Automatic identification of eye movements using the largest lyapunov exponent

Chaos analysis of the brain topology in first-episode psychosis and clinical high risk patients

Structural MRI studies in first-episode psychosis (FEP) and in clinical high risk (CHR) patients have consistently shown volumetric abnormalities in frontal, temporal, and cingulate cortex areas. The aim of the present study was to employ chaos analysis for the identification of brain topology differences in people with psychosis. Structural MRI were acquired from 77 FEP, 73 CHR and 44 healthy controls (HC). Chaos analysis of the gray matter distribution was performed: First, the distances of each voxel from the center of mass in the gray matter image was calculated. Next, the distances multiplied by the voxel intensity were represented as a spatial-series, which then was analyzed by extracting the Largest-Lyapunov-Exponent (lambda). The lambda brain map depicts thus how the gray matter topology changes. Between-group differences were identified by (a) comparing the lambda brain maps, which resulted in statistically significant differences in FEP and CHR compared to HC; and (b) matching the lambda series with the Morlet wavelet, which resulted in statistically significant differences in the scalograms of FEP against CHR and HC. The proposed framework using spatial-series extraction enhances the between-group differences of FEP, CHR and HC subjects, verifies diagnosis-relevant features and may potentially contribute to the identification of structural biomarkers for psychosis.

Automatic Diagnosis of Epileptic Seizures in EEG Signals Using Fractal Dimension Features and Convolutional Autoencoder Method

This paper proposes a new method for epileptic seizure detection in electroencephalography (EEG) signals using nonlinear features based on fractal dimension (FD) and a deep learning (DL) model. Firstly, Bonn and Freiburg datasets were used to perform experiments. The Bonn dataset consists of binary and multi-class classification problems, and the Freiburg dataset consists of two-class EEG classification problems. In the preprocessing step, all datasets were prepossessed using a Butterworth band pass filter with 0.5–60 Hz cut-off frequency. Then, the EEG signals of the datasets were segmented into different time windows. In this section, dual-tree complex wavelet transform (DT-CWT) was used to decompose the EEG signals into the different sub-bands. In the following section, in order to feature extraction, various FD techniques were used, including Higuchi (HFD), Katz (KFD), Petrosian (PFD), Hurst exponent (HE), detrended fluctuation analysis (DFA), Sevcik, box counting (BC), multiresolution box-counting (MBC), Margaos-Sun (MSFD), multifractal DFA (MF-DFA), and recurrence quantification analysis (RQA). In the next step, the minimum redundancy maximum relevance (mRMR) technique was used for feature selection. Finally, the k-nearest neighbors (KNN), support vector machine (SVM), and convolutional autoencoder (CNN-AE) were used for the classification step. In the classification step, the K-fold cross-validation with k = 10 was employed to demonstrate the effectiveness of the classifier methods. The experiment results show that the proposed CNN-AE method achieved an accuracy of 99.736% and 99.176% for the Bonn and Freiburg datasets, respectively.

Aging and eye tracking: in the quest for objective biomarkers

Recent applications of eye tracking for diagnosis, prognosis and follow-up of therapy in age-related neurological or psychological deficits have been reviewed. The review is focused on active aging, neurodegeneration and cognitive impairments. The potential impacts and current limitations of using characterizing features of eye movements and pupillary responses (oculometrics) as objective biomarkers in the context of aging are discussed. A closer look into the findings, especially with respect to cognitive impairments, suggests that eye tracking is an invaluable technique to study hidden aspects of aging that have not been revealed using any other noninvasive tool. Future research should involve a wider variety of oculometrics, in addition to saccadic metrics and pupillary responses, including nonlinear and combinatorial features as well as blink- and fixation-related metrics to develop biomarkers to trace age-related irregularities associated with cognitive and neural deficits.

A novel method based on the pseudo-orbits to calculate the largest Lyapunov exponent from chaotic equations

To reduce parameter error caused by human factors and ensure the accuracy of the largest Lyapunov exponent (LLE) obtained from chaotic equations, this paper proposes a simple method based on two nearby pseudo-orbits. First, a point is selected from a solution trajectory of chaotic equation by the roundoff error. Second, the selected point is used as an initial condition to solve the same equation to obtain another solution trajectory. Third, the evolution distance of the two solution trajectories is calculated. Finally, the LLE is the slope of the linear region in the curve of the track distance of the natural algorithm. Our method has been successfully applied to simulate five well-known chaotic systems and some non-chaotic systems. The results show that, compared with other traditional methods, the proposed method is efficient, simple, and robust without reconstructing phase space and computing the Jacobian matrix.

Identifying the linear region based on machine learning to calculate the largest Lyapunov exponent from chaotic time series

To reduce the error caused by the human factor, this paper proposes a modification of a well-known small data method to obtain the largest Lyapunov exponent more accurately, which is based on machine learning for better identification of linear region. Firstly, we use the k-d tree neighborhood search algorithm to improve the computational efficiency of the average divergence index data. Secondly, the unsaturated data are obtained by the density peak based clustering algorithm from the average divergence index data. Thirdly, we use the density peak based clustering algorithm to identify the linear region from the first-order difference curve of the retained data. Finally, the largest Lyapunov exponent is obtained by using the least squares method to fit the linear region. Our method is applied to simulate five famous theoretical chaotic systems, the results show that the proposed method can automatically identify the linear region, which is more accurate than the small data method for the largest Lyapunov exponent calculation and the effectiveness of our method is verified through the simulation of two real-world time series.