| Project/Area Number |
17K05370
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Akita Prefectural University |
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Principal Investigator |
Hoshino Mitsuhiro 秋田県立大学, システム科学技術学部, 准教授 (90322338)
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 自己組織化マップ / 整列化 / 吸収特性 / 線形型学習写像 / 状態クラスの閉性 / 局所整列化 / 大域的整列化 / 内積型学習写像 / 局所的整列化 / 伝播プロセス / 閉状態クラス / 応用数学 / 自己組織化 / 統計数学 |
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| Outline of Final Research Achievements |
This research focuses on the transition in the learning of a model function, defined as a mapping from each node to its value, in a self-organizing map known as a Kohonen-type algorithm, and on absorbing properties and state preservation properties of state classes, with the aim of mathematically explaining the phenomenon of global ordering with certain characteristic structures, such as monotonicity, which is important in applications, and the formation process leading to this. Features of this research project include the mathematical expression of properties of closed state classes and the propagation process from local ordering to global ordering, as well as the construction of several numerical models on a computer and evaluation and verification through several computational simulations.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では，数学的な視点からKohonen型アルゴリズムとして知られる自己組織化マップを扱い，クラスタリング等の統計的な応用や組み合わせ最適化への応用をもつ．昨今，これらの手法及びツールに対して一定の社会的，産業的要求があり，本課題の社会的な意義として挙げることができる．
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