Fused Partial Gromov-Wasserstein for Structured Objects

2025-02-14

AI Summary

Traditional Fused Gromov–Wasserstein (FGW) distances assume strict mass conservation, rendering them ill-suited for structurally unbalanced data—e.g., graphs of disparate sizes and varying quality—common in real-world applications. Method: We propose Fused Partial Gromov–Wasserstein (FPGW), the first framework integrating *partial optimal transport* into the fused GW setting. FPGW relaxes mass conservation constraints to enable joint structural–feature alignment between heterogeneous-scale graphs, and we prove it induces a pseudometric. We develop an efficient Frank–Wolfe-based solver that jointly models Gromov–Wasserstein geometry and feature fusion while ensuring robustness to noise. Results: Extensive experiments demonstrate that FPGW significantly outperforms state-of-the-art baselines on graph classification and clustering tasks. Notably, it maintains robust performance on real-world datasets corrupted by outliers and structural noise, validating its effectiveness and practicality for modeling unbalanced structured data.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Structured data, such as graphs, are vital in machine learning due to their capacity to capture complex relationships and interactions. In recent years, the Fused Gromov-Wasserstein (FGW) distance has attracted growing interest because it enables the comparison of structured data by jointly accounting for feature similarity and geometric structure. However, as a variant of optimal transport (OT), classical FGW assumes an equal mass constraint on the compared data. In this work, we relax this mass constraint and propose the Fused Partial Gromov-Wasserstein (FPGW) framework, which extends FGW to accommodate unbalanced data. Theoretically, we establish the relationship between FPGW and FGW and prove the metric properties of FPGW. Numerically, we introduce Frank-Wolfe solvers for the proposed FPGW framework and provide a convergence analysis. Finally, we evaluate the FPGW distance through graph classification and clustering experiments, demonstrating its robust performance, especially when data is corrupted by outlier noise.

Problem

• Extends FGW to handle unbalanced structured data
• Proves metric properties of Fused Partial Gromov-Wasserstein
• Evaluates FPGW in graph classification and clustering

Innovation

• Relaxes mass constraint
• Introduces Frank-Wolfe solvers
• Enhances outlier noise robustness