Earthmover-based manifold learning for analyzing molecular conformation spaces

TL;DR

This paper introduces a novel manifold learning method combining Earthmover's distance with diffusion maps, effectively capturing the shape space of macromolecules with fewer samples and reduced computational cost.

Contribution

It presents a new EMD-based diffusion maps approach for analyzing molecular conformations, improving sample efficiency and computational feasibility over traditional methods.

Findings

EMD-based diffusion maps require fewer samples to recover intrinsic geometry.

Wavelet approximation significantly reduces EMD computation time.

Method effectively analyzes protein shape spaces using simulated data.

Abstract

In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of this approach for learning shape spaces of proteins and other flexible macromolecules using a simulated dataset of 3-D density maps that mimic the non-uniform rotary motion of ATP synthase. Our results show that EMD-based diffusion maps require far fewer samples to recover the intrinsic geometry than the standard diffusion maps algorithm that is based on the Euclidean distance. To reduce the computational burden of calculating the EMD for all volume pairs, we employ a wavelet-based approximation to the EMD which reduces the computation of the pairwise EMDs to a computation of pairwise weighted-$\ell_1$ distances between wavelet coefficient vectors.