An Effective Classification Framework for Brain–Computer Interfacing Based on a Combinatoric Setting

This paper proposes a general framework that is able to define a set of classification algorithms for brain-computer interfacing (BCI). We define a distributed representation of the EEG based on multichannel autoregressive models. In a subsequent step, we extend this multichannel modeling in a combinatoric setting, which is able to describe with a class of nonlinear combinatoric operators the embedded relationships that the EEG shows in the manifolds. The generality and the flexibility of the nonlinear combinatoric operators and their mathematical properties allow the design of an indefinite number of classification algorithms each displaying relevant properties, such as linearity with respect to the parameters, noise rejection, low computational complexity of the classification procedure. In such a way, we obtain an intuitive and rigorous way to design new BCI algorithms. As an example of this theoretical framework, we present a novel classification algorithm based on four properties of this nonlinear combinatoric operator. The method was validated on the classification of single-trial EEG signals recorded during motor imagination, and it was compared on two additional standard datasets obtained from the BCI competition, with other feature extraction and classification techniques based on common spatial pattern, common spatial subspace decomposition and Fisher discriminant analysis, linear discriminant analysis, Markov chains, and expectation maximization. In conclusion, the proposed framework is suited for a broad number of BCI applications.