One-Versus-the-Rest(OVR) Algorithm: An Extension of Common Spatial Patterns(CSP) Algorithm to Multi-class Case

Extraction of relevant features that capture the invariant characteristics specific to each brain state is very important in order to implement a suitable brain-computer interface (BCI) system. This paper presents an algorithm called one-versus-the-rest (OVR), which is an extension of a well-known method called common spatial patterns (CSP) to multi-class case, to extract signal components specific to one condition from electroencephalography (EEG) data sets of multiple conditions. The algorithm was previously mentioned in a paper by Dornhege et al. (2004), yet without an elaborate description. In this paper, detailed mathematical derivation of the algorithm is given, followed by a computer simulation. The computer simulation suggests that the algorithm is capable of reconstructing the actual specific part of each condition with high quality, even when the data are contaminated with considerable noise. We also hint future possible applications of the algorithm in the context of BCI at the end of the paper