Functional Analytic Methods For EEG Data

The research on cognitive neuroscience has becomes a hot research topic currently.With the development of the technology, the electroencephalogram (EEG) becomes themain way of brain research for its high time resolution and low hurt to human body.How to seek the information from EEG signals is the core in EEG signals processing andanalysis. Further discovering the hidden and unknown information in EEG will deepenthe understanding of neural mechanisms of brain. EEG research covers a wide ?eld,such as physiology, psychology, pathophysiological, cognitive science, social psychology,information and signal processing, mathematics and statistics. Di?erent ?elds analyze theEEG data with di?erent goals and methods, di?erent results may be obtained if di?erentmethods or views are used. This paper analyzes the EEG data from the view of functionaldata and non-linear dynamics.In functional data analysis, data are analyzed from functional view and taken asan entirety, which is shown as a smooth curve or continuous functions, and that canestimate the value of the function and its derivative at any time. Functional data arevery common in economical, meteorology, psychology research. The research in these?elds had just begun and exhibited a broad prospect. What’s more, this method isseldom used in EEG data analysis. This paper utilizes the FDA method into EEG dataanalysis from two main problems: extracting event relation potential (ERP) by FDAmethod. Recognizing possible homogeneity among observations in order to increase theaccuracy of ERP analysis. At last, the feasibility and superiority are proved through theexample of lateralized readiness potential (LRP) analysis. The FDA method especiallysuitable for the EEG data which contains time series, such as the ERP analysis. TheFDA method provides a powerful tool for EEG analysis.Non-linear dynamics is a newly arisen research direction of EEG, which mines theinformation of EEG data from mathematics and systems point of view, more and more scientists are investigating the non-linear characteristics of brain. In this paper,weinvestigate the unobservable inner state by combining the‘black box‘idea. the nonlinearobserver design provides a new way to explore the information hidden in the’black box’.In this paper, based on the one-sided Lipschitz condition instead of traditional Lipschitzcondition, su?cient conditions for the existence of observers of the class of nonlinearsystems are presented. The method given in this paper makes the applicable class largerthan that given in the literature. Finally, we use the proposed method to design observersfor three simulative examples and the e?ect of each state trajectory tracking is verysatisfactory. This will help us analyze the nonlinear characteristics of the systems.The EEG analysis based on FDA method and non-linear dynamics is still at theexploration stage. With the development of information and computer technology, thesemethods can be applied to broadly...