Intra-fused Gromov Wasserstein Discrepancy: A Smooth Metric for Cross-Domain structured Data
Keywords: Optimal transport, alignment, geometric learning
Abstract: Optimal Transport (OT) theory, particularly the Wasserstein distance, is pivotal in comparing probability distributions and has significant applications in signal and image analysis. The Gromov-Wasserstein (GW) distance extends OT to structured data, effectively comparing different graph structures. This paper presents the Intra-fused Gromov-Wasserstein (IFGW) distance, a novel metric that combines the Wasserstein and Gromov-Wasserstein distances to capture both feature and structural information of graphs within a single optimal transport framework. We review related work on graph neural networks and existing transport-based metrics, highlighting their limitations. The IFGW distance aims to overcome these by providing an efficient, isometry-aware method for graph comparison that applies to tasks such as domain adaptation, word embedding, and graph classification, with applications in computer vision, natural language processing, and bioinformatics. We detail the mathematical foundation of IFGW and discuss optimization strategies for practical implementation.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 11235
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