Classification of Multichannel Signals With Cumulant-Based Kernels

We consider the problem of training a discriminative classifier given a set of labelled multivariate time series (a.k.a. multichannel signals or vector processes). We propose a novel kernel function that exploits the spectral information of tensors of fourth-order cross-cumulants associated to each multichannel signal. Contrary to existing approaches the arising procedure does not require an (often nontrivial) blind identification step. Nonetheless, insightful connections with the dynamics of the generating systems can be drawn under specific modeling assumptions. The method is illustrated on both synthetic examples as well as on a brain decoding task where the direction, either left of right, towards where the subject modulates attention is predicted from magnetoencephalography (MEG) signals. Kernel functions for unstructured data do not leverage the underlying dynamics of multichannel signals. A comparison with these kernels as well as with state-of-the-art approaches, including generative methods, shows the merits of the proposed technique.