@techreport{oai:ipsj.ixsq.nii.ac.jp:00229215,
 author = {須山, 未侑羅 and 坂野, 鋭 and Suyama, Miura and Hitoshi, Sakano},
 issue = {48},
 month = {Nov},
 note = {本研究では，高次元データを人間が理解可能な 2，3  次元に圧縮するための非線形次元圧縮法，Isomap の近傍パラメータの決定方法を提案する．画像などの高次元データは人間にとって知覚が難しく，線形変換では十分な分析が難しいため，非線形次元圧縮が用いられることが多い．しかし，これらの方法には任意性のあるパラメータが存在し，その決定が問題となる．そこで，位相的データ解析の一環として発展してきたパーシステントホモロジー技術を活用し，高次元空間の分布形状を数値的に捉え，次元圧縮のパラメータ決定のヒントを提供する手法を提案する．, In this study, we propose a method to determine the neighborhood parameters of Isomap, a nonlinear dimensionality reduction technique, to compress high-dimensional data into 2 or 3 dimensions that humans can understand. High-dimensional data, such as images, are challenging for humans to perceive, and linear transformations often fall short in providing adequate analysis. As a result, nonlinear dimensionality reduction methods are frequently used. However, these methods come with arbitrary parameters, making their determination a challenge. To address this, we leverage persistent homology technology, which has evolved as part of topological data analysis. This technology numerically captures the distribution shape in high-dimensional spaces and offers insights into parameter determination for dimensionality reduction.},
 title = {位相幾何学に基づくIsomapのパラメーター決定法},
 year = {2023}
}