Asymptotic behavior of self-organizing maps with nonuniform stimuli distribution

• 成果类型: Article
• 署名作者: Sadeghi, AA
• 署名单位: University of Kaiserslautern
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1998
• 页码: 281-299
• 关键词: kohonen algorithm; CONVERGENCE; ORGANIZATION; systems

摘要

Here the almost sure convergence of one-dimensional Kohonen's algorithm in its general form, namely, the SK-neighbor setting with a nonuniform stimuli distribution, is proved. We show that the asymptotic behavior of the algorithm is governed by a cooperative system of differential equations which is irreducible. The system of differential equations possesses an asymptotically stable equilibrium, a compact subset of whose domain of attraction will be visited by the state variable X-n infinitely often. The assumptions on the stimuli distribution and the neighborhood functions are weakened, too.