On Kernel design for online model selection by Gaussian multikernel adaptive filtering

Osamu Toda, Masahiro Yukawa

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

4 Citations (Scopus)

Abstract

In this paper, we highlight a design of Gaussian kernels for online model selection by the multikernel adaptive filtering approach. In the typical multikernel adaptive filtering, the maximum value that each kernel function can take is one. This means that, if one employs multiple Gaussian kernels with multiple variances, the one with the largest variance would become dominant in the kernelized input vector (or matrix). This makes the autocorrelation matrix of the the kernelized input vector be ill-conditioned, causing significant deterioration in convergence speed. To avoid this ill-conditioned problem, we consider the normalization of the Gaussian kernels. Because of the normalization, the condition number of the autocorrelation matrix is improved, and hence the convergence behavior is improved considerably. As a possible alternative to the original multikernel-based online model selection approach using the Moreau-envelope approximation, we also study an adaptive extension of the generalized forward-backward splitting (GFBS) method to suppress the cost function without any approximation. Numerical examples show that the original approximate method tends to select the correct center points of the Gaussian kernels and thus outperforms the exact method.

Original languageEnglish
Title of host publication2014 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Print)9786163618238
DOIs
Publication statusPublished - 2014 Feb 12
Event2014 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2014 - Chiang Mai, Thailand
Duration: 2014 Dec 92014 Dec 12

Other

Other2014 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2014
CountryThailand
CityChiang Mai
Period14/12/914/12/12

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ASJC Scopus subject areas

  • Signal Processing
  • Information Systems

Cite this

Toda, O., & Yukawa, M. (2014). On Kernel design for online model selection by Gaussian multikernel adaptive filtering. In 2014 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2014 [7041802] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/APSIPA.2014.7041802