Abstract
In this paper we propose a new flexible group tensor analysis model called the linked CP tensor decomposition (LCPTD). The LCPTD method can decompose given multiple tensors into common factor matrices, individual factor matrices, and core tensors, simultaneously. We applied the Hierarchical Alternating Least Squares (HALS) algorithm to the LCPTD model; besides we impose additional constraints to obtain sparse and nonnegative factors. Furthermore, we conducted some experiments of this model to demonstrate its advantages over existing models.
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References
Bro, R.: Multi-way analysis in the food industry - models, algorithms, and applications. Tech. rep., MRI, EPG and EMA, Proc. ICSLP 2000 (1998)
Carroll, J., Chang, J.J.: Analysis of individual differences in multidimensional scaling via an n-way generalization of eckart-young decomposition. Psychometrika 35, 283–319 (1970)
Cichocki, A.: Tensor decompositions: New concepts for brain data analysis? Journal of Control, Measurement, and System Integration (SICE) 7, 507–517 (2011)
Cichocki, A., Phan, A.: Fast local algorithms for large scale nonnegative matrix and tensor factorizations. IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences E92-A (3), 708–721 (2009)
Cichocki, A., Zdunek, R., Amari, S.-I.: 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 Publishing (2009)
Guo, Y., Pagnoni, G.: A unified framework for group independent component analysis for multi-subject fMRI data. NeuroImage 42(3), 1078–1093 (2008)
Harshman, R.: Foundations of the parafac procedure: Model and conditions for an ’explanatory’ multi-mode factor analysis. UCLA Working Papers in phonetics 16, 1–84 (1970)
Jolliffe, I.T., Trendafilov, N.T., Uddin, M.: A modified principal component technique based on the LASSO. Journal of Computational and Graphical Statistics 12(3), 531–547 (2003)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)
Lee, H., Choi, S.: Group nonnegative matrix factorization for EEG classification. Journal of Machine Learning Research - Proceedings Track 5, 320–327 (2009)
Phan, A., Cichocki, A.: Tensor decompositions for feature extraction and classification of high dimensional datasets. IEICE, NOLTA 1(1), 37–68 (2010)
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Yokota, T., Cichocki, A., Yamashita, Y. (2012). Linked PARAFAC/CP Tensor Decomposition and Its Fast Implementation for Multi-block Tensor Analysis. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34487-9_11
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DOI: https://doi.org/10.1007/978-3-642-34487-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34486-2
Online ISBN: 978-3-642-34487-9
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