本研究では，データ空間の距離および曲率に着目し，α，β距離という２種類の距離変換を組み合わせた新しい統計解析手法を提案した．さらに，その手法を，年周期により生じる幾何学的特徴を活かした一般化分散の計算に応用し，降雨量データの新しい異常変動を捉えることに成功した．また，β距離変換の提案時にデータ解析に始めて導入した計量錐の理論を，グラフ埋め込みに応用し，ネットワークデータの階層構造を自動的に抽出する新しい手法を提案した．これらの結果を国際学会および学術論文にて発表した．
In this study, we proposed a new statistical analysis method that combines two types of distance transformations, namely α and β distances, by focusing on the distance and curvature of the data space. Furthermore, we applied this method to calculate generalized variances that take advantage of geometric features caused by annual cycles, successfully capturing new abnormal variations in rainfall data. Additionally, we applied the theory of metric cones, which was introduced for the first time in data analysis during the proposal of β distance transformation, to graph embedding, proposing a new method that automatically extracts the hierarchical structure of network data. These results were presented at international conferences and published as academic papers.

研究種目 : 基盤研究 (C) (一般)
研究期間 : 2019～2022
課題番号 : 19K03642
研究分野 : 統計科学