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A Guide to the Tucker Tensor Decomposition for Data Mining: Exploratory Analysis, Clustering and Classification

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Transactions on Large-Scale Data- and Knowledge-Centered Systems LIV

Part of the book series: Lecture Notes in Computer Science ((TLDKS,volume 14160))

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Abstract

Tensors are powerful multi-dimensional mathematical objects, that easily embed various data models such as relational, graph or time series. Furthermore, tensor decomposition operators are of great utility to reveal hidden patterns and complex relationships in data. Among these decompositions, the Tucker decomposition allows to factorize a tensor into a smaller core tensor and a set of factor matrices. In this article, we propose to study the capabilities of the Tucker decomposition when it is used in data mining techniques such as exploratory analysis, clustering and classification of data. We apply these different techniques on practical examples using several datasets having a ground truth. It is a preliminary work to add the Tucker decomposition to the Tensor Data Model, a model aiming at making tensors data-centric, and at optimizing operators in order to enable the manipulation of large tensors.

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Notes

  1. 1.

    https://github.com/AnnabelleGillet/Tucker-experiments.

  2. 2.

    https://archive.ics.uci.edu/ml/datasets/iris.

  3. 3.

    Most of the works presenting the classification technique do not perform a duplication, and directly compare the partial core tensor against each sample and each class [5, 11]. It is less efficient as it implies at most \(s \times c\) comparisons, while duplicating the element reduce the number of comparisons to c. During our experiments, we find it more efficient to duplicate the element, as it allows to compare a unified pattern of a class with the sample without focusing on an outlier that could negatively impact the result.

References

  1. Al-Sharoa, E., Al-Khassaweneh, M., Aviyente, S.: A tensor based framework for community detection in dynamic networks. In: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 2312–2316. IEEE (2017)

    Google Scholar 

  2. Angles, R., Arenas, M., Barceló, P., Hogan, A., Reutter, J., Vrgoč, D.: Foundations of modern query languages for graph databases. ACM Comput. Surv. (CSUR) 50(5), 1–40 (2017)

    Article  Google Scholar 

  3. Araujo, M., et al.: Com2: fast automatic discovery of temporal (‘Comet’) communities. In: Tseng, V.S., Ho, T.B., Zhou, Z.-H., Chen, A.L.P., Kao, H.-Y. (eds.) PAKDD 2014. LNCS (LNAI), vol. 8444, pp. 271–283. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-06605-9_23

    Chapter  Google Scholar 

  4. Atikoglu, B., Xu, Y., Frachtenberg, E., Jiang, S., Paleczny, M.: Workload analysis of a large-scale key-value store. In: ACM SIGMETRICS Performance Evaluation Review, vol. 40, pp. 53–64. ACM (2012)

    Google Scholar 

  5. Brandoni, D., Simoncini, V.: Tensor-train decomposition for image recognition. Calcolo 57, 1–24 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chachlakis, D.G., Prater-Bennette, A., Markopoulos, P.P.: L1-norm tucker tensor decomposition. IEEE Access 7, 178454–178465 (2019)

    Article  Google Scholar 

  7. Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, Chichester (2009)

    Book  Google Scholar 

  8. De Lathauwer, L., De Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4), 1253–1278 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Deng, L.: The MNIST database of handwritten digit images for machine learning research [best of the web]. IEEE Signal Process. Mag. 29(6), 141–142 (2012)

    Article  Google Scholar 

  10. Duan, L., Xiao, C., Li, M., Ding, M., Yang, C.: a-tucker: fast input-adaptive and matricization-free tucker decomposition of higher-order tensors on GPUs. CCF Trans. High Perform. Comput. 5(1), 12–25 (2023)

    Article  Google Scholar 

  11. Eldén, L.: Matrix methods in data mining and pattern recognition. In: SIAM (2007)

    Google Scholar 

  12. Fernandes, S., Fanaee-T, H., Gama, J.: Tensor decomposition for analysing time-evolving social networks: an overview. Artif. Intell. Rev. 54, 2891–2916 (2021)

    Article  Google Scholar 

  13. Gillet, A., Leclercq, É., Cullot, N.: MuLOT: multi-level optimization of the canonical polyadic tensor decomposition at large-scale. In: Bellatreche, L., Dumas, M., Karras, P., Matulevičius, R. (eds.) ADBIS 2021. LNCS, vol. 12843, pp. 198–212. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-82472-3_15

    Chapter  Google Scholar 

  14. Gillet, A., Leclercq, E., Sautot, L.: The tucker tensor decomposition for data analysis: capabilities and advantages. In: 38ème Conférence sur la Gestion de Données (BDA) (2022)

    Google Scholar 

  15. Gillet, A., Leclercq, É., Savonnet, M., Cullot, N.: Empowering big data analytics with polystore and strongly typed functional queries. In: Symposium on International Database Engineering & Applications, pp. 1–10 (2020)

    Google Scholar 

  16. Gray, J., et al.: Data cube: a relational aggregation operator generalizing group-by, cross-tab, and sub-totals. Data Min. Knowl. Disc. 1(1), 29–53 (1997)

    Article  Google Scholar 

  17. Hamilton, J.D.: Time Series Analysis. Princeton University Press, Princeton (2020)

    Book  Google Scholar 

  18. Hore, V., et al.: Tensor decomposition for multiple-tissue gene expression experiments. Nat. Genet. 48(9), 1094–1100 (2016)

    Article  Google Scholar 

  19. Hou, Z., Li, W., Tao, R., Du, Q.: Three-order tucker decomposition and reconstruction detector for unsupervised hyperspectral change detection. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 14, 6194–6205 (2021)

    Article  Google Scholar 

  20. Huang, H., Ding, C., Luo, D., Li, T.: Simultaneous tensor subspace selection and clustering: the equivalence of high order SVD and k-means clustering. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 327–335 (2008)

    Google Scholar 

  21. Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2, 193–218 (1985)

    Article  MATH  Google Scholar 

  22. Jang, J.G., Kang, U.: D-tucker: fast and memory-efficient tucker decomposition for dense tensors. In: 2020 IEEE 36th International Conference on Data Engineering (ICDE), pp. 1850–1853. IEEE (2020)

    Google Scholar 

  23. Jang, J.G., Kang, U.: Static and streaming tucker decomposition for dense tensors. ACM Trans. Knowl. Discov. Data 17(5), 1–34 (2023)

    Article  Google Scholar 

  24. Kanellakis, P.C.: Elements of relational database theory. In: Formal Models and Semantics, pp. 1073–1156. Elsevier (1990)

    Google Scholar 

  25. Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, Hoboken (2009)

    MATH  Google Scholar 

  26. Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2(3), 203–271 (2014)

    Article  Google Scholar 

  27. Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455–500 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Leclercq, É., Gillet, A., Grison, T., Savonnet, M.: Polystore and tensor data model for logical data independence and impedance mismatch in big data analytics. In: Hameurlain, A., Wagner, R. (eds.) Transactions on Large-Scale Data- and Knowledge-Centered Systems XLII. LNCS, vol. 11860, pp. 51–90. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-662-60531-8_3

    Chapter  Google Scholar 

  29. Lee, J., Chon, K.W., Kim, M.S.: A GPU-based tensor decomposition method for large-scale tensors. In: 2023 IEEE International Conference on Big Data and Smart Computing (BigComp), pp. 77–80. IEEE (2023)

    Google Scholar 

  30. Li, L., Lin, X., Liu, H., Lu, W., Zhou, B., Zhu, J.: Displacement data imputation in urban internet of things system based on tucker decomposition with l2 regularization. IEEE Internet Things J. 9(15), 13315–13326 (2022)

    Article  Google Scholar 

  31. Nene, S.A., Nayar, S.K., Murase, H., et al.: Columbia object image library (coil-20) (1996)

    Google Scholar 

  32. Osman, A.S.: Data mining techniques. Int. J. Data Sci. Res. 2 (2019)

    Google Scholar 

  33. Pandey, S.K., Shekhawat, H.S., Prasanna, S.: Attention gated tensor neural network architectures for speech emotion recognition. Biomed. Signal Process. Control 71, 103173 (2022)

    Article  Google Scholar 

  34. Papalexakis, E.E., Akoglu, L., Ience, D.: Do more views of a graph help? Community detection and clustering in multi-graphs. In: International Conference on Information Fusion, pp. 899–905. IEEE (2013)

    Google Scholar 

  35. Papalexakis, E.E., Faloutsos, C., Sidiropoulos, N.D.: Tensors for data mining and data fusion: models, applications, and scalable algorithms. Trans. Intell. Syst. Technol. (TIST) 8(2), 16 (2016)

    Google Scholar 

  36. Petersohn, D., et al.: Towards scalable dataframe systems. arXiv preprint arXiv:2001.00888 (2020)

  37. Phan, A.H., Cichocki, A.: Extended HALS algorithm for nonnegative tucker decomposition and its applications for multiway analysis and classification. Neurocomputing 74(11), 1956–1969 (2011)

    Article  Google Scholar 

  38. Romeo, S., Tagarelli, A., Ienco, D.: Semantic-based multilingual document clustering via tensor modeling. In: EMNLP: Empirical Methods in Natural Language Processing, pp. 600–609 (2014)

    Google Scholar 

  39. Rush, A.: Tensor Considered Harmful. Technical report, Harvard NLP (2010). http://nlp.seas.harvard.edu/NamedTensor

  40. Shao, P., Zhang, D., Yang, G., Tao, J., Che, F., Liu, T.: Tucker decomposition-based temporal knowledge graph completion. Knowl.-Based Syst. 238, 107841 (2022)

    Article  Google Scholar 

  41. Sidiropoulos, N.D., De Lathauwer, L., Fu, X., Huang, K., Papalexakis, E.E., Faloutsos, C.: Tensor decomposition for signal processing and machine learning. Trans. Signal Process 65(13), 3551–3582 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  42. Stehlé, J., et al.: High-resolution measurements of face-to-face contact patterns in a primary school. PLoS ONE 6(8), e23176 (2011)

    Article  Google Scholar 

  43. Sun, J., Papadimitriou, S., Lin, C.Y., Cao, N., Liu, S., Qian, W.: Multivis: content-based social network exploration through multi-way visual analysis. In: Proceedings of the 2009 SIAM International Conference on Data Mining, pp. 1064–1075. SIAM (2009)

    Google Scholar 

  44. Sun, J., Tao, D., Faloutsos, C.: Beyond streams and graphs: dynamic tensor analysis. In: ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 374–383. ACM (2006)

    Google Scholar 

  45. Tucker, L.R.: Some mathematical notes on three-mode factor analysis. Psychometrika 31(3), 279–311 (1966)

    Article  MathSciNet  Google Scholar 

  46. Yang, K., et al.: Tagited: predictive task guided tensor decomposition for representation learning from electronic health records. In: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence (2017)

    Google Scholar 

  47. Zhou, G., Cichocki, A., Zhao, Q., Xie, S.: Efficient nonnegative tucker decompositions: algorithms and uniqueness. IEEE Trans. Image Process. 24(12), 4990–5003 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LIB Univ. Bourgogne Franche Comté EA7534, Dijon, France

    Annabelle Gillet & Éric Leclercq

  2. UMR TETIS, AgroParisTech, Montpellier, France

    Lucile Sautot

Authors
  1. Annabelle Gillet
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  2. Éric Leclercq
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  3. Lucile Sautot
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Correspondence to Annabelle Gillet .

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Editors and Affiliations

  1. Paul Sabatier University, IRIT, Toulouse, France

    Abdelkader Hameurlain

  2. Technical University of Vienna, IFS, Vienna, Austria

    A Min Tjoa

  3. Aix-Marseille University, LIS, Marseille, France

    Omar Boucelma

  4. Université Clermont Auvergne, CNRS, LIMOS, Aubiere, France

    Farouk Toumani

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Gillet, A., Leclercq, É., Sautot, L. (2023). A Guide to the Tucker Tensor Decomposition for Data Mining: Exploratory Analysis, Clustering and Classification. In: Hameurlain, A., Tjoa, A.M., Boucelma, O., Toumani, F. (eds) Transactions on Large-Scale Data- and Knowledge-Centered Systems LIV. Lecture Notes in Computer Science(), vol 14160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-68014-8_3

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