Quaternion Singular Spectrum Analysis of Electroencephalogram With Application in Sleep Analysis

A novel quaternion-valued singular spectrum analysis (SSA) is introduced for multichannel analysis of electroencephalogram (EEG). The analysis of EEG typically requires the decomposition of data channels into meaningful components despite the notoriously noisy nature of EEG-which is the aim of SSA. However, the singular value decomposition involved in SSA implies the strict orthogonality of the decomposed components, which may not reflect accurately the sources which exhibit similar neural activities. To allow for the modelling of such co-channel coupling, the quaternion domain is considered for the first time to formulate the SSA using the augmented statistics. As an application, we demonstrate how the augmented quaternion-valued SSA (AQSSA) can be used to extract the sources, even at a signal-to-noise ratio as low as -10 dB. To illustrate the usefulness of our quaternion-valued SSA in a rehabilitation setting, we employ the proposed SSA for sleep analysis to extract statistical descriptors for five-stage classification (Awake, N1, N2, N3 and REM). The level of agreement using these descriptors was 74% as quantified by the Cohen's kappa.

[1]  Anatoly A. Zhigljavsky,et al.  Analysis of Time Series Structure - SSA and Related Techniques , 2001, Monographs on statistics and applied probability.

[2]  E. Niedermeyer.  Alpha rhythms as physiological and abnormal phenomena. , 1997, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[3]  Saeid Sanei,et al.  Assessing rehabilitative reach and grasp movements with Singular Spectrum Analysis , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[4]  Kazuyuki Aihara,et al.  Quaternion-valued short term joint forecasting of three-dimensional wind and atmospheric parameters , 2011 .

[5]  D. P. Mandic,et al.  Multivariate empirical mode decomposition , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  Alexander E. Hramov,et al.  Sleep spindles and spike–wave discharges in EEG: Their generic features, similarities and distinctions disclosed with Fourier transform and continuous wavelet analysis , 2009, Journal of Neuroscience Methods.

[7]  Hamid Reza Mohseni,et al.  Localizing Heart Sounds in Respiratory Signals Using Singular Spectrum Analysis , 2011, IEEE Transactions on Biomedical Engineering.

[8]  Rahim Mahmoudvand,et al.  Separability and window length in singular spectrum analysis , 2011 .

[9]  Saeid Sanei,et al.  Singular spectrum analysis for tracking of P300 , 2014, 2014 International Joint Conference on Neural Networks (IJCNN).

[10]  Z J Koles,et al.  EEG source localization: implementing the spatio-temporal decomposition approach. , 1998, Electroencephalography and clinical neurophysiology.

[11]  Saeid Sanei,et al.  An eigen-based approach for complex-valued Forecasting , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[12]  R. Godbout,et al.  Hemispheric lateralization of the EEG during wakefulness and REM sleep in young healthy adults , 2003, Brain and Cognition.

[13]  Danilo P. Mandic,et al.  Fast Independent Component Analysis Algorithm for Quaternion Valued Signals , 2011, IEEE Transactions on Neural Networks.

[14]  A. Chesson,et al.  The American Academy of Sleep Medicine (AASM) Manual for the Scoring of Sleep and Associated Events: Rules, Terminology and Technical Specifications , 2007 .

[15]  Mervyn V. M. Yeo,et al.  Can SVM be used for automatic EEG detection of drowsiness during car driving , 2009 .

[16]  Danilo P. Mandic,et al.  Augmented Complex Common Spatial Patterns for Classification of Noncircular EEG From Motor Imagery Tasks , 2014, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[17]  Jason Farquhar,et al.  Singular spectrum analysis as a preprocessing filtering step for fNIRS brain computer interfaces , 2014, 2014 22nd European Signal Processing Conference (EUSIPCO).

[18]  T. Penzel,et al.  Computer based sleep recording and analysis. , 2000, Sleep medicine reviews.

[19]  M. Ferrara,et al.  Sleep spindles: an overview. , 2003, Sleep medicine reviews.

[20]  Jesús Navarro-Moreno,et al.  A Quaternion Widely Linear Series Expansion and Its Applications , 2012, IEEE Signal Processing Letters.

[21]  A. Chesson,et al.  The AASM Manual for the Scoring of Sleep and Associated Events: Rules, Terminology, and Techinical Specifications , 2007 .

[22]  K. Müller,et al.  Automatic sleep stage classification using two-channel electro-oculography , 2007, Journal of Neuroscience Methods.

[23]  Hojjat Adeli,et al.  A Wavelet-Chaos Methodology for Analysis of EEGs and EEG Subbands to Detect Seizure and Epilepsy , 2007, IEEE Transactions on Biomedical Engineering.

[24]  A. Rechtschaffen,et al.  Relationships among wake episode lengths, contiguous sleep episode lengths, and electroencephalographic delta waves in rats with suprachiasmatic nuclei lesions. , 1987, Sleep.

[25]  Saeid Sanei,et al.  Adaptive Processing of Brain Signals , 2013 .

[26]  Danilo P. Mandic,et al.  Augmented second-order statistics of quaternion random signals , 2011, Signal Process..

[27]  Marimuthu Palaniswami,et al.  Support Vector Machines for Automated Recognition of Obstructive Sleep Apnea Syndrome From ECG Recordings , 2009, IEEE Transactions on Information Technology in Biomedicine.

[28]  J. Mattout,et al.  Automatic analysis of single-channel sleep EEG: validation in healthy individuals. , 2007, Sleep.

[29]  I. Fried,et al.  Sleep Spindles in Humans: Insights from Intracranial EEG and Unit Recordings , 2011, The Journal of Neuroscience.

[30]  S. Sanei,et al.  Tensor Based Singular Spectrum Analysis for Automatic Scoring of Sleep EEG , 2015, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[31]  Nicolas Le Bihan,et al.  Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing , 2004, Signal Process..