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

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?CLeibler (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.