Distance-Based Generalisation Operators for Graphs

Distances and similarity functions between structured data- types, such as graphs, have been widely employed in machine learning since they are able to identify similar cases or prototypes from which decisions can be made. In these distance-based methods the justification of the labelling of a new case a is usually based on expressions such as "label(a)=label(b) because case a is similar to case b". However, a more meaningful pattern, such as "because case a and b have properties x and y" is usually more dicult to find since the connection of this pattern with the distance-based method might be inconsistent (4). In this paper we study possible consistent generalisation operators for the particular case of graphs embedded in metric spaces.