Gromov-Wasserstein Averaging of Kernel and Distance Matrices
Peyré, Gabriel; Cuturi, Marco; Solomon, Justin (2016), Gromov-Wasserstein Averaging of Kernel and Distance Matrices, Proceedings of the 33rd International Conference on International Conference on Machine Learning, ACM - Association for Computing Machinery : New York, NY
TypeCommunication / Conférence
Conference title33rd International Conference on International Conference on Machine Learning
Conference cityNew York
Conference countryUnited States
Book titleProceedings of the 33rd International Conference on International Conference on Machine Learning
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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 noncon-vex 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.
Subjects / KeywordsGromov-Wasserstein; Optimal Transport; Wasserstein; metric spaces; shapes
Showing items related by title and author.
Solomon, Justin; De Goes, Fernando; Peyré, Gabriel; Cuturi, Marco; Butscher, Adrian; Nguyen, Andy; Du, Tao; Guibas, Leonidas (2015) Article accepté pour publication ou publié