Multivariate assessment of event-related potentials with the t-CWT method.

Vladimir Bostanov

doi:10.1186/s12868-015-0185-z

Abstract

BackgroundEvent-related brain potentials (ERPs) are usually assessed with univariate statistical tests although they are essentially multivariate objects. Brain–computer interface applications are a notable exception to this practice, because they are based on multivariate classification of single-trial ERPs. Multivariate ERP assessment can be facilitated by feature extraction methods. One such method is t-CWT, a mathematical-statistical algorithm based on the continuous wavelet transform (CWT) and Student’s t-test.ResultsThis article begins with a geometric primer on some basic concepts of multivariate statistics as applied to ERP assessment in general and to the t-CWT method in particular. Further, it presents for the first time a detailed, step-by-step, formal mathematical description of the t-CWT algorithm. A new multivariate outlier rejection procedure based on principal component analysis in the frequency domain is presented as an important pre-processing step. The MATLAB and GNU Octave implementation of t-CWT is also made publicly available for the first time as free and open source code. The method is demonstrated on some example ERP data obtained in a passive oddball paradigm. Finally, some conceptually novel applications of the multivariate approach in general and of the t-CWT method in particular are suggested and discussed.ConclusionsHopefully, the publication of both the t-CWT source code and its underlying mathematical algorithm along with a didactic geometric introduction to some basic concepts of multivariate statistics would make t-CWT more accessible to both users and developers in the field of neuroscience research.Electronic supplementary materialThe online version of this article (doi:10.1186/s12868-015-0185-z) contains supplementary material, which is available to authorized users.

Highlights

Event-related brain potentials (ERPs) are usually assessed with univariate statistical tests they are essentially multivariate objects
In the present article, some basic concepts of multivariate statistics were introduced as geometric notions
ERPs were defined as random vectors in a metric space, in which the distance between two points was derived in a natural way from the covariance of the data

Summary

Introduction

Event-related brain potentials (ERPs) are usually assessed with univariate statistical tests they are essentially multivariate objects. Since the EEG is a stochastic process, the ERP is a multivariate statistical object, as well It is a set of random curves (one curve per EEG channel), and a random curve cannot be represented by a single univariate feature (or a curve parameter) without loosing a lot of potentially useful information. An ERP component is usually assessed by its peak value or by the area under the curve in a narrow time window around the peak.

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Conclusion