Seminar| Institute of Mathematical Sciences
Time: Friday, November 14th, 2025,10:30-11:30
Location: RS408, IMS
Speaker: Ruoxu Tan, Tongji University
Abstract: Unknown manifold structures may arise in functional data, especially when functional data exhibit the phase variation. Our work is built upon this manifold assumption. Under the unsupervised setting, we extend a geodesic distance estimation technique for high-dimensional data to functional data, derive the asymptotic convergence under observational errors, and propose a clustering procedure based on manifold learning outcomes. Under the supervised setting, we propose a label-weighted geodesic distance to incorporate the label information. When the manifold learning outcomes are coupled with multivariate classifiers, the procedure induces a family of new functional classifiers. In theory, we show that our functional classifier induced by the k-NN classifier is asymptotically optimal. Numerical examples show some gain of our clustering and classification algorithms.
谭若虚，同济大学助理教授，主要从事函数型数据分析，因果推断，流形学习等方面的研究，相关工作发表在JMLR，JCGS，Stat. Sin.等期刊，主持国家青年科学基金（C类），入选上海市海外高层次人才计划、国家博士后有关专项计划。