On The Similarity Metric
United States Service Academies
In mathematics, and more specifically in topology, the notion of distance metric is well known since the nineteenth century. It is used to measure the "difference" between two objects. When it comes to characterizing the similarity between two objects, a similarity metric is needed. Although widely used in computer science, such a metric is not clearly defined mathematically. We fill in the existing gap in the current literature concerning similarity metrics, connecting them to the well-known notion of partial metrics in general topology.
Elie Alhajjar and Clément Lefèvrey. "On The Similarity Metric". Mathematica Militaris, Volume 24. 2019.