Distances between sets based on set commonality

Abstract

We construct a new family of normalised metrics for measuring the dissimilarity of finite sets in terms of the sizes of the sets and of their intersection. The family normalises a set-based analogue of the Minkowski metric family. It is parametrised by a real variable p≥1, is monotonic decreasing in p, equals the normalised set difference metric when p=1 and equals the normalised maximum difference metric in the limit p→∞. These metrics are suitable for comparison of finite sets in any context. Several applications to comparison of finite graphs are described.