Common SpatioTemporal Pattern Analysis

In this work we present a method for the estimation of a rank-one pattern living in two heterogeneous spaces, when observed through a mixture in multiple observation sets. Using a well chosen representation for an observed set of second order tensors (matrices), a singular value decomposition of the set structure yields an accurate estimate under some widely acceptable conditions. The method performs a completely algebraic estimation in both heterogeneous spaces without the need for heuristic parameters. Contrary to existing methods, neither independence in one of the spaces, nor joint decorrelation in both of the heterogeneous spaces is required. In addition, because the method is not variance based in the input space, it has the critical advantage of being applicable with low signal-to-noise ratios. This makes this method an excellent candidate ,e.g., for the direct estimation of the spatio-temporal P300 pattern in passive exogenous brain computer interface paradigms. For these applications it is often sufficient to consider quasi-decorrelation in the temporal space only, while we do not want to impose a similar constraint in the spatial domain.