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Nonnegative Matrix and Tensor Decomposition of EEG

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Signal Processing in Neuroscience

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Abstract

Power spectrum and time-frequency representation (TFR) are two significant methods to analyze EEG data in the frequency and in the time-frequency domain. The nonnegative data in the two domains can be modeled using bilinear and multi-linear transform. In this chapter, the nonnegative matrix factorization (NMF) and tensor decomposition of the canonical polyadic and Tucker models are introduced for decomposing the two-way data and the multi-way data including the modes of time, frequency, space, and subject. The strength of each decomposition model is shown by real EEG data example.

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References

  • Becker H, et al. EEG extended source localization: tensor-based vs. conventional methods. Neuroimage. 2014;96(8):143–57.

    Article  CAS  PubMed  Google Scholar 

  • Beckmann CF, Smith SM, Beckmann CF, Smith SM. Tensorial extensions of independent component analysis for multisubject FMRI analysis. Neuroimage. 2005;25(1):294–311.

    Google Scholar 

  • Bro R. Multi-way analysis in the food industry: theory, algorithms and applications. Doctoral Dissertation: University of Amsterdam; 1998.

    Google Scholar 

  • Carroll JD, Chang JJ. Analysis of individual differences in multidimensional scaling via an N-way generalization of. Psychometrika. 1970;35(3):283–319.

    Article  Google Scholar 

  • Cichocki A. Tensor decompositions: a new concept in brain data analysis? 2013;7(2011).

    Google Scholar 

  • Cichocki et al. Nonnegative matrix and tensor factorizations. 2009.

    Google Scholar 

  • Cong F, et al. Extract mismatch negativity and P3a through two-dimensional nonnegative decomposition on time-frequency represented event-related potentials. Berlin/Heidelberg: Springer; 2010. p. 385–91.

    Google Scholar 

  • Cong F, et al. Benefits of multi-domain feature of mismatch negativity extracted by non-negative tensor factorization from EEG collected by low-density array. Int J Neural Syst. 2012;22(6):1415–28.

    Article  Google Scholar 

  • Cong F, et al. Multi-domain feature extraction for small event-related potentials through nonnegative multi-way array decomposition from low dense array EEG. Int J Neural Syst. 2013;23(2):1350006. 10.1142/S0129065713500068

    Google Scholar 

  • Cong F, et al. Low-rank approximation based non-negative multi-way array decomposition on event-related potentials. Int J Neural Syst. 2014;24(8):1440005. 10.1142/S012906571440005X

    Google Scholar 

  • Dempster AP. Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion. in J R Stat Soc Ser B. 1977.

    Google Scholar 

  • Harshman RA. Foundations of the PARAFAC procedure: model and conditions for an “explanatory” multi-mode factor analysis. In UCLA working papers in. 1969.

    Google Scholar 

  • Kroonenberg PM. Applied multiway data analysis. Ppsw.rug.nl. 2008.

    Google Scholar 

  • Lee DD, Seung HS. Learning the parts of objects by non-negative matrix factorization. Nature. 1999;401(6755):788–91.

    Article  CAS  PubMed  Google Scholar 

  • Lee DD, Seung HS. Algorithms for non-negative matrix factorization. In: In NIPS. 2001.

    Google Scholar 

  • Paatero P. Least squares formulation of robust non-negative factor analysis. Chemom Intell Lab Syst. 1997;37(96):23–35.

    Article  CAS  Google Scholar 

  • Paatero P, Tapper U. ‡, Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values †. Environmetrics. 1994;5(2):111–26.

    Article  Google Scholar 

  • Phan AH, Cichocki A. Extended HALS algorithm for nonnegative Tucker decomposition and its applications for multiway analysis and classification. Neurocomputing. 2011;74(11):1956–69.

    Article  Google Scholar 

  • Saul L, Pereira F. Aggregate and mixed-order Markov models for statistical language processing. eprint arXiv:cmp-lg/9706007, 1997;81–9.

    Google Scholar 

  • Tucker LR. Some mathematical notes on three-mode factor analysis. Psychometrika. 1966;31(3):279–311.

    Article  CAS  PubMed  Google Scholar 

  • Zhao Q, et al. Kernelization of tensor-based models for multiway data analysis: processing of multidimensional structured data. IEEE Signal Process Mag. 2013;30(4):137–48.

    Article  Google Scholar 

  • Zhou G, Cichocki A, Xie S. Fast nonnegative matrix/tensor factorization based on low-rank approximation. Signal Proces IEEE Transact. 2012;60(6):2928–40.

    Article  Google Scholar 

Download references

Acknowledgement

This work was supported by the Fundamental Research Funds for the Central Universities [DUT16JJ(G)03] in Dalian University of Technology, and National Natural Science Foundation of China (Grant No. 81471742).

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Authors and Affiliations

  1. Department of Biomedical Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China

    Fengyu Cong

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  1. Fengyu Cong
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Correspondence to Fengyu Cong .

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Editors and Affiliations

  1. Beijing Normal University, State Key Lab Cognit Neurosci & Learning, Beijing, Beijing, China

    Xiaoli Li

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Cong, F. (2016). Nonnegative Matrix and Tensor Decomposition of EEG. In: Li, X. (eds) Signal Processing in Neuroscience. Springer, Singapore. https://doi.org/10.1007/978-981-10-1822-0_14

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