title: Multivariate assessment of event-related potentials with the t-CWT method.
abstract: BACKGROUND
  Event-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.
  
  
  RESULTS
  This 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.
  
  
  CONCLUSIONS
  Hopefully, 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.
authors.affiliation: Institute of Medical Psychology and Behavioral Neurobiology, University of Tübingen, Gartenstr. 29, 72074, Tübingen, Germany. bostanov@uni-tuebingen.de.
authors.forename: Vladimir
authors.initials: V
authors.lastname: Bostanov
mesh_terms: D003627:Data Interpretation, Statistical; D004569:Electroencephalography / Q000379:methods*; D005071:Evoked Potentials / Q000502:physiology*; D006801:Humans; D015999:Multivariate Analysis; D025341:Principal Component Analysis; D058067:Wavelet Analysis