When similarity measures lie

Abstract

Do similarity or distance measures ever go wrong? The inherent subjectivity in similarity discernment has long supported the view that all judgements of similarity are equally valid, and that any selected similarity measure may only be considered more effective in some chosen domain. This paper presents evidence that such a view is incorrect for structural similarity comparisons. Similarity and distance measures occasionally do go wrong, and produce judgements that can be considered as errors in judgement. This claim is supported by a novel method for assessing the quality of similarity and distance functions, which is based on relative scale of similarity with respect to chosen reference objects. The method may be applied in any domain, and is demonstrated for common measures of structural similarity in graphs. Finally, the paper identifies three distinct kinds of relative similarity judgement errors, and shows how the distribution of these errors is related to graph properties under common similarity measures.