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Multi-Step Linear Discriminant Analysis and Its Applications

  • We introduce a multi-step machine learning approach and use it to classify data from EEG-based brain computer interfaces. This approach works very well for high-dimensional EEG data. First all features are divided into subgroups and linear discriminant analysis is used to obtain a score for each subgroup. Then it is applied to subgroups of the resulting scores. This procedure is iterated until there is only one score remaining and this one is used for classification. In this way we avoid estimation of the high-dimensional covariance matrix of all features. We investigate the classifification performance with special attention to the small sample size case. For the normal model, we study the asymptotic error rate when dimension p and sample size n tend to infinity. This indicates how to defifine the sizes of subgroups at each step. In addition we present a theoretical error bound for the spatio-temporal normal model with separable covariance matrix, which results in a recommendation on how subgroups should be formed for this kind of data. Finally some techniques, for example wavelets and independent component analysis, are used to extract features of some kind of EEG-based brain computer interface data.
  • Gegenstand der vorliegenden Arbeit ist ein Mehrschrittverfahren zur Klassifikation von Daten. Die mathematischen Eigenschaften werden untersucht und eine Anwendung auf EEG-Daten vorgestellt. Es stellt sich heraus, dass es insbesondere für hochdimensionale EEG-Daten sehr gut geeignet ist.

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Author: Hoang Huy Nguyen
Title Additional (English):Multi-Step Linear Discriminant Analysis and Its Applications
Title Additional (German):Multi-Step Linear Discriminant Analysis and Its Applications
Advisor: Christoph Bandt
Document Type:Doctoral Thesis
Date of Publication (online):2013/01/28
Granting Institution:Ernst-Moritz-Arndt-Universität, Mathematisch-Naturwissenschaftliche Fakultät (bis 31.05.2018)
Date of final exam:2013/01/25
Release Date:2013/01/28
Tag:Hoch-dimensionale Daten
Classification, High-Dimensional Data, Statistics
GND Keyword:Maschinelles Lernen, Statistik
Faculties:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik und Informatik
DDC class:500 Naturwissenschaften und Mathematik / 510 Mathematik