Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Reduced Gaussian Kernel Least-Mean-Square Algorithm for Nonlinear Adaptive Signal Processing

A Reduced Gaussian Kernel Least-Mean-Square Algorithm for Nonlinear Adaptive Signal Processing The purpose of kernel adaptive filtering (KAF) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems. However, the growth of the weighted networks for KAF based on existing kernel functions leads to high computational complexity. This paper introduces a reduced Gaussian kernel that is a finite-order Taylor expansion of a decomposed Gaussian kernel. The corresponding reduced Gaussian kernel least-mean-square (RGKLMS) algorithm is derived. The proposed algorithm avoids the sustained growth of the weighted network in a nonstationary environment via an implicit feature map. To verify the performance of the proposed algorithm, extensive simulations are conducted based on scenarios involving time-series prediction and nonlinear channel equalization, thereby proving that the RGKLMS algorithm is a universal approximator under suitable conditions. The simulation results also demonstrate that the RGKLMS algorithm can exhibit a comparable steady-state mean-square-error performance with a much lower computational complexity compared with other algorithms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Circuits, Systems and Signal Processing Springer Journals

A Reduced Gaussian Kernel Least-Mean-Square Algorithm for Nonlinear Adaptive Signal Processing

Download PDF
24 pages

Loading next page...
 
/lp/springer_journal/a-reduced-gaussian-kernel-least-mean-square-algorithm-for-nonlinear-WgjFet8CM8
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Engineering; Circuits and Systems; Electrical Engineering; Signal,Image and Speech Processing; Electronics and Microelectronics, Instrumentation
ISSN
0278-081X
eISSN
1531-5878
DOI
10.1007/s00034-018-0862-0
Publisher site
See Article on Publisher Site

Abstract

The purpose of kernel adaptive filtering (KAF) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems. However, the growth of the weighted networks for KAF based on existing kernel functions leads to high computational complexity. This paper introduces a reduced Gaussian kernel that is a finite-order Taylor expansion of a decomposed Gaussian kernel. The corresponding reduced Gaussian kernel least-mean-square (RGKLMS) algorithm is derived. The proposed algorithm avoids the sustained growth of the weighted network in a nonstationary environment via an implicit feature map. To verify the performance of the proposed algorithm, extensive simulations are conducted based on scenarios involving time-series prediction and nonlinear channel equalization, thereby proving that the RGKLMS algorithm is a universal approximator under suitable conditions. The simulation results also demonstrate that the RGKLMS algorithm can exhibit a comparable steady-state mean-square-error performance with a much lower computational complexity compared with other algorithms.

Journal

Circuits, Systems and Signal Processing – Springer Journals

Published: Jun 2, 2018

References

  • Quantized kernel least mean square algorithm
    Chen, B; Zhao, S; Zhu, P; Principe, JC
  • Kalman filter-trained recurrent neural equalizers for time-varying channels
    Choi, J; Lima, ACC; Haykin, S
  • An Introduction to Support Vector Machines: and Other Kernel-Based Learning Methods
    Cristianini, N; Shawe-Taylor, J
  • The kernel recursive least-squares algorithm
    Engel, Y; Mannor, S; Meir, R
  • Efficient SVM training using low-rank kernel representations
    Fine, S; Scheinberg, K
  • Online dictionary learning for kernel LMS
    Gao, W; Chen, J; Richard, C; Bermudez, JCM; Huang, J
  • Dependent online kernel learning with constant number of random fourier features
    Hu, Z; Lin, M; Zhang, C
  • A resource-allocating network for function interpolation
    John, CP
  • Using recurrent neural networks for adaptive communication channel equalization
    Kechriotis, G; Zervas, E; Manolakos, ES
  • Transfer learning in adaptive filters: the nearest-instance-centroid-estimation kernel least-mean-square algorithm
    Li, K; Principe, JC
  • Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters
    Liang, Q; Mendel, JM
  • An information theoretic approach of designing sparse kernel adaptive filters
    Liu, W; Park, I; Principe, JC
  • Extended kernel recursive least squares algorithm
    Liu, W; Park, I; Wang, Y; Principe, JC
  • The kernel least-mean-square algorithm
    Liu, W; Pokharel, PP; Principe, JC
  • Kernel affine projection algorithms
    Liu, W; Principe, JC
  • Kernel Adaptive Filtering: A Comprehensive Introduction
    Liu, W; Principe, JC; Haykin, S
  • An introduction to kernel-based learning algorithms
    Muller, K; Mika, S; Ratsch, G; Tsuda, K; Scholkopf, B; Muller, KR; Ratsch, G; Scholkopf, B
  • Nonlinear channel equalization for wireless communication systems using Legendre neural networks
    Patra, JC; Meher, PK; Chakraborty, G
  • A kernel adaptive algorithm for quaternion-valued inputs
    Paul, TK; Ogunfunmi, T
  • Online prediction of time series data with kernels
    Richard, C; Bermudez, JCM; Honeine, P
  • An approximation of the gaussian rbf kernel for efficient classification with svms
    Ring, M; Eskofier, BM
  • Efficient dictionary-refining kernel adaptive filter with fundamental insights
    Takizawa, MA; Yukawa, M
  • Regularized kernel least mean square algorithm with multiple-delay feedback
    Wang, S; Zheng, Y; Ling, C
  • Robust blind learning algorithm for nonlinear equalization using input decision information
    Xu, L; Huang, D; Guo, Y
  • Fixed budget quantized kernel least-mean-square algorithm
    Zhao, S; Chen, B; Zhu, P; Principe, JC
  • A modified quantized kernel least mean square algorithm for prediction of chaotic time series
    Zheng, Y; Wang, S; Feng, J; Chi, KT