Conclusions

A kernel-based version of the RLS algorithm was presented. Its main features are the introduction of regularization against overfitting (by penalizing the solutions) and the combination of a sliding-window approach and efficient matrix inversion formulas to keep the complexity of the problem bounded. Thanks to the use of a sliding-window the algorithm is able to provide tracking in a time-varying environment.

First results of this algorithm are promising, and suggest it can be extended to deal with the nonlinear extensions of most problems that are classically solved by linear RLS. Future research lines also include its direct application to online kernel canonical correlation analysis (kernel CCA).