Kernel Correntropy Conjugate Gradient Algorithms Based on Half-Quadratic Optimization.

Area of Science:

• Signal Processing
• Machine Learning
• Nonlinear Dynamics

Background:

• Correntropic loss (C-Loss) offers robust nonlinear similarity measurement by extracting high-order statistics.
• Kernel adaptive filters (KAFs) using C-Loss with stochastic gradient descent (SGD) exhibit slow convergence and poor performance.
• Existing methods struggle with computational complexity and filter structure efficiency.

Purpose of the Study:

• To develop a more efficient and robust kernel adaptive filter algorithm.
• To improve the convergence rate and accuracy of C-Loss based filters.
• To address the computational complexity and network growth issues in KCCG.

Main Methods:

• Developed a conjugate gradient (CG)-based correntropy algorithm (KCCG) by combining half-quadratic (HQ) optimization and weighted least-squares (LS).
• Proposed the Random Fourier Features KCCG (RFFKCCG) algorithm by mapping data to a fixed-dimensional random Fourier features space (RFFS).
• Validated algorithms using Monte Carlo simulations for chaotic time series prediction and large-scale dataset regression.

Main Results:

• The KCCG algorithm demonstrates comparable performance to the kernel recursive maximum correntropy (KRMC) algorithm with reduced computational complexity.
• RFFKCCG provides a more efficient filter structure with sparsification, outperforming other KAFs.
• Both proposed algorithms show superior robustness, filtering accuracy, and efficiency compared to existing methods.

Conclusions:

• The KCCG and RFFKCCG algorithms offer significant improvements in kernel adaptive filtering.
• These novel algorithms effectively handle nonlinear similarity measures and high-order statistics.
• The proposed methods are validated for diverse applications including time series prediction and large-scale regression.