Research Interests

My research focuses on manifold learning and its applications. High dimensional data often possess an underlying low dimensional structure, which can be modeled as an unknown manifold. Manifold learning uses tools from differential geometry and data analysis to uncover and characterize this intrinsic structure. My research interests include the following directions:

  1. Dimension Reduction
    I develop the mathematical foundations of nonlinear dimension reduction methods, including Locally Linear Embedding (LLE) and Diffusion Maps (kernel graph Laplacians).
  2. Nonparametric Statistics on Manifolds
    I apply manifold learning techniques to problems in nonparametric statistics, with a particular focus on Gaussian process regression on manifold domains.
  3. Methodological Development
    I develop new manifold learning methods together with their theoretical foundations.