Please help transcribe this video using our simple transcription tool. You need to be logged in to do so.
We present a distance metric based upon the notion of minimum-cost injective mappings between sets. Our function satisfies metric properties as long as the cost of the minimum mappings is derived from a semimetric, for which the triangle inequality is not necessarily satisfied. We show that the Jaccard distance (alternatively biotope, Tanimoto, or Marczewski-Steinhaus distance) may be considered the special case for finite sets where costs are derived from the discrete metric. Extensions that allow premetrics (not necessarily symmetric), multisets (generalized to include probability distributions), and asymmetric mappings are given that expand the versatility of the metric without sacrificing metric properties. The function has potential applications in pattern recognition, machine learning, and information retrieval.
Questions and AnswersYou need to be logged in to be able to post here.