## New relations between similarity measures for vectors based on vector norms Universiteit Hasselt Universiteit Antwerpen

The well-known similarity measures Jaccard, Salton’s cosine, Dice and several related overlap measures for vectors are compared. While general relations are not possible to prove, we study these measures on the “trajectories” of the form , where is a constant and denotes the Euclidean norm of a vector. In this case, direct functional relations between these measures are proved. For Jaccard we prove that it is a convexly increasing function ...