Parametric recurrence quantification analysis of autoregressive processes for pattern recognition in multichannel electroencephalographic data

Abstract Recurrence quantification analysis (RQA) is an acknowledged method for the characterization of experimental time series. We propose a parametric version of RQA, pRQA, allowing a fast processing of spatial arrays of time series, once each is modeled by an autoregressive stochastic process. This method relies on the analytical derivation of asymptotic expressions for five current RQA measures as a function of the model parameters. By avoiding the construction of the recurrence plot of the time series, pRQA is computationally efficient. As a proof of principle, we apply pRQA to pattern recognition in multichannel electroencephalographic (EEG) data from a patient with a brain tumor.

[1]  Charles L. Webber,et al.  Recurrence Quantification Analysis , 2015 .

[2]  Rodrigo Fernandes de Mello,et al.  Semi-supervised time series classification on positive and unlabeled problems using cross-recurrence quantification analysis , 2018, Pattern Recognit..

[3]  J Pardey,et al.  A review of parametric modelling techniques for EEG analysis. , 1996, Medical engineering & physics.

[4]  Marian Grendar,et al.  Strong Laws for Recurrence Quantification Analysis , 2013, Int. J. Bifurc. Chaos.

[5]  Sofiane Ramdani,et al.  Recurrence Quantification Analysis of Human Postural Fluctuations in Older Fallers and Non-fallers , 2013, Annals of Biomedical Engineering.

[6]  Frédéric Bouchara,et al.  Probabilistic analysis of recurrence plots generated by fractional Gaussian noise. , 2018, Chaos.

[7]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[8]  R. O. Dendy,et al.  Recurrence plot statistics and the effect of embedding , 2005 .

[9]  David Schultz,et al.  Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice , 2016 .

[10]  Jurandy Almeida,et al.  Fusion of time series representations for plant recognition in phenology studies , 2016, Pattern Recognit. Lett..

[11]  J. Kurths,et al.  Estimation of dynamical invariants without embedding by recurrence plots. , 2004, Chaos.

[12]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[13]  Tobias Rawald,et al.  PyRQA - Conducting recurrence quantification analysis on very long time series efficiently , 2017, Comput. Geosci..

[14]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[15]  Norbert Marwan,et al.  How to Avoid Potential Pitfalls in Recurrence Plot Based Data Analysis , 2010, Int. J. Bifurc. Chaos.

[16]  Hui Yang,et al.  Local recurrence based performance prediction and prognostics in the nonlinear and nonstationary systems , 2011, Pattern Recognit..

[17]  Jessica K. Hodgins,et al.  Hierarchical Aligned Cluster Analysis for Temporal Clustering of Human Motion , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Arnaud Delorme,et al.  EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis , 2004, Journal of Neuroscience Methods.

[19]  Jürgen Kurths,et al.  Influence of observational noise on the recurrence quantification analysis , 2002 .

[20]  J. Zbilut,et al.  Embeddings and delays as derived from quantification of recurrence plots , 1992 .

[21]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[22]  Rodrigo Quian Quiroga,et al.  Nonlinear multivariate analysis of neurophysiological signals , 2005, Progress in Neurobiology.

[23]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[24]  David Schultz,et al.  Approximation of diagonal line based measures in recurrence quantification analysis , 2015 .

[25]  Patrick Pérez,et al.  View-Independent Action Recognition from Temporal Self-Similarities , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Frédéric Bouchara,et al.  Recurrence plots of discrete-time Gaussian stochastic processes , 2016 .

[27]  Kazuyuki Aihara,et al.  Devaney's chaos on recurrence plots. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Annick Lesne,et al.  Recurrence Plots for Symbolic Sequences , 2010, Int. J. Bifurc. Chaos.

[29]  F. Takens Detecting strange attractors in turbulence , 1981 .

[30]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[31]  Marco Thiel,et al.  Recurrences determine the dynamics. , 2009, Chaos.

[32]  A. Genz Numerical Computation of Multivariate Normal Probabilities , 1992 .

[33]  Jürgen Kurths,et al.  A recurrence quantification analysis-based channel-frequency convolutional neural network for emotion recognition from EEG. , 2018, Chaos.

[34]  Norbert Marwan,et al.  Extended Recurrence Plot Analysis and its Application to ERP Data , 2002, Int. J. Bifurc. Chaos.

[35]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[36]  D. Farina,et al.  Nonlinear surface EMG analysis to detect changes of motor unit conduction velocity and synchronization. , 2002, Journal of applied physiology.

[37]  Gustavo K. Rohde,et al.  Stochastic analysis of recurrence plots with applications to the detection of deterministic signals , 2008 .

[38]  C L Webber,et al.  Dynamical assessment of physiological systems and states using recurrence plot strategies. , 1994, Journal of applied physiology.

[39]  Philippe Faure,et al.  A new method to estimate the Kolmogorov entropy from recurrence plots: its application to neuronal signals , 1998 .

[40]  J. Kurths,et al.  Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  W. Gersch Spectral analysis of EEG's by autoregressive decomposition of time series , 1970 .