Abstract: Principal component analysis (PCA) is well-studied and widely adopted in applications, but extending it to complex data analysis in metric spaces remains a challenge. In this work, we propose a unified framework, Geodesic-PCA (G-PCA), extending beyond traditional manifolds to geodesic spaces. We develop robust and optimal theoretical results for G-PCA, and validate the reliability and effectiveness through extensive simulations. In real application, the proposed method is adopted to analyze brain corpus callosum and task-fMRI data, highlighting its potential in practice, such as neuroimaging.

Bio: Ting Li is an assistant professor in the Department of Applied Mathematics at Hong Kong Polytechnic University. Prior to joining PolyU, he was a postdoctoral associate in Yale University. He received his PhD in Hong Kong University of Science and Technology. His research focuses on the development of novel statistical learning methods for complex data analysis, including network data analysis, brain data analysis, and imaging genetics. His research papers have appeared in high impact journals and conferences, such as Annals of Statistics, JASA, AOAS, ICML, Genome Research, and Human Brain Mapping.