Manifold coordinates with physical meaning
Samson J. Koelle, Hanyu Zhang, Marina Meilă and Yu-Chia Chen
Second Workshop on Machine Learning and the Physical Sciences (NeurIPS 2019), 2019
Abstract
One of the aims of both linear and non-linear dimension reduction is to find a reduced set of collective variables that describe the data manifold. While algorithms return abstract coordinates such as spaces spanned by eigenvectors of data-dependent matrices, one can often associate these with features of the data, and hence with domain-related meaning. Usually, finding these domain-related or physical meanings is done via visual inspection by an expert. Our work formulates this problem as sparse, non-parametric, non-linear recovery of the manifold coordinates over a user-defined dictionary of domain-related functions. We show that the original problem can be transformed into a linear Group Lasso problem, and demonstrate the effectiveness of the method on molecular simulation data.
Recommended citation
Samson J. Koelle, Hanyu Zhang, Marina Meilă and Yu-Chia Chen. Manifold Coordinates with Physical Meaning. Second Workshop on Machine Learning and the Physical Sciences (NeurIPS 2019), Vancouver, Canada, December, 2019