Quantized kernel least mean square algorithm.

Area of Science:

• Signal Processing
• Machine Learning
• Adaptive Filtering

Background:

• Kernel adaptive filtering methods face challenges with computational complexity due to the growth of radial basis function structures.
• Sparsification is a common approach to mitigate this complexity, but it can lead to information loss.

Purpose of the Study:

• To propose and analyze a quantization approach as an alternative to sparsification for kernel adaptive filtering.
• To develop and evaluate a Quantized Kernel Least Mean Square (QKLMS) algorithm.

Main Methods:

• Developed a QKLMS algorithm utilizing an online vector quantization method to compress the input feature space.
• Conducted analytical studies on mean square convergence, establishing an energy conservation relation for QKLMS.
• Derived a sufficient condition for mean square convergence and determined bounds for steady-state excess mean square error.

Main Results:

• The QKLMS algorithm effectively curbs the growth of the radial basis function structure.
• Analytical studies confirmed mean square convergence properties.
• Demonstrated excellent performance in static function estimation and chaotic time-series prediction tasks.

Conclusions:

• Quantization offers a viable alternative to sparsification in kernel adaptive filtering.
• The QKLMS algorithm provides a computationally efficient and effective solution for managing complexity.
• The proposed method shows strong potential for applications in signal processing and time-series analysis.