On some semi-absorbing state classes and ordering in Self-organizing map processes

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540134
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Akita Prefectural University
• Principal Investigator: Mitsuhiro Hoshino 秋田県立大学, システム科学技術学部, 准教授 (90322338)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 自己組織化 / 吸収状態 / 準吸収的特性 / 学習過程 / 順序化 / 整列化

Outline of Final Research Achievements

We consider mathematical models of self-organizing maps referred to as Kohonen type algorithm, which is very practical and has many useful applications, such as a semantic map, a diagnosis of speech voicing, the traveling-salesman problem, and so on. The purpose of this research is to make a study of closed classes of states and their characterization in self-organizing map models.We obtained a condition that the learning mapping is non-expansive in self-organizing maps with inputs in an inner product space. We have given an extended learning process with a variable learning rate factor and a sufficient condition that a learning process forms a closed class of states. Furthermore, we have made a study of ordering of node values on learning process by several numerical examples and their calculations from various angles.sional arrayed self-organizing maps with a one dimensional input space.

Free Research Field

数理モデル，統計数学