Earthmover-based manifold learning for analyzing molecular conformation spaces
This addresses the challenge of analyzing flexible macromolecules like proteins for computational biology, though it is incremental as it builds on existing diffusion maps with a new distance metric.
The paper tackles the problem of learning molecular conformation manifolds by combining Earthmover's distance with diffusion maps, showing that this approach recovers intrinsic geometry with far fewer samples than standard Euclidean-based methods.
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.