• 研究概要
• 略歴
• 論文
• お問い合わせ

研究概要

My research area is applied topology, with a focus on topological data analysis (TDA). TDA studies datasets through their underlying shape, allowing us to detect topological features and encode them in concise descriptors—such as persistence diagrams/barcodes and mapper graphs—that are useful for inference and learning.

I currently focus on persistent homology, one of the main tools in TDA. My work draws on the representation theory of algebras, probability, and statistics. In the standard one-parameter context, I used to investigate applying the persistent homology theory to high-dimensional, low-sample-size data in some practical and specified settings, motivated by the single-cell RNA sequencing data analysis. In generalized persistent homology (e.g., multiparameter persistence), data analysis is substantially harder than in the one-parameter case because of algebraic complications. I have developed both theoretical and computational aspects for studying some invariants of persistent homology, which are closely related to the algebraic (homological) approximation of the persistent homology obtained. I am continuing to develop this line of work.

略歴

2025年京都大学大学院理学研究科博士後期課程修了（専門：トポロジカルデータ解析）。2025年10月より京都大学高等研究院ヒト生物学高等研究拠点（ASHBi）特定研究員。トポロジー的手法を用いた複雑データ解析の数学的手法の開発に関心を持ち、研究を行っている。

論文

Yasuaki Hiraoka, Yusuke Imoto, Shu Kanazawa, Enhao Liu. Curse of Dimensionality on Persistence Diagrams. Foundations of Data Science. 2025. doi: 10.3934/fods.2025008

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