A family of graph GOSPA metrics for graphs with different sizes
This work addresses a domain-specific problem in graph theory and machine learning, offering incremental improvements over existing graph GOSPA metrics.
The paper tackles the problem of measuring distances between graphs of different sizes by proposing a family of graph GOSPA metrics, which generalizes penalties for edge mismatches and is shown to improve classification tasks on real-world datasets.
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.