Abstract
Tensor train (TT) is one of the modern tensor decomposition models for low-rank approximation of high-order tensors. For nonnegative multiway array data analysis, we propose a nonnegative TT (NTT) decomposition algorithm for the NTT model and a hybrid model called the NTT-Tucker model. By employing the hierarchical alternating least squares approach, each fiber vector of core tensors is optimized efficiently at each iteration. We compared the performances of the proposed method with a standard nonnegative Tucker decomposition (NTD) algorithm by using benchmark data sets including event-related potential data and facial image data in multi-domain feature extraction and clustering tasks. It is illustrated that the proposed algorithm extracts physically meaningful features with relatively low storage and computational costs compared to the standard NTD model.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Cichocki, A., Zdunek, R., Amari, S.: Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 169–176. Springer, Heidelberg (2007)
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)
Cong, F., Phan, A.-H., Astikainen, P., Zhao, Q., Wu, Q., Hietanen, J.K., Ristaniemi, T., Cichocki, A.: Multi-domain feature extraction for small event-related potentials through nonnegative multi-way array decomposition from low dense array EEG. Int. J. Neural Syst. 23, 1350006 (2013)
Cong, F., Lin, Q.-H., Kuang, L.-D., Gong, X.-F., Astikainen, P., Ristaniemi, T.: Tensor decomposition of EEG signals: a brief review. J. Neurosci. Methods 248, 59–69 (2015)
Dolgov, S., Khoromskij, B.: Two-level QTT-Tucker format for optimized tensor calculus. SIAM J. Matrix Anal. Appl. 34, 593–623 (2013)
Holtz, S., Rohwedder, T., Schneider, R.: The alternating linear scheme for tensor optimization in the tensor train format. SIAM J. Sci. Comput. 34, A683–A713 (2012)
Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51, 455–500 (2009)
Lee, N., Cichocki, A.: Fundamental tensor operations for large-scale data analysis in tensor train formats. ArXiv preprint arXiv:1405.7786 (2014)
Oseledets, I.V.: Tensor-train decomposition. SIAM J. Sci. Comput. 33, 2295–2317 (2011)
Phan, A.H., Cichocki, A.: Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification. Neurocomputing 74, 1956–1969 (2011)
Samaria, F.S., Harter, A.C.: Parameterisation of a stochastic model for human face identification. In: Proceedings of the Second IEEE Workshop on Applications of Computer Vision, pp. 138–142. lEEE Computer Society Press (1994)
Zhou, G., Cichocki, A., Xie, S.: Fast nonnegative matrix/tensor factorization based on low-rank approximation. IEEE T. Signal Process. 60, 2928–2940 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Lee, N., Phan, AH., Cong, F., Cichocki, A. (2016). Nonnegative Tensor Train Decompositions for Multi-domain Feature Extraction and Clustering. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds) Neural Information Processing. ICONIP 2016. Lecture Notes in Computer Science(), vol 9949. Springer, Cham. https://doi.org/10.1007/978-3-319-46675-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-46675-0_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-46674-3
Online ISBN: 978-3-319-46675-0
eBook Packages: Computer ScienceComputer Science (R0)