Probabilistic Models for Common Spatial Patterns: Parameter-Expanded EM and Variational Bayes

Abstract

Common spatial patterns (CSP) is a popular feature extraction method for discriminating between positive and negative classes in electroencephalography (EEG) data. Two probabilistic models for CSP were recently developed: probabilistic CSP (PCSP), which is trained by expectation maximization (EM), and variational Bayesian CSP (VBCSP) which is learned by variational approximation. Parameter expansion methods use auxiliary parameters to speed up the convergence of EM or the deterministic approximation of the target distribution in variational inference. In this paper, we describe the development of parameter-expanded algorithms for PCSP and VBCSP, leading to PCSP-PX and VBCSP-PX, whose convergence speed-up and high performance are emphasized. The convergence speed-up in PCSP-PX and VBCSP-PX is a direct consequence of parameter expansion methods. The contribution of this study is the performance improvement in the case of CSP, which is a novel development. Numerical experiments on the BCI competition datasets, III IV a and IV 2a demonstrate the high performance and fast convergence of PCSP-PX and VBCSP-PX, as compared to PCSP and VBCSP.