演講者：胡全燊博士 ( 新加坡南洋理工大學數理科學院 )

日   期：2025 年 06 月 11 日（星期三）13:30

地   點：國立高雄大學理學院 408 室

講   題：Topological Data Analysis-Driven AI Models and Their Applications in Imaging and Materials Science

摘   要：

Topological Data Analysis (TDA) serves as a robust framework for extracting shape-based features from complex data, with persistent homology (PH) as a central technique for identifying and quantifying topological structures such as connected components, loops, and voids across multiple spatial or parametric scales. This presentation provides an overview of the foundational concepts of TDA, emphasizing the intuition and computational process behind PH, including the construction of filtrations, the computation of homological features, the generation of persistence diagrams, and the stability of these representations under perturbations. Building on this foundation, recent advancements that enrich PH by incorporating complementary geometric information, such as spatial relationships, periodicity, local densities, and metric properties, are explored. These enhanced topological descriptors are then integrated into machine learning models to improve the representation of complex structural patterns in data, enabling more effective classification, regression, and clustering tasks. Case studies include applications in medical and bioinformatics image analysis, such as skin lesion classification and cell structure characterization, as well as in the design and evaluation of high-performance solar cell materials. These examples highlight the potential of TDA-enhanced AI models to bridge rigorous mathematical theory with impactful applications in imaging and materials science.