Kernel Recursive Least Squares Algorithm Based on the Nystr }}}}m Method With k-Means Sampling

The kernel recursive least squares (KRLS) algorithm is used to improve the convergence rate and filtering accuracy of kernel adaptive filters (KAFs) in the Gaussian noise case. However, the linear growing network size in KRLS poses a huge amount of time and storage consumption. To address this issue...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 27; pp. 361 - 365
Main Authors: Zhang, Tao, Wang, Shiyuan, Huang, Xuewei, Jia, Lei
Format: Journal Article
Language:English
Published: IEEE 2020
Subjects:
<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> k</tex-math> </inline-formula>-means sampling
Approximation algorithms
Eigenvalues and eigenfunctions
Kernel
Kernel adaptive filters
kernel recursive least squares
Nonlinear systems
Nystr<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> {\rm {{ \ddot{\bf{o}}}}}</tex-math> </inline-formula>m method
Prediction algorithms
Sampling methods
Signal processing algorithms
ISSN:1070-9908, 1558-2361
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Description
Summary:The kernel recursive least squares (KRLS) algorithm is used to improve the convergence rate and filtering accuracy of kernel adaptive filters (KAFs) in the Gaussian noise case. However, the linear growing network size in KRLS poses a huge amount of time and storage consumption. To address this issue, a novel Nyström kernel recursive least squares (NysKRLS) algorithm is proposed by approximating the Gaussian kernel with the Nyström method. In addition, the k-means sampling is adopted in NysKRLS to develop another Nyström kernel recursive least squares with k-means sampling (NysKRLS-KM) algorithm for further improving the approximation accuracy. NysKRLS-KM with a fixed dimensional network structure can achieve significantly better performance than the KAFs based on the stochastic gradient descent (SGD) method, and almost the same performance as KRLS efficiently. Monte Carlo simulations on nonlinear system identification and prediction of real-world data illustrate the superiorities of the proposed NysKRLS-KM algorithm from the aspects of computational and spatial complexity.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2020.2972164