Geometric manifold learning methods and collective variables (Joint with IP seminar)  

 Abstract:  In recent years, manifold learning has become increasingly popular as a tool for
 performing non-linear dimensionality reduction and for discovering collective variables. I will present a set of advanced manifold learning methods, that all aim to uncover and preserve the geometric properties of the data. 

Among these will be a method to estimate vector fields on a manifold,
 estimation of the kernel width and intrinsic dimension, a relaxation
 method to remove distortions induced by the embedding algorithms, and
 a method to parametrize a manifold by functions in a
 dictionary. These methods all build on on the Diffusion maps
 framework, and exploit the relationship between the Laplace-Beltrami
 operator and the Riemannian metric on a manifold

Joint work with Dominique Perrault-Joncas, James McQueen, Jacob VanderPlas, Zhongyue Zhang, Samson Koelle, Yu-chia Chen, Hanyu Zhang