Hamid Reza KOBRAVI, Ali MOGHİMİ, Saleh LASHKAR, Mohammad Reza HASHEMI GOLPAYEGAN, Ali SHEIKHANI

Topological feature extraction of nonlinear signals and trajectories and its application in EEG signals classification

This study introduces seven topological features that characterize attractor dynamic of nonlinear and chaotic trajectories in a phase space. These features quantify volume, occupied space, nonuniformity, and curvature of trajectory. The features are evaluated as initial point invariant measures by a practical approach, which means that a feature is only sensitive to dynamic changes. The Lorenz and Rossler system trajectories are employed in this evaluation. Moreover, the proposed features are used in a real world application, i.e. epileptic seizure electroencephalogram signal classification. As the result shows, these features are efficient in this task in comparison with others studies that used the same dataset and evaluation method.

PDF

___

Zhu G, Li Y, Wen P. Analysis and classification of sleep stages based on difference visibility graphs from a singlechannel EEG signal. IEEE J Biomed Health Inform 2014; 18: 1813-1821.
Kumar Y, Dewal ML, Anand RS. Epileptic seizure detection using DWT based fuzzy approximate entropy and support vector machine. Neurocomputing 2014; 133: 271-279.
Parvez MZ, Paul M. Epileptic seizure detection by analyzing EEG signals using different transformation techniques. Neurocomputing 2014; 145: 190-200.
Das AB, Bhuiyan MIH, Alam SMS. Classification of EEG signals using normal inverse Gaussian parameters in the dual-tree complex wavelet transform domain for seizure detection. Signal Image Video Process 2016; 10: 259-266.
Rajendra Acharya U, Vinitha Sree S, Alvin APC, Suri JS. Use of principal component analysis for automatic classification of epileptic EEG activities in wavelet framework. Expert Syst Appl 2012; 39: 9072-9078.
Niknazar M, Mousavi SR, Vosoughi Vahdat B, Sayyah M. A new framework based on recurrence quantification analysis for epileptic seizure detection. IEEE J Biomed Health Inform 2013; 17: 572-578.
Riaz F, Hassan A, Rehman S, Niazi IK, Dremstrup K. EMD-based temporal and spectral features for the classification of EEG signals using supervised learning. IEEE T Neural Syst Rehabil Eng 2016; 24: 28-35.
Alam SMA, Bhuiyan MIH. Detection of seizure and epilepsy using higher order statistics in the EMD domain. IEEE J Biomed Health Inform 2013; 17: 312-318.
Jarque CM, Bera AK. Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Econ Lett 1980; 6: 255-259.
Andrzejak RG, Lehnertz K, Mormann F, Rieke C, David P, Elger CE. Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 64: 061907.
Allwein E, Schapire R, Singer Y. Reducing multiclass to binary: a unifying approach for margin classifiers. J Mach Learn Res 2001; 1: 113-141.
Browne TR, Holmes GL. Handbook of Epilepsy. 4th ed. Philadelphia, PA, USA: Lippincott Williams & Wilkins, 2008.
Thomasson N, Hoeppner TJ, Webber CL, Zbilut JP. Recurrence quantification in epileptic EEGs. Phys Lett A 2001; 279: 94-101.
Rössler OE. An equation for continuous chaos. Phys Lett A 1976; 57: 397-398.
Fraser AM, Swinney HL. Independent coordinates for strange attractors from mutual information. Phys Rev A 1986; 33: 1134-1140.
Kennel MB, Brown R, Abarbanel HD. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev At Mol Opt Phys 1992; 45: 3403-3411.
Takens F. Detecting strange attractors in turbulence. In: Rand D, Young LS, editors. Dynamical Systems and Turbulence. Berlin, Germany: Springer, 1981, pp. 366-381.
Packard NH, Crutchfield JP, Farmer JD, Shaw RS. Geometry from a time series. Phys Rev Lett 1980; 45: 712-716.
Gandhi AB, Joshi JB, Kulkarni AA, Jayaraman VK, Kulkarni BD. SVR-based prediction of point gas hold-up for bubble column reactor through recurrence quantification analysis of LDA time-series. Int J Multiph 2008; 34:1099-1107.
Banerjee A, Pohit G. Crack investigation of rotating cantilever beam by fractal dimension analysis. Procedia Technol 2014; 14: 188-195.
Caesarendra W, Kosasih B, Tieu AK, Moodie CA. Application of the largest Lyapunov exponent algorithm for feature extraction in low speed slew bearing condition monitoring. Mech Syst Signal Process 2015; 50: 116-138.
Song Y, Crowcroft J, Zhang J. Automatic epileptic seizure detection in EEGs based on optimized sample entropy and extreme learning machine. J Neurosci Methods 2012; 210: 132-146.
Cullen J, Saleem A, Swindell R, Burt P, Moore C. Measurement of cardiac synchrony using Approximate Entropy applied to nuclear medicine scans. Biomed Signal Process 2010; 5: 32-36.
Katz MJ. Fractals and the analysis of waveforms. Comput Biol Med 1988; 18: 145-156.
Marwan N, Carmenromano M, Thiel M, Kurths J. Recurrence plots for the analysis of complex systems. Phys Rep 2007; 438: 237-329.
Eckmann JP, Kamphorst SO, Ruelle D. Recurrence plots of dynamical systems. Europhys Lett 1987; 4: 973-977.
Niknazar H, Nasrabadi AM, Shamsollahi MB. Volumetric behavior quantification to characterize trajectory in phase space. Chaos Solitons Fractals 2017; 103: 294-306.
Sadri S, Wu CQ. Modified Lyapunov exponent, new measure of dynamics. Nonlinear Dyn 2017; 78: 2731-2750.
Higuchi T. Approach to an irregular time series on the basis of the fractal theory. Phys Nonlinear Phenom 1988; 31: 277-283.
Grassberger P. Generalized dimensions of strange attractors. Phys Lett 1983; 97: 227-230.
C¸inlar E. Probability and Stochastics. vol. 261. New York, NY, USA: Springer, 2011.
Falconer KJ, Fractal Geometry: Mathematical Foundations and Applications. Chichester, UK: Wiley, 1990.
Sagan H. Space-Filling Curves. New York, NY, USA: Springer, 1994.
Mandelbrot B. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 1967; 156: 636-638.
Richman JS, Moorman JR. Physiological time-series analysis using approximate entropy and sample entropy. Am J Physiol Heart Circ Physiol 2000; 278: 2039-2049.
Pincus S. Approximate entropy (ApEn) as a complexity measure. Chaos Interdiscip J Nonlinear Sci 1995; 5: 110-117.