Quantized kernel recursive least squares algorithm.

Area of Science:

• Signal Processing
• Machine Learning
• Adaptive Filtering

Background:

• Kernel-based adaptive filtering algorithms, such as the least mean square (LMS) and recursive least squares (RLS), are fundamental in signal processing.
• Traditional methods often face challenges with computational complexity and memory requirements, especially in high-dimensional input spaces.
• Quantization techniques offer a way to manage complexity by partitioning the input space.

Purpose of the Study:

• To propose and derive the optimal solution for quantized kernel least squares regression.
• To develop an efficient recursive algorithm for updating the quantized kernel least squares solution.
• To evaluate the performance of the proposed algorithm using simulations.

Main Methods:

• Development of a quantized kernel least squares regression framework.
• Derivation of the optimal solution for the quantized problem.
• Incorporation of an online vector quantization method for recursive updates.
• Implementation of the quantized kernel recursive least squares (QKRLS) algorithm.

Main Results:

• The QKRLS algorithm provides an efficient recursive update mechanism for quantized kernel least squares regression.
• Monte Carlo simulations demonstrate the effectiveness and good performance of the proposed QKRLS algorithm.
• The algorithm's network size is bounded by the quantization codebook size, offering computational advantages.

Conclusions:

• The proposed quantized kernel recursive least squares algorithm is a computationally efficient and effective method for adaptive filtering.
• The integration of quantization and kernel methods provides a powerful approach for handling complex signal processing tasks.
• The QKRLS algorithm shows significant promise for applications requiring adaptive learning with bounded complexity.