A Class of New Metrics for n-Dimensional Unit Hypercube

Abstract EN

We study the metric on the n-dimensional unit hypercube.

We introduce a class of new metrics for the space, which is information theoretically motivated and has close relation to Jensen-Shannon divergence.

These metrics are obtained by discussing a function FDα(P,Q) with the parameter α.

We come to the conclusion that the sufficient and necessary condition of the function being a metric is 0<α≤1/2.

Finally, by computing basic examples of codons, we show some numerical comparison of the new metrics to the former metric.