On the similarity metric and the distance metric

Similarity and dissimilarity measures are widely used in many research areas and applications. When a dissimilarity measure is used, it is normally required to be a distance metric. However, when a similarity measure is used, there is no formal requirement. In this article, we have three contributions. First, we give a formal definition of similarity metric. Second, we show the relationship between similarity metric and distance metric. Third, we present general solutions to normalize a given similarity metric or distance metric.