Similarity metric induced metrics with application in machine learning and bioinformatics

Similarity metric and distance metric are widely used in many research areas and applications. In this paper, for a given similarity metric, we will introduce a family of distance metrics of Minkowski type. We will then show general solutions to construct normalized similarity metric and normalized distance metric from a similarity metric and a distance metric. Applying the general solutions to a given non-negative similarity metric and its induced family of distance metrics, we derive general normalized similarity metrics and normalized distance metrics. Finally we briefly discuss some of the applications of our general similarity and distance metric formulations.