Abstract
As an important tool of multi-way/tensor data analysis tool, Tucker decomposition has been applied widely in various fields. But traditional sequential Tucker algorithms have been outdated because tensor data is growing rapidly in term of size. To address this problem, in this paper, we focus on parallel Tucker decomposition of dense tensors on distributed-memory systems. The proposed method uses Hierarchical SVD to accelerate the SVD step in traditional sequential algorithms, which usually takes up most computation time. The data distribution strategy is designed to follow the implementation of Hierarchical SVD. We also find that compared with the state-of-the-art method, the proposed method has lower communication cost in large-scale parallel cases under the assumption of the α–β model.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Barmpoutis, A.: Tensor body: real-time reconstruction of the human body and avatar synthesis from RGB-D. IEEE Trans. Cybern. 43(5), 1347–1356 (2013)
Tao, D., Li, X., Wu, X., Maybank, S.J.: General tensor discriminant analysis and Gabor features for gait recognition. IEEE Trans. Pattern Anal. Mach. Intell. 29(10), 1700–1715 (2007)
Li, X., Lin, S., Yan, S., Xu, D.: Discriminant locally linear embedding with high-order tensor data . IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 38(2), 342–352 (2008)
Signoretto, M., Tran Dinh, Q., De Lathauwer, L., Suykens, J.A.K.: Learning with tensors: a framework based on convex optimization and spectral regularization. Mach. Learn. 94(3), 303–351 (2013). https://doi.org/10.1007/s10994-013-5366-3
Mørup, M., Hansen, L.K., Herrmann, C.S., Parnas, J., Arnfred, S.M.: Parallel factor analysis as an exploratory tool for wavelet transformed event-related EEG. NeuroImage 29(3), 938–947 (2006)
Mørup, M.: Applications of tensor (multiway array) factorizations and decompositions in data mining. Wiley Interdisc. Rev. Data Mining Knowl. Disc. 1(1), 24–40 (2011)
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)
Tucker, L.R.: Some mathematical notes on three-mode factor analysis. Psychometrika 31(3), 279–311 (1966)
De Lathauwer, L., De Moor, B., Vandewalle, J.: On the best rank-1 and rank-(R1, R2,…, RN) approximation of high-order tensors. SIAM J. Matrix Anal. Appl. 21(4), 1324–1342 (2000)
Lathauwer, L.D., Moor, B.D., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21, 1253–1278 (2000)
Vannieuwenhoven, N., Vandebril, R., Meerbergen, K.: A new truncation strategy for the higher-order singular value decomposition. SIAM J. Sci. Comput. 34(2), A1027–A1052 (2012)
Hadoop information. https://hadoop.apache.org/
Jeon, I., Papalexakis, E.E., Kang, U., Faloutsos, C.: HaTen2: billion-scale tensor decompositions. In: 2015 IEEE 31st International Conference on Data Engineering, Seoul, 2015, pp. 1047–1058. https://doi.org/10.1109/ICDE.2015.7113355
Austin, W., Ballard, G., Kolda, T.G.: Parallel tensor compression for large-scale scientific data. In: 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS), Chicago, IL, pp. 912–922 (2016). https://doi.org/10.1109/IPDPS.2016.67
Chakaravarthy, V.T., Choi, J.W., Joseph, D.J., Murali, P., Sreedhar, D.: On optimizing distributed tucker decomposition for sparse tensors. In: ICS 2018: Proceedings of the 2018 International Conference on Supercomputing, pp. 374–384 (2018)
Zou, B., Li, C., Tan, L., Chen, H.: GPUTensor: efficient tensor factorization for context-aware recommendations. Inf. Sci. 299(4), 159–177 (2015)
Iwen, M.A., Ong, B.W.: A distributed and incremental SVD algorithm for agglomerative data analysis on large networks. SIAM J. Matrix Anal. Appl. 37(4), 1699–1718 (2016)
Acknowledgements
The work was supported by the National Key Research and Development Project of China (Grant No. 2019YFB2102500).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Fang, Z., Qi, F., Dong, Y., Zhang, Y., Feng, S. (2021). Distributed Dense Tucker Decomposition Based on Hierarchical SVD. In: Ning, L., Chau, V., Lau, F. (eds) Parallel Architectures, Algorithms and Programming. PAAP 2020. Communications in Computer and Information Science, vol 1362. Springer, Singapore. https://doi.org/10.1007/978-981-16-0010-4_31
Download citation
DOI: https://doi.org/10.1007/978-981-16-0010-4_31
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-0009-8
Online ISBN: 978-981-16-0010-4
eBook Packages: Computer ScienceComputer Science (R0)