Generalized regression neural networks in time-varying environment

Area of Science:

• Signal Processing
• Machine Learning
• Artificial Intelligence

Background:

• Analysis of nonstationary processes is challenging due to signal variability.
• Existing methods often simplify signals to stationary for easier analysis, despite their nonstationary nature.
• Universal tools for diverse nonstationary signals are currently limited.

Purpose of the Study:

• To propose a novel class of generalized regression neural networks (GRNN) capable of operating in nonstationary environments.
• To develop adaptive GRNN that can track time-varying regression functions.
• To analyze the convergence and performance of these GRNNs under various nonstationarities.

Main Methods:

• Development of adaptive GRNN architectures.
• Theoretical analysis of GRNN convergence using general learning theorems.
• Implementation of GRNN with Parzen and orthogonal series kernels.
• Empirical investigation of convergence speed and performance across different nonstationary signal types.

Main Results:

• Demonstrated adaptive GRNN's ability to track time-varying regression functions.
• Proved convergence of the proposed GRNN models under specific conditions.
• Compared the performance of GRNNs utilizing Parzen and orthogonal series kernels.
• Evaluated GRNN effectiveness on diverse nonstationarities including multiplicative, additive, scale change, and movable argument.

Conclusions:

• The proposed adaptive GRNN offers a robust solution for analyzing nonstationary signals.
• Specific GRNN designs using Parzen and orthogonal series kernels show convergence guarantees.
• The study provides insights into the speed of convergence and comparative performance of different GRNN structures.