Improved generalized fractal dimensions in the discrimination between Healthy and Epileptic EEG Signals

Characterization of nonlinear dynamic systems for engineering purposes – a partial review

“…For an extensive discussion of the entropies and their use in characterizing chaotic systems (see Easwaramoorthy and Uthayakumar 2011).…”

Multifractal-Wavelet Based Denoising in the Classification of Healthy and Epileptic Eeg Signals

“…They also lead to a spectrum of indices of fractal [21] and Hentschel and Procaccia [23] systematically developed the multifractal theory, which is based upon GFD. In this section, we describe the GFD Method [21,23,24,27]. Now we define a probability distribution of a given fractal time series by the following construction.…”

“…The usage of the whole family of fractal dimensions should be very useful in comparison with using only some of the dimensions. Unlike the Fourier spectra, the fractal spectra consists of a family of fractal dimensions that characterize the fractal time series from both the amplitude and the frequency point of view [20,[24][25][26][27]. So generalized fractal spectra is very efficient technique to quantify the chaotic nature of the EEG signals and employs in the classification of healthy and epileptic EEG signals [20,26,27].…”

Automatic Seizure Detection Based on Nonlinear Dynamical Analysis of EEG Signals and Mutual Information

“…A series of studies have focused on Nonlinear Dynamical Analysis (NDA) of EEG signals to extract features for detection of epilepsy (Srinivasan, Eswaran, & Sriraam, 2007; Chen et al, 2011; Niknazar et al, 2013; Yaylali, Koçak, & Jayakar, 1996; Cerf, Amri, Ouasdad, & Hirsch, 1999; Adeli, Ghosh-Dastidar, & Dadmehr, 2007; Ghosh-Dastidar, Adeli, & Dadmehr, 2007; Iasemidis et al, 2003; Van Drongelen et al, 2003; Easwaramoorthy & Uthayakumar, 2011; Zhou, Liu, Yuan, & Li, 2013; Zabihi et al, 2016; Thomasson, Hoeppner, Webber, & Zbilut, 2001; Li, Ouyang, Yao, & Guan, 2004; Ouyang, Li, Dang, & Richards, 2008; Niknazar, Mousavi, Vahdat, & Sayyah 2013). These features include Approximate Entropy (ApEn) (Srinivasan et al, 2007; Chen et al, 2011; Niknazar et al, 2013), correlation dimension (Yaylali et al, 1996; Cerf et al, 1999; Adeli et al, 2007; Ghosh-Dastidar et al, 2007), Lyapunov exponent (Niknazar et al, 2013; Adeli et al, 2007; Ghosh-Dastidar et al, 2007; Iasemidis et al, 2003), Kolmogorov entropy (Van Drongelen et al, 2003), fractal dimension (Niknazar et al, 2013; Easwaramoorthy & Uthayakumar, 2011), lacunarity (Zhou et al, 2013), and features extracted from Poincaré section (Zabihi et al, 2016) as well as Recurrence Quantification Analysis (RQA) (Niknazar et al, 2013; Thomasson et al, 2001; Li et al, 2004; Ouyang et al, 2008; Niknazar et al, 2013).…”

“…These features include Approximate Entropy (ApEn) (Srinivasan et al, 2007; Chen et al, 2011; Niknazar et al, 2013), correlation dimension (Yaylali et al, 1996; Cerf et al, 1999; Adeli et al, 2007; Ghosh-Dastidar et al, 2007), Lyapunov exponent (Niknazar et al, 2013; Adeli et al, 2007; Ghosh-Dastidar et al, 2007; Iasemidis et al, 2003), Kolmogorov entropy (Van Drongelen et al, 2003), fractal dimension (Niknazar et al, 2013; Easwaramoorthy & Uthayakumar, 2011), lacunarity (Zhou et al, 2013), and features extracted from Poincaré section (Zabihi et al, 2016) as well as Recurrence Quantification Analysis (RQA) (Niknazar et al, 2013; Thomasson et al, 2001; Li et al, 2004; Ouyang et al, 2008; Niknazar et al, 2013). …”