主持人：袁海荣 教授

报告简介：Traditional statistical methods may have limitations in capturing structural relationships inherent in complex datasets. Topological data analysis provides an alternative approach by utilizing the shape of data to extract meaningful data patterns. Using concepts from topology, such as persistent homology, topological analysis captures hierarchical and multi-scale geometric structures that conventional statistical techniques might miss. This makes topological analysis particularly valuable for analyzing high-dimensional, noisy, or non-Euclidean data, showing hidden structures within complex datasets. Among various geometric approaches, persistent homology is an efficient tool for understanding data through its shape. In this talk, we will introduce topological analysis through persistent homology, which reveals hierarchical structural patterns in data. To utilize the advantages of topological methods in solving real-world problems, integrating topological approaches with machine learning is essential. We will discuss how to incorporate topological analysis into machine learning frameworks. As an example, we will explain some machine learning applications through topological data analysis, including image classification with convolutional neural networks, knowledge distillation, and time series data analysis for optimizing filtration spaces.

主讲人简介：Jae-Hun Jung教授，数值分析和计算数学专家，现任韩国浦项科技大学（POSTECH）数学系主任，POSTECH数据科学数学研究所所长（Director）。他在首尔国立大学获得天体物理学学士和硕士学位后，于2002年在美国布朗大学获得博士学位，然后在University of British Columbia 以及 Pacific Institute for the Mathematical Sciences (PIMS) 作博士后。2005年—2020年，他先后在美国University of Massachusetts Dartmouth 以及SUNY Buffalo担任助理教授和副教授。2017年—2020年担任韩国亚洲大学AI与Data Science教授，2020年至今任POSTECH数学系教授。