Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification

Mengyu Li, Jun Yu, Hongteng Xu & Cheng Meng
As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high computational complexity. To overcome this challenge, we propose a novel importance sparsification method, called Spar-GW, to approximate GW distance efficiently. In particular, instead of considering a dense coupling matrix, our method leverages a simple but effective sampling strategy to...
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