Multilinear Discriminant Analysis With Subspace Constraints for Single-Trial Classification of Event-Related Potentials

The classification accuracy of a brain-computer interface (BCI) frequently suffers from ill-posed and overfitting problems. To avoid and alleviate these problems, we propose a method of a multilinear discriminant analysis with constraints to augment parameter reduction, regularization, and additional prior information for event-related potential (ERP)-based BCIs. The method reduces the number of parameters by multilinearization, regularizes the ill-posedness via subspaces that constrain the parameter spaces, and incorporates a brain functional connectivity through the constraints. The experimental results show that the proposed method improved the classification accuracy rates in a single-trial ERP processing.

[1]  Jie Li,et al.  A Prior Neurophysiologic Knowledge Free Tensor-Based Scheme for Single Trial EEG Classification , 2009, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[2]  Jing-Yu Yang,et al.  Face recognition based on the uncorrelated discriminant transformation , 2001, Pattern Recognit..

[3]  J. Friedman.  Regularized Discriminant Analysis , 1989 .

[4]  Bin He,et al.  Noninvasive Brain-Computer Interfaces Based on Sensorimotor Rhythms , 2015, Proceedings of the IEEE.

[5]  G. McCarthy,et al.  Augmenting mental chronometry: the P300 as a measure of stimulus evaluation time. , 1977, Science.

[6]  John C Gore,et al.  Assessing functional connectivity in the human brain by fMRI. , 2007, Magnetic resonance imaging.

[7]  Toshihisa Tanaka,et al.  Smoothing of spatial filter by graph Fourier transform for EEG signals , 2014, Signal and Information Processing Association Annual Summit and Conference (APSIPA), 2014 Asia-Pacific.

[8]  Qibin Zhao,et al.  Uncorrelated Multiway Discriminant Analysis for Motor Imagery EEG Classification , 2015, Int. J. Neural Syst..

[9]  Guillaume Gibert,et al.  xDAWN Algorithm to Enhance Evoked Potentials: Application to Brain–Computer Interface , 2009, IEEE Transactions on Biomedical Engineering.

[10]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[11]  Cuntai Guan,et al.  Regularizing Common Spatial Patterns to Improve BCI Designs: Unified Theory and New Algorithms , 2011, IEEE Transactions on Biomedical Engineering.

[12]  José del R. Millán,et al.  Brain-Computer Interfaces , 2020, Handbook of Clinical Neurology.

[13]  Haiping Lu,et al.  MPCA: Multilinear Principal Component Analysis of Tensor Objects , 2008, IEEE Transactions on Neural Networks.

[14]  Olivier Ledoit,et al.  A well-conditioned estimator for large-dimensional covariance matrices , 2004 .

[15]  Danilo P. Mandic,et al.  Comparison of P300 Responses in Auditory, Visual and Audiovisual Spatial Speller BCI Paradigms , 2013, ArXiv.

[16]  Haiping Lu,et al.  Uncorrelated Multilinear Discriminant Analysis With Regularization and Aggregation for Tensor Object Recognition , 2009, IEEE Transactions on Neural Networks.

[17]  Dennis J. McFarland,et al.  Brain–computer interfaces for communication and control , 2002, Clinical Neurophysiology.

[18]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[19]  Masa-aki Sato,et al.  Estimation of hyper-parameters for a hierarchical model of combined cortical and extra-brain current sources in the MEG inverse problem , 2014, NeuroImage.

[20]  Klaus-Robert Müller,et al.  A regularized discriminative framework for EEG analysis with application to brain–computer interface , 2010, NeuroImage.

[21]  Fabien Lotte,et al.  Signal Processing Approaches to Minimize or Suppress Calibration Time in Oscillatory Activity-Based Brain–Computer Interfaces , 2015, Proceedings of the IEEE.

[22]  Haiping Lu,et al.  Regularized Common Spatial Pattern With Aggregation for EEG Classification in Small-Sample Setting , 2010, IEEE Transactions on Biomedical Engineering.

[23]  Toshihisa Tanaka,et al.  Simultaneous Design of FIR Filter Banks and Spatial Patterns for EEG Signal Classification , 2013, IEEE Transactions on Biomedical Engineering.

[24]  E. Donchin,et al.  Talking off the top of your head: toward a mental prosthesis utilizing event-related brain potentials. , 1988, Electroencephalography and clinical neurophysiology.

[25]  Motoaki Kawanabe,et al.  Invariant Common Spatial Patterns: Alleviating Nonstationarities in Brain-Computer Interfacing , 2007, NIPS.

[26]  J. Polich.  Updating P300: An integrative theory of P3a and P3b , 2007, Clinical Neurophysiology.

[27]  M. Roth,et al.  Single‐trial analysis of oddball event‐related potentials in simultaneous EEG‐fMRI , 2007, Human brain mapping.

[28]  Febo Cincotti,et al.  Towards Noninvasive Hybrid Brain–Computer Interfaces: Framework, Practice, Clinical Application, and Beyond , 2015, Proceedings of the IEEE.

[29]  Dean J Krusienski,et al.  A comparison of classification techniques for the P300 Speller , 2006, Journal of neural engineering.

[30]  Mahmoud Hassan,et al.  EEG Source Connectivity Analysis: From Dense Array Recordings to Brain Networks , 2014, PloS one.

[31]  R. Näätänen,et al.  The mismatch negativity (MMN) in basic research of central auditory processing: A review , 2007, Clinical Neurophysiology.

[32]  J. Schoffelen,et al.  Source connectivity analysis with MEG and EEG , 2009, Human brain mapping.

[33]  E. Sellers,et al.  How many people are able to control a P300-based brain–computer interface (BCI)? , 2009, Neuroscience Letters.

[34]  Klaus-Robert Müller,et al.  Learning From More Than One Data Source: Data Fusion Techniques for Sensorimotor Rhythm-Based Brain–Computer Interfaces , 2015, Proceedings of the IEEE.

[35]  Pascal Frossard,et al.  The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains , 2012, IEEE Signal Processing Magazine.

[36]  Motoaki Kawanabe,et al.  Divergence-Based Framework for Common Spatial Patterns Algorithms , 2014, IEEE Reviews in Biomedical Engineering.

[37]  K. Strimmer,et al.  Statistical Applications in Genetics and Molecular Biology A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics , 2011 .

[38]  Christopher D. Wickens,et al.  The effects of stimulus sequence on event related potentials: A comparison of visual and auditory sequences , 1977 .

[39]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[40]  Nicole Krämer,et al.  Time Domain Parameters as a feature for EEG-based Brain-Computer Interfaces , 2009, Neural Networks.

[41]  G. Pfurtscheller,et al.  Optimal spatial filtering of single trial EEG during imagined hand movement. , 2000, IEEE transactions on rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society.

[42]  Toshihisa Tanaka,et al.  Regularization using similarities of signals observed in nearby sensors for feature extraction of brain signals , 2013, 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[43]  Haiping Lu,et al.  A survey of multilinear subspace learning for tensor data , 2011, Pattern Recognit..

[44]  Andrzej Cichocki,et al.  Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis , 2014, IEEE Signal Processing Magazine.

[45]  Xiaofeng Gong,et al.  Tensor decomposition of EEG signals: A brief review , 2015, Journal of Neuroscience Methods.

[46]  K. Jellinger.  Toward Brain-Computer Interfacing , 2009 .

[47]  Stefan Haufe,et al.  Single-trial analysis and classification of ERP components — A tutorial , 2011, NeuroImage.

[48]  Dan Schonfeld,et al.  Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  Motoaki Kawanabe,et al.  Learning a common dictionary for subject-transfer decoding with resting calibration , 2015, NeuroImage.