Learning non-linear time-scales with kernel γγ-filters

A family of kernel methods, based on the γγ-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) γγ-filter [G. Camps-Valls, M. Martínez-Ramón, J.L. Rojo-Álvarez, E. Soria-Olivas, Robust γγ-filter using support vector machines, Neurocomput. J. 62(12) (2004) 493–499.], 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 γγ-filters. The improved performance in several application examples suggests that a more appropriate representation of signal states is achieved.