The analysis of a stochastic differential approach for Langevin competitive learning algorithm

Recently, various types of neural network models have been used successfully to applications in pattern recognition, control, signal processing, and so on. However, the previous models are not suitable for hardware implementation due to their complexity. In this paper, we present a survey of the stochastic analysis for the Langevin competitive learning algorithm, known for its easy hardware implementation. Since the Langevin competitive learning algorithm uses a time-invariant learning rate and a stochastic reinforcement term, it is necessary to analyze with stochastic differential or difference equation. The result of the analysis verifies that the Langevin competitive learning process is equal to the standard Ornstein-Uhlenback process and has a weak convergence property. The experimental results for Gaussian distributed data confirm the analysis provided in this paper.