Harmonic Mean of Kullback---Leibler Divergences for Optimizing Multi-Class EEG Spatio-Temporal Filters

Authors:
Haixian Wang
Affiliations:
Key Laboratory of Child Development and Learning Science of Ministry of Education, Research Center for Learning Science, Southeast University, Nanjing, China 210096
Venue:
Neural Processing Letters
Year:
2012

Citing 4
Cited 0

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Abstract

The common spatial patterns (CSP) is a classical approach to spatial filtering of electroencephalogram (EEG) used in brain-computer interfaces. The local temporal common spatial patterns (LTCSP) method is a temporal generalization of CSP. Both CSP and LTCSP, however, are only suitable for the two-class paradigm. In this paper, we address this limitation under the framework of Kullback---Leibler (KL) divergence. We show that CSP is equivalent to maximizing the symmetric KL divergence of two class-conditional probability density functions under the Gaussian assumption. This analysis establishes a probabilistic interpretation for CSP, as well as LTCSP. Based on the KL formulation, we propose a new multi-class extension to optimizing the spatio-temporal filters by maximizing the harmonic mean of all pairs of symmetric KL divergences between the filtered class-conditional densities. Experiments of classification of multiple EEG classes on the data sets of BCI competition show the effectiveness of the proposed methods.