Learning non-linear time-scales with kernel -filters

A family of kernel methods, based on the -filter structure, is presented for non- linear system identification and time series prediction. The kernel trick allows us to develop the natural non-linear extension of the (linear) Support Vector Machine (SVM) -filter (1), but this approach yields a rigid system model without non-linear cross relation between time-scales. Several functional analysis properties allow us to develop a full, principled family of kernel -filters. The improved performance in several application examples suggest that a more appropriate representation of signal states is achieved.