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- Material Type
- 文書・図像類
- Author/Editor
- 末谷, 大道
- Author Heading
- Publication, Distribution, etc.
- Alternative Title
- Model Reduction for High-dimensional Nonlinear Chaotic Dynamical Systems Based on Kernel Multivariate Analysis
- Text Language Code
- jpn
- Target Audience
- 一般
- Note (General)
- 2010-2011年度科学研究費助成事業(科学研究費補助金(若手研究(B)))研究成果報告書 課題番号：22740258 研究代表者：末谷大道 (鹿児島大学大学院理工学研究科(理学系)准教授)本研究課題ではRANSACアルゴリズムを用いて測地線距離の誤推定を防ぐことによってISOMAPを改良した多様体学習法を提案した。それを水滴落下の現象論的モデルであるバネ−質点系モデルの数値シミュレーションデータに適用し、従来のISOMAPでは解析が困難であった折り畳まれた紐状の多様体に対して適切な座標系を与え、その座標系を用いて新たにポアンカレ写像を得た。さらに、実際の水滴落下装置を作成し、水滴の落下間隔の実験データからポアンカレ写像の再構成に成功した。We improved ISOMAP, which is a representative manifold learning method, by preventing mistakes in estimating geodesics between points in a manifold using RANSAC. We applied the proposed approach to the numerical simulation data generated from a mass-spring model for dripping faucet in order to demonstrate the usefulness. Furthermore, we tried to analyze real data of the dripping faucet experiment and obtained promising results.