Kernel Risk-Sensitive Mean p-Power Error Algorithms for Robust Learning

Area of Science:

• Signal Processing
• Machine Learning
• Robust Learning

Background:

• Correntropic loss (C-Loss) is a nonlinear similarity measure in reproducing kernel Hilbert spaces (RKHS) used in robust learning.
• The non-convex nature of C-Loss can degrade performance.
• Kernel risk-sensitive loss (KRL) offers a convex alternative for similarity measurement in RKHS.

Purpose of the Study:

• To propose a novel nonlinear similarity measure, kernel risk-sensitive mean p-power error (KRP), as a generalization of KRL.
• To develop robust recursive kernel adaptive filters based on the KRP criterion.
• To enhance the robustness and reduce the network size of kernel recursive least squares algorithms (KRLS).

Main Methods:

• Introduced the kernel risk-sensitive mean p-power error (KRP) by integrating mean p-power error into KRL.
• Proposed two robust recursive kernel adaptive filters: recursive minimum kernel risk-sensitive mean p-power error algorithm (RMKRP) and its quantized version (QRMKRP).
• Utilized Monte Carlo simulations to evaluate the performance of the proposed algorithms.

Main Results:

• The proposed KRP measure generalizes KRL and can outperform it with appropriate parameter selection.
• The RMKRP and QRMKRP algorithms demonstrate superior robustness and reduced network size compared to existing methods.
• Simulation results validate the effectiveness of the proposed RMKRP and QRMKRP.

Conclusions:

• The novel KRP measure provides a flexible and effective approach for similarity measurement in RKHS.
• The RMKRP and QRMKRP algorithms represent significant advancements in robust kernel adaptive filtering.
• The proposed methods offer practical benefits for applications requiring robust signal processing and learning.