A Class of New Metrics for n-Dimensional Unit Hypercube

Abstract

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 $F{D}_{\alpha }(P,Q)$ with the parameter α. We come to the conclusion that the sufficient and necessary condition of the function being a metric is . Finally, by computing basic examples of codons, we show some numerical comparison of the new metrics to the former metric.