Kernel Adaptive Filtering Over Complex Networks

Area of Science:

• Signal Processing
• Machine Learning
• Network Science

Background:

• Complex networks present challenges for traditional adaptive filtering due to interconnected nodes and nonlinear dynamics.
• Kernel methods offer a powerful approach to handle nonlinearities in adaptive filtering.
• Understanding and controlling the convergence of adaptive filters in networked systems is crucial.

Purpose of the Study:

• To develop and analyze kernel adaptive filtering algorithms for complex networks.
• To establish theoretical guarantees for the convergence of these algorithms.
• To propose practical implementations for improved filtering performance.

Main Methods:

• Development of a coupled kernel least mean square (KLMS) algorithm for individual network nodes.
• Derivation of an upper bound for the step-size in KLMS to ensure mean square convergence.
• Proposal of a coupled kernel recursive least square (KRLS) algorithm for enhanced performance.
• Utilizing input-output data for nonlinear measurement function estimation.

Main Results:

• The derived upper bound on the KLMS step-size is dependent on network coupling weights.
• An optimal step-size is identified for fastest convergence, alongside a suboptimal one for practical use.
• The coupled KRLS algorithm demonstrates improved filtering performance compared to KLMS.
• Simulations validate the theoretical findings for the proposed algorithms.

Conclusions:

• The developed coupled KLMS and KRLS algorithms effectively address kernel adaptive filtering in complex networks.
• Theoretical analysis provides crucial insights into convergence properties and step-size selection.
• The proposed methods offer robust solutions for nonlinear system identification in networked environments.