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2 results

  • 3 - Kernel-Based Adaptive Filtering

  • Paulo S. R. Diniz, Universidade Federal do Rio de Janeiro, Marcello L. R. de Campos, Universidade Federal do Rio de Janeiro, Wallace A. Martins, University of Luxembourg, Markus V. S. Lima, Universidade Federal do Rio de Janeiro, Jose A. Apolinário, Jr
  • Book:
    Online Learning and Adaptive Filters
    Published online:
    24 November 2022
    Print publication:
    08 December 2022, pp 60-108

  • Summary

    This chapter explains the basic concepts of kernel-based methods, a widely used tool in machine learning. The idea is to present online parameter estimation of nonlinear models using kernel-based tools. The chapters aim is to introduce the kernel version of classical algorithms such as least mean square (LMS), recursive least squares (RLS), affine projection (AP), and set membership affine projection (SM-AP). In particular, we will discuss how to keep the dictionary of the kernel finite through a series of model reduction strategies. This way, all discussed kernel algorithms are tailored for online implementation.

  • Kernel-function Based Primal-Dual Algorithms for P * (κ) Linear Complementarity Problems

  • M. EL Ghami, T. Steihaug
  • Journal:
    RAIRO - Operations Research / Volume 44 / Issue 3 / July 2010
    Published online by Cambridge University Press:
    23 July 2010, pp. 185-205
    Print publication:
    July 2010

  • Recently, [Y.Q. Bai, M. El Ghami and C. Roos,SIAM J. Opt. 15 (2004) 101–128]investigated a new class of kernel functions which differs from theclass of self-regular kernel functions. The class is defined by somesimple conditions on the growth and the barrier behavior of thekernel function. In this paper we generalize theanalysis presented in the above paper for P * (κ) LinearComplementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysisfor linear optimization. Several new tools and techniques are derived in this paper.