This paper investigates the characterization ability of linear and nonlinear features and proposes combining such features in order to improve the classification of biological signals, in particular single-trial electroencephalogram (EEG) and electrocardiogram (ECG) data. For this purpose, three data sets composed of ECG, epileptic EEG and finger-movement EEG were utilized. The characterization ability of seven nonlinear features namely the approximate entropy, largest Lyapunov exponents, correlation dimension, nonlinear prediction error, Hurst exponent, higher order autocovariance and asymmetry due to time reversal are compared with two linear features namely the autoregressive (AR) reflection coefficients and AR model coefficients. The features were tested by their ability to differentiate between different classes of data using a linear discriminant analysis (LDA) method with tenfold cross-validation. The class separability of combined linear and nonlinear features was assessed using sequential floating forward search with linear discriminant analysis method (SFFS-LDA). The results demonstrated that linear and nonlinear features on their own provided comparable results for the ECG data set and the finger-movement EEG data set whilst the linear features provided a better class separability compared to nonlinear features for the epileptic EEG data set. Combining linear and nonlinear features demonstrated a significant improvement in the class separability for all of the data sets where an average improvement of 20.56% was obtained with the ECG data set, 7.45% with finger-movement data set and 6.62% with the epileptic EEG data set. Overall results suggest that the use of combined linear and nonlinear feature sets would be a better approach for the characterization and classification of biological signals such as EEG and ECG.
The use of both linear autoregressive model coefficients and nonlinear measures for classification of EEG signals recorded from healthy subjects and epilepsy patients is investigated. A total of seven nonlinear measures namely the approximate entropy, largest lyapunov exponent, correlation dimension, nonlinear prediction error, hurst exponent, third order autocovariance, asymmetry due to time reversal, are used in this study. The class separability of individual and combined feature sets is measured using Linear Discriminant Analysis (LDA) algorithm where the multiple features are selected by sequential floating forward search (SFFS) algorithm. The results have shown that the use of combined feature sets provide a better characterization of EEG signals compared to individual features.
Biological signal is a common term used for time series measurements that are obtained from biological mechanisms and basically represent some form of energy produced by the biological mechanisms. Examples of such signals are electroencephalogram (EEG), which is the electrical activity of brain recorded by electrodes placed on the scalp; electrocardiogram (ECG), which is electrical activity of heart recorded from chest, and electromyogram (EMG), which is recorded from skin as electrical activity generated by skeletal muscles (Akay, 2000). Nowadays, biological signals such as EEG and ECG are analysed extensively for diagnosing conditions like cardiac arrhythmias in the case of ECG and epilepsy, memory impairments, and sleep disorders in case of EEG. Apart from clinical diagnostic purposes, in recent years there have been many developments for utilising EEG for brain computer interface (BCI) designs (Vaughan & Wolpaw, 2006). The field of signal processing provides many methods for analysis of biological signals. One of the most important steps in biological signal processing is the extraction of features from the signals. The assessment of such information can give further insights to the functioning of the biological system. The selection of proper methods and algorithms for feature extraction (i.e., linear/nonlinear methods) are current challenges in the design and application of real time biological signal analysis systems. Traditionally, linear methods are used for the analysis of biological signals (mostly in analysis of EEG). Although the conventional linear analysis methods simplify the implementation, they can only give an approximation to the underlying properties of the signal when the signal is in fact nonlinear. Because of this, there has been an increasing interest for utilising nonlinear analysis techniques in order to obtain a better characterisation of the biological signals. This chapter will lay the backgrounds to linear and nonlinear modeling of EEG signals, and propose a novel nonlinear model based on exponential autoregressive (EAR) process, which proves to be superior to conventional linear modeling techniques.
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