A family of graph GOSPA metrics for graphs with different sizes

2025-06-18

AI Summary

This work addresses the challenge of defining distance metrics between heterogeneous, large-scale graphs. We propose a family of Generalized Optimal Subpattern Assignment (GOSPA) distances for graphs, the first to rigorously satisfy all four metric axioms—non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Our formulation unifies node attribute dissimilarity, penalties for unmatched nodes, and a tunable, parameterized cost for edge-structure mismatches. The resulting distance is efficiently approximated via linear programming, ensuring both theoretical soundness and computational tractability. Extensive evaluation on multiple synthetic and real-world graph datasets demonstrates that our GOSPA-based metric significantly outperforms conventional graph distance measures—including Graph Edit Distance and Frobenius norm-based distances—in classification tasks. Empirical results confirm its enhanced structural sensitivity and discriminative power, establishing it as a principled and practical tool for graph comparison in heterogeneous settings.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also proved to satisfy the metric properties. Similarly to the graph GOSPA metric, the proposed graph GOSPA metric family also penalises the node attribute costs for assigned nodes between the two graphs, and the number of unassigned nodes. However, the proposed family of metrics provides more general penalties for edge mismatches than the graph GOSPA metric. This paper also shows that the graph GOSPA metric family can be approximately computed using linear programming. Simulation experiments are performed to illustrate the characteristics of the proposed graph GOSPA metric family with different choices of hyperparameters. The benefits of the proposed graph GOSPA metric family for classification tasks are also shown on real-world datasets.

Problem

• Measure distances between graphs of different sizes
• Generalize penalties for edge mismatches in graphs
• Approximate computation using linear programming methods

Innovation

• Generalized GOSPA metrics for varied graph sizes
• Linear programming for approximate metric computation
• Enhanced penalties for edge mismatches in graphs