Explicit recursive and adaptive filtering in reproducing kernel hilbert spaces

Devis Tuia, Jordi Munoz-Mari, Jose Luis Rojo-Alvarez, Manel Martinez-Ramon, Gustavo Camps-Valls

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)


This brief presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces. Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define the model recursivity in the Hilbert space. For that, we exploit some properties of functional analysis and recursive computation of dot products without the need of preimaging or a training dataset. We illustrate the feasibility of the methodology in the particular case of the γ-filter, which is an infinite impulse response filter with controlled stability and memory depth. Different algorithmic formulations emerge from the signal model. Experiments in chaotic and electroencephalographic time series prediction, complex nonlinear system identification, and adaptive antenna array processing demonstrate the potential of the approach for scenarios where recursivity and nonlinearity have to be readily combined.

Original languageEnglish
Article number6722955
Pages (from-to)1413-1419
Number of pages7
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number7
Publication statusPublished - Jul 2014
Externally publishedYes


  • Adaptive
  • autoregressive and moving-average
  • filter
  • kernel methods
  • recursive

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