[MDS Job Talk] Multiview manifold learning for high-dimensional and noisy datasets

Speaker: Xiucai Ding (UC Davis)

Date: 1/10/25

Abstract: A longstanding challenge in data science is to effectively quantify systems of interest by integrating information from heterogeneous datasets, a problem known as multiview learning. In this talk, I will present recent advancements in this direction, focusing on techniques based on convolutions of diffusion maps and kernel embeddings. Within the common manifold framework, the proposed algorithm can be interpreted through its connection to limiting Laplacian and integral operators. Additionally, we demonstrate that the method is robust against high-dimensional noise via the analysis of the underlying kernel random matrices. I will also demonstrate how these algorithms can be applied to analyze single-cell RNA sequencing data and study sleep patterns. This talk is based on several joint works, primarily with Hau-Tieng Wu (NYU Courant).