时 间：2025年4月24日（周四）10：00 – 11：00
地 点：理科大楼A1514室
报告人：谭若虚 同济大学助理教授
主持人：王亚平 华东师范大学教授
摘 要：
Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In contrast, we investigate this topic from the perspective of manifold learning. It is assumed that functional data lie on an unknown low-dimensional manifold, and we expect that better classifiers can be built upon the manifold structure. To this end, we propose a novel proximity measure that takes the label information into account to learn the low-dimensional representations, also known as the supervised manifold learning outcomes. When the 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. In practice, we show that our method, coupled with several classical multivariate classifiers, achieves outstanding classification performance compared to existing functional classifiers in both synthetic and real data examples.
报告人简介：
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Statistica Sinica，Statistics in Medicine等期刊，主持国家青年科学基金、国家博士后有关专项计划。