Explicit recursivity into reproducing kernel Hilbert spaces

Devis Tuia*, Gustavo Camps-Valls, Manel Martinez-Ramon

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paper

2 Citations (Scopus)

Abstract

This paper presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces (RKHS). Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define model recursivity in the Hilbert space. The method exploits some properties of functional analysis and recursive computation of dot products without the need of pre-imaging. We illustrate the feasibility of the methodology in the particular case of the gamma-filter, an infinite impulse response (IIR) filter with controlled stability and memory depth. Different algorithmic formulations emerge from the signal model. Experiments in chaotic and electroencephalographic time series prediction scenarios demonstrate the potentiality of the approach.

Original languageEnglish
Title of host publication2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Pages4148-4151
Number of pages4
ISBN (Electronic)9781457705397
DOIs
Publication statusPublished - 18 Aug 2011
Externally publishedYes
Event36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic
Duration: 22 May 201127 May 2011

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Conference

Conference36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
CountryCzech Republic
CityPrague
Period22/05/1127/05/11

Keywords

  • functional analysis
  • gamma filter
  • kernel methods
  • pre-image
  • Recursive filter

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  • Cite this

    Tuia, D., Camps-Valls, G., & Martinez-Ramon, M. (2011). Explicit recursivity into reproducing kernel Hilbert spaces. In 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings (pp. 4148-4151). [5947266] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2011.5947266