Abstract: Data in various domains, such as neuroimaging and network data analysis, often come in complex forms without possessing a Hilbert structure. The complexity necessitates innovative approaches for effective analysis. We propose a novel measure of heterogeneity, ball impurity, which is designed to work with complex non-Euclidean objects. Our approach extends the notion of impurity to general metric spaces, providing a versatile tool for feature selection and tree models. The ball impurity measure exhibits desirable properties, such as the triangular inequality, and is computationally tractable, enhancing its practicality and usefulness. Extensive experiments on synthetic data and real data from the UK Biobank validate the efficacy of our approach in capturing data heterogeneity. Remarkably, our results compare favorably with state-of-the-art methods in metric spaces, highlighting the potential of ball impurity as a valuable tool for addressing complex data analysis tasks.

Bio: Wenliang Pan is an Associate Research Fellow and doctoral supervisor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interests include statistical learning, medical imaging analysis, and nonparametric methods in metric spaces. He has published over 30 papers in leading journals, including The Annals of Statistics, JASA, and IEEE TPAMI. He received the Second Prize of the 2022 Higher Education Outstanding Scientific Research Achievement Award (Natural Sciences) from the Ministry of Education of China (ranked second). He has led several NSFC-funded projects, including the Young Scientists Fund (Category B) and the General Program. He also serves as Vice President of the Beijing Biometrics Association, Supervisor of the Chinese Association for Applied Statistics, and Deputy Secretary-General of its Division of Interdisciplinary Statistical Research.