Marina Meila, University of Washington

Abstract

We ask if it is possible, in the case of scientific data where quantitative prior knowledge is abundant, to explain a data manifold by new coordinates, chosen from a set of scientifically meaningful functions? The algorithm I will present, ManifoldLasso, can discover a subset of relevant coordinates from a user defined dictionary in fully non-parametric fashion. This is suppoerted by experiments on real data and theoretical recovery conditions.

Second, we ask how popular Manifold Learning tools and their applications can be recreated in the space of  vector fields and flows on a manifold. Central to this approach is the order 1-Laplacian, $Delta_1$, whose eigen-decomposition into gradient, harmonic, and curl  provides a basis for all vector fields on a manifold. We present an estimator for $Delta_1$, and based on it a new algorithm for finding shortest independent loops.

Joint work with  Yu-Chia Chen, Samson Koelle, Hanyu Zhang, Weicheng Wu and Ioannis Kevrekidis

[Video]    [Slides]