Gromov-wasserstein averaging of kernel and distance matrices
Name
Solomon_Gromov-wasserstein.pdf
Size
3.96 MB
Format
Adobe PDF
Checksum (MD5)
a04906c15e478e1e656b47c67d68ee5f
Author(s)
Peyre, Gabriel
Cuturi, Marco
Solomon, Justin
Date Issued
June 2016
Journal
Proceedings of the 33rd International Conference on International Conference on Machine Learning
Publisher
Association for Computing Machinery
Citation
Peyre, Gabriel, Marco Cuturi and Justin Solomon. "Gromov-wasserstein averaging of kernel and distance matrices." Proceedings of the 33rd International Conference on International Conference on Machine Learning ICML'16, New York, NY, 19-24 June, 2016. Vol. 48, Association for Computing Machinery, 2016. pp. 2664-2672.
Version
Author's final manuscript
Abstract
This paper presents a new technique for computing the barycenter of a set of distance or kernel matrices. These matrices, which define the interrelationships between points sampled from individual domains, are not required to have the same size or to be in row-by-row correspondence. We compare these matrices using the softassign criterion, which measures the minimum distortion induced by a probabilistic map from the rows of one similarity matrix to the rows of another; this criterion amounts to a regularized version of the Gromov-Wasserstein (GW) distance between metric-measure spaces. The barycenter is then defined as a Fréchet mean of the input matrices with respect to this criterion, minimizing a weighted sum of softassign values. We provide a fast iterative algorithm for the resulting nonconvex optimization problem, built upon state-of-the-art tools for regularized optimal transportation. We demonstrate its application to the computation of shape barycenters and to the prediction of energy levels from molecular configurations in quantum chemistry.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://dl.acm.org/citation.cfm?id=3045671
