基于改进张量链分解的多聚类算法

张宏俊; 张泽宇; 张颖娇; 叶昊; 潘高军

doi:10.11959/j.issn.1000-0801.2025043

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基于改进张量链分解的多聚类算法

研究与开发 | 更新时间：2025-06-28

- 基于改进张量链分解的多聚类算法
- Multi-clustering algorithm based on improved tensor chain decomposition
- 电信科学 2025年41卷第6期页码：103-120
- 作者机构：
  
  1.中国通信服务股份有限公司，北京 100073
  2.南京邮电大学物联网学院，江苏南京 210003
  3.曼彻斯特大学人工智能学院，英国曼彻斯特 M13 9PL
  4.南京邮电大学现代邮政学院，江苏南京 210003
  5.华为技术有限公司南京研究所，江苏南京 210012
  6.北京外企德科人力资源服务上海有限公司，上海 200011
  7.浙江省通信产业服务有限公司，浙江杭州 310052
- 作者简介：
  
  [ "张宏俊（1985- ），男，博士，中国通信服务股份有限公司正高级工程师，主要研究方向为高性能计算、大数据关键技术。" ]
  [ "张泽宇（2000- ），男，曼彻斯特大学人工智能学院硕士生，主要研究方向为机器学习、数据挖掘以及图像识别。" ]
  [ "张颖娇（2000- ），女，南京邮电大学现代邮政学院硕士生，主要研究方向为网络安全、物流隐私自动化。" ]
  [ "叶昊（1999- ），男，华为技术有限公司南京研究所助理工程师，主要研究方向为智能制造、自动化容器编排平台、云服务安全测试以及数据挖掘。" ]
  [ "潘高军（1977- ），男，浙江省通信产业服务有限公司高级工程师，主要研究方向为物联网、大数据关键技术、人工智能、区块链。" ]
- 基金信息：
  
  国家自然科学基金资助项目(61972208;62102194;62272239);江苏省研究生科研与实践创新计划项目（No.KYCX22_1027(SJCX24_0339);No.SJCX24_0346;南京邮电大学大学生创新训练计划项目(XZD2019116;XYB2019331)
- DOI：10.11959/j.issn.1000-0801.2025043
  中图分类号： TP393
- 收稿日期：2024-11-23，
  
  修回日期：2025-02-25，
  
  纸质出版日期：2025-06-20
- 稿件说明：
移动端阅览
张宏俊,张泽宇,张颖娇等.基于改进张量链分解的多聚类算法[J].电信科学,2025,41(06):103-120.

ZHANG Hongjun,ZHANG Zeyu,ZHANG Yingjiao,et al.Multi-clustering algorithm based on improved tensor chain decomposition[J].Telecommunications Science,2025,41(06):103-120.
张宏俊,张泽宇,张颖娇等.基于改进张量链分解的多聚类算法[J].电信科学,2025,41(06):103-120. DOI： 10.11959/j.issn.1000-0801.2025043.

ZHANG Hongjun,ZHANG Zeyu,ZHANG Yingjiao,et al.Multi-clustering algorithm based on improved tensor chain decomposition[J].Telecommunications Science,2025,41(06):103-120. DOI： 10.11959/j.issn.1000-0801.2025043.

摘要

随着大数据时代的到来，高阶数据的有效表示和分析成为一项重大挑战。基于此，聚焦于张量分解技术在多聚类算法中的应用，特别是针对大型多源异构数据集的处理，深入研究并改进了张量链（tensor train，TT）分解方法，通过引入新的优化策略，显著提高了其在多聚类任务中的性能。创新主要体现在两个方面：一是提出了一种新的张量分解框架，该框架通过优化目标函数，有效降低了存储成本并提高了计算效率；二是将改进的张量分解技术应用于3种主要的多聚类算法中，包括自加权多视图聚类（self-weighted multi-view clustering，SwMC）、潜在多视图子空间聚类（latent multi-view subspace clustering，LMSC）和具有完整性感知相似性的多视图子空间聚类（multi-view subspace clustering with intactness-aware similarity，MSC IAS），显著提升了聚类的准确性和效率。为了验证方法的有效性，在7个真实的数据集上进行了全面的实验评估，包括准确性（accuracy，ACC）、归一化互信息（normalized mutual information，NMI）和纯度等3个指标。实验结果表明，所提出的方法在提取有意义的模式和提高聚类性能方面具有显著优势。

Abstract

With the advent of the era of big data

the effective representation and analysis of high-level data has become a major challenge. Based on this

the application of tensor decomposition technology in multi-clustering algorithms was focused on especially for the processing of large multi-source heterogeneous datasets. The tensor train (TT) method was studied and improved in depth

which had significantly improved its performance in multi-clustering tasks by introducing a new optimization strategy. The innovations were mainly reflected in two aspects: firstly

a new tensor decomposition framework was proposed

which effectively reduced the storage cost and improved the computational efficiency by optimizing the objective function; secondly

the improved tensor decomposition technique was applied to three main multi-clustering algorithms

including self-weighted multi-view clustering (SwMC)

latent multi-view subspace clustering (LMSC)

and multi-view subspace clustering with intactness-aware similarity (MSC IAS)

which significantly improved the accuracy and efficiency of clustering. To validate the effectiveness of the proposed methodology

comprehensive experiments were conducted on seven real-world datasets

including assessments of key metrics such as accuracy (ACC)

normalized mutual information (NMI)

and purity. Experimental results show that the proposed method has significant advantages in extracting meaningful patterns and improving clustering performance.

关键词

Keywords

references

ZHAO Y L , YANG L T , ZHANG R H . A tensor-based multiple clustering approach with its applications in automation systems [J ] . IEEE Transactions on Industrial Informatics , 2018 , 14 ( 1 ): 283 - 291 .

MAI Q , ZHANG X , PAN Y Q , et al . A doubly enhanced EM algorithm for model-based tensor clustering [J ] . Journal of the American Statistical Association , 2022 , 117 ( 540 ): 2120 - 2134 .

KOWALSKI P A , JECZMIONEK E . Parallel complete gradient clustering algorithm and its properties [J ] . Information Sciences , 2022 , 600 : 155 - 169 .

SEDIGHIN F , CICHOCKI A , PHAN A H . Adaptive rank selection for tensor ring decomposition [J ] . IEEE Journal of Selected Topics in Signal Processing , 2021 , 15 ( 3 ): 454 - 463 .

TICHAVSKÝ P , PHAN A H , CICHOCKI A . Krylov-levenberg-marquardt algorithm for structured tucker tensor decompositions [J ] . IEEE Journal of Selected Topics in Signal Processing , 2021 , 15 ( 3 ): 550 - 559 .

ZHENG Y L , LIU Q S . A review of distributed optimization: problems, models and algorithms [J ] . Neurocomputing , 2022 , 483 : 446 - 459 .

MICKELIN O , KARAMAN S . On algorithms for and computing with the tensor ring decomposition [J ] . Numerical Linear Algebra with Applications , 2020 , 27 ( 3 ): e2289 .

BOSE A , WALTERS P L . A multisite decomposition of the tensor network path integrals [J ] . The Journal of Chemical Physics , 2022 , 156 ( 2 ): 024101 .

LIU H Z , YANG L T , YAO T , et al . Tensor-train-based higher order dominant Z-eigen decomposition for multi-modal prediction and its cloud/edge implementation [J ] . IEEE Transactions on Network Science and Engineering , 2021 , 8 ( 2 ): 1353 - 1366 .

ASANTE-MENSAH M G , AHMADI-ASL S , CICHOCKI A . Matrix and tensor completion using tensor ring decomposition with sparse representation [J ] . Machine Learning: Science and Technology , 2021 , 2 ( 3 ): 035008 .

CHEN H Y , AHMAD F , VOROBYOV S , et al . Tensor decompositions in wireless communications and MIMO radar [J ] . IEEE Journal of Selected Topics in Signal Processing , 2021 , 15 ( 3 ): 438 - 453 .

LIN Z C , LIU R S , SU Z X , et al . Linearized alternating direction method with adaptive penalty for low-rank representation [C ] // Proceedings of the 25th International Conference on Neural Information Processing Systems . New York : ACM Press , 2011 : 612 - 620 .

ZHANG C Q , HU Q H , FU H Z , et al . Latent multi-view subspace clustering [C ] // Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) . Piscataway : IEEE Press , 2017 : 4333 - 4341 .

CHENG Y , ZHAO R L . Multiview spectral clustering via ensemble [C ] // Proceedings of the 2009 IEEE International Conference on Granular Computing . Piscataway : IEEE Press , 2009 : 101 - 106 .

ELHAMIFAR E , VIDAL R . Sparse subspace clustering: algorithm, theory, and applications [J ] . IEEE Transactions on Pattern Analysis and Machine Intelligence , 2013 , 35 ( 11 ): 2765 - 2781 .

HU H , LIN Z C , FENG J J , et al . Smooth representation clustering [C ] // Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition . Piscataway : IEEE Press , 2014 : 3834 - 3841 .

WANG X B , LEI Z , GUO X J , et al . Multi-view subspace clustering with intactness-aware similarity [J ] . Pattern Recognition , 2019 , 88 : 50 - 63 .

WHITE M , YU Y L , ZHANG X H , et al . Convex multi-view subspace learning [C ] // Proceedings of the 25th Annual Conference on Neural Information Processing Systems . Lake Tahoe, USA : NIPS , 2012 , 1673 - 1681 .

KRUSKAL J B . Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics [J ] . Linear Algebra and Its Applications , 1977 , 18 ( 2 ): 95 - 138 .

SIDIROPOULOS N D , BRO R . On the uniqueness of multilinear decomposition of N-way arrays [J ] . Journal of Chemometrics , 2000 , 14 ( 3 ): 229 - 239 .

CICHOCKI A , MANDIC D , DE LATHAUWER L , et al . Tensor decompositions for signal processing applications: from two-way to multiway component analysis [J ] . IEEE Signal Processing Magazine , 2015 , 32 ( 2 ): 145 - 163 .

KOLDA T G , BADER B W . Tensor decompositions and applications [J ] . SIAM Review , 2009 , 51 ( 3 ): 455 - 500 .

GRASEDYCK L , KRESSNER D , TOBLER C . A literature survey of low-rank tensor approximation techniques [J ] . GAMM-Mitteilungen , 2013 , 36 ( 1 ): 53 - 78 .

PHAN A H , TICHAVSKÝ P , CICHOCKI A . Fast alternating LS algorithms for high order CANDECOMP/PARAFAC tensor factorizations [J ] . IEEE Transactions on Signal Processing , 2013 , 61 ( 19 ): 4834 - 4846 .

CHEN D , HU Y Y , WANG L Z , et al . H-PARAFAC: hierarchical parallel factor analysis of multidimensional big data [J ] . IEEE Transactions on Parallel and Distributed Systems , 2017 , 28 ( 4 ): 1091 - 1104 .

ANDERSSON C A , BRO R . The N-way toolbox for MATLAB [J ] . Chemometrics and Intelligent Laboratory Systems , 2000 , 52 ( 1 ): 1 - 4 .

CHEN Y N , HAN D R , QI L Q . New ALS methods with extrapolating search directions and optimal step size for complex-valued tensor decompositions [J ] . IEEE Transactions on Signal Processing , 2011 , 59 ( 12 ): 5888 - 5898 .

KIERS H A L . A three-step algorithm for CANDECOMP/PARAFAC analysis of large data sets with multicollinearity [J ] . Journal of Chemometrics , 1998 , 12 ( 3 ): 155 - 171 .

ACAR E , DUNLAVY D M , KOLDA T G . A scalable optimization approach for fitting canonical tensor decompositions [J ] . Journal of Chemometrics , 2011 , 25 ( 2 ): 67 - 86 .

COHEN J , FARIAS R C , COMON P . Fast decomposition of large nonnegative tensors [J ] . IEEE Signal Processing Letters , 2015 , 22 ( 7 ): 862 - 866 .

PAATERO P . A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis [J ] . Chemometrics and Intelligent Laboratory Systems , 1997 , 38 ( 2 ): 223 - 242 .

PHAN A H , TICHAVSKÝ P , CICHOCKI A . Low complexity damped Gauss: Newton algorithms for CANDECOMP/PARAFAC [J ] . SIAM Journal on Matrix Analysis and Applications , 2013 , 34 ( 1 ): 126 - 147 .

DE LATHAUWER L . A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization [J ] . SIAM Journal on Matrix Analysis and Applications , 2006 , 28 ( 3 ): 642 - 666 .

DE LATHAUWER L , CASTAING J . Blind identification of underdetermined mixtures by simultaneous matrix diagonalization [J ] . IEEE Transactions on Signal Processing , 2008 , 56 ( 3 ): 1096 - 1105 .

DE LATHAUWER L , DE MOOR B , VANDEWALLE J . A multilinear singular value decomposition [J ] . SIAM Journal on Matrix Analysis and Applications , 2000 , 21 ( 4 ): 1253 - 1278 .

CICHOCKI A , ZDUNEK R , PHAN A H , et al . Nonnegative matrix and tensor factorizations: applications to exploratory multi-way data analysis and blind source separation [M ] . New Jersey : Wiley , 2009 .

MØRUP M , HANSEN L K , ARNFRED S M . Algorithms for sparse nonnegative tucker decompositions [J ] . Neural Computation , 2008 , 20 ( 8 ): 2112 - 2131 .

KIM Y D , CHOI S . Nonnegative tucker decomposition [C ] // Proceedings of the 2007 IEEE Conference on Computer Vision and Pattern Recognition . Piscataway : IEEE Press , 2007 : 1 - 8 .

CICHOCKI A , ZDUNEK R , CHOI S , et al . Non-negative tensor factorization using alpha and beta divergences [C ] // Proceedings of the 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07 . Piscataway : IEEE Press , 2007 : III-1393-III-1396.

AHMADI-ASL S , ABUKHOVICH S , ASANTE-MENSAH M G , et al . Randomized algorithms for computation of tucker decomposition and higher order SVD (HoSVD) [J ] . IEEE Access , 2021 , 9 : 28684 - 28706 .

LI H C , LIU S , FENG X R , et al . Sparsity-constrained coupled nonnegative matrix-tensor factorization for hyperspectral unmixing [J ] . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 2020 , 13 : 5061 - 5073 .

MARMORET A , COHEN J E , BERTIN N , et al . Uncovering audio patterns in music with nonnegative tucker decomposition for structural segmentation [EB ] . 2021 .

HAGHSHENAS R , GRAY J , POTTER A C , et al . Variational power of quantum circuit tensor networks [J ] . Physical Review X , 2022 , 12 : 011047 .

CICHOCKI A , LEE N , OSELEDETS I , et al . Tensor networks for dimensionality reduction and large-scale optimization: part 1 low-rank tensor decompositions [J ] . Foundations and Trends® in Machine Learning , 2016 , 9 ( 4/5 ): 249 - 429 .

ORÚS R . A practical introduction to tensor networks: matrix product states and projected entangled pair states [J ] . Annals of Physics , 2014 , 349 : 117 - 158 .

HANDSCHUH S . Changing the topology of tensor networks [J ] . arXiv preprint , 2014 : 1203 .1503.

HÜBENER R , NEBENDAHL V , DÜR W . Concatenated tensor network states [J ] . New Journal of Physics , 2010 , 12 ( 2 ): 025004 .

GRASEDYCK L . Hierarchical singular value decomposition of tensors [J ] . SIAM Journal on Matrix Analysis and Applications , 2010 , 31 ( 4 ): 2029 - 2054 .

ZHAO Y L , YANG L T , ZHANG R . Tensor-based multiple clustering approaches for cyber-physical-social applications [J ] . IEEE Transactions on Emerging Topics in Computing , 2018 , 8 ( 1 ): 69 - 81 .

PAN F , ZHANG P . Simulation of quantum circuits using the big-batch tensor network method [J ] . Physical Review Letters , 2022 , 128 ( 3 ): 030501 .

张宏俊 , 李鹏 , 王汝传 , 等 . 一种基于张量的多维印章数据处理方法 : CN117592951A [P ] . 2024-02-23 .

ZHANG H J , LI P , WANG R C , et al . A tensor-based multi-dimensional seal data processing method : CN117592951A [P ] . 2024-02-23 .

OSELEDETS I V . Tensor-train decomposition [J ] . SIAM Journal on Scientific Computing , 2011 , 33 ( 5 ): 2295 - 2317 .

QIN Y L , TANG Z J , WU H Z , et al . Flexible tensor learning for multi-view clustering with Markov chain [J ] . IEEE Transactions on Knowledge and Data Engineering , 2024 , 26 ( 4 ): 1552 - 1565 .

BARCZA G , LEGEZA , MARTI K H , et al . Quantum-information analysis of electronic states of different molecular structures [J ] . Physical Review A , 2011 , 83 : 012508 .

EHLERS G , SÓLYOM J , LEGEZA , et al . Entanglement structure of the Hubbard model in momentum space [J ] . Physical Review B , 2015 , 92 ( 23 ): 235116 .

ZHAO Q , ZHOU G , XIE S , et al . Tensor ring decomposition [J ] . arXiv preprint , 2016 : 1606 .05535.

WANG W Q , AGGARWAL V , AERON S . Efficient low rank tensor ring completion [C ] // Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV) . Piscataway : IEEE Press , 2017 : 5698 - 5706 .

STAHLG , STAHLG . Contributions to a theoretical framework for CSCL [C ] // Proceedings of the Conference on Computer Support for Collaborative Learning: Foundations for a CSCL Community . New York : ACM Press , 2002 : 62 - 71 .

SHAIBU M . Assessment of physicochemical parameters and organochlorine pesticide residues in selected vegetable farmlands soil in Zamfara state, Nigeria [J ] . Science Progress and Research , 2022 , 2 ( 2 ): 559 - 566 .

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