A class of new metrics for \(n\)-dimensional unit hypercube (Q1791396)

Summary: 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 \(FD_\alpha(P,Q)\) with the parameter \(\alpha \). We come to the conclusion that the sufficient and necessary condition of the function being a metric is \(0<\alpha\leq1\). Finally, by computing basic examples of codons, we show some numerical comparison of the new metrics to the former metric.