A family of graph GOSPA metrics for graphs with different sizes

TL;DR

This paper introduces a flexible family of graph GOSPA metrics for comparing graphs of varying sizes, with improved edge mismatch penalties and efficient linear programming computation, enhancing graph classification tasks.

Contribution

It extends the graph GOSPA metric to a more general family, allowing better edge mismatch handling and approximate computation, with demonstrated benefits in classification.

Findings

The proposed metrics satisfy metric properties.

They can be computed approximately via linear programming.

They improve classification performance on real-world datasets.

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.