of Wisconsin
,
Dimitrios Gunopulos
University of California, Riverside

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 20 August 2006

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KDD06: The 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

August 20 - 23, 2006

PA, Philadelphia, USA

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Overall Acceptance Rate 1,133 of 8,635 submissions, 13%

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Cited By

Henneberger KQin J(2025)Hyperspectral Band Selection via Tensor Low Rankness and Generalized 3DTVRemote Sensing10.3390/rs1704056717:4(567)Online publication date: 7-Feb-2025
https://doi.org/10.3390/rs17040567
Hamlomo SAtemkeng MBrima YNunhokee CBaxter J(2025)A systematic review of low-rank and local low-rank matrix approximation in big data medical imagingNeural Computing and Applications10.1007/s00521-025-11055-2Online publication date: 4-Mar-2025
https://doi.org/10.1007/s00521-025-11055-2
Allen KLai MShen Z(2024)Maximal volume matrix cross approximation for image compression and least squares solutionAdvances in Computational Mathematics10.1007/s10444-024-10196-750:5Online publication date: 16-Sep-2024
https://doi.org/10.1007/s10444-024-10196-7
Salut MAnderson D(2023)Tensor Robust CUR for Compression and Denoising of Hyperspectral DataIEEE Access10.1109/ACCESS.2023.329763011(77492-77505)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3297630
Deshpande APratap R(2023)One-Pass Additive-Error Subset Selection for $$\ell _{p}$$ Subspace Approximation and (k, p)-ClusteringAlgorithmica10.1007/s00453-023-01124-085:10(3144-3167)Online publication date: 11-May-2023
https://doi.org/10.1007/s00453-023-01124-0
Qin ZLidiak AGong ZTang GWakin MZhu ZKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Error analysis of tensor-train cross approximationProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3601305(14236-14249)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3601305
Ida YKanai SFujiwara YIwata TTakeuchi KKashima HDaumé HSingh A(2020)Fast deterministic CUR matrix decomposition with accuracy assuranceProceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525365(4594-4603)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.5555/3524938.3525365
Traoré ABérar MRakotomamonjy AWallach HLarochelle HBeygelzimer Ad'Alché-Buc FFox E(2019)SingleshotProceedings of the 33rd International Conference on Neural Information Processing Systems10.5555/3454287.3454853(6304-6315)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3454287.3454853
Baladevi CHarikumar S(2018)Semantic Representation of Documents Based on Matrix Decomposition2018 International Conference on Data Science and Engineering (ICDSE)10.1109/ICDSE.2018.8527824(1-6)Online publication date: Aug-2018
https://doi.org/10.1109/ICDSE.2018.8527824
Kim MCandan K(2016)Decomposition-by-normalization (DBN)Data Mining and Knowledge Discovery10.1007/s10618-015-0401-630:1(1-46)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1007/s10618-015-0401-6
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