Canberra distance on ranked lists

The Canberra distance is the sum of absolute values of the differences between ranks divided by their sum, thus it is a weighted version of the L1 distance. As a metric on permutation groups, the Canberra distance is a measure of disarray for ranked lists, where rank differences in top positions need to pay higher penalties than movements in the bottom part of the lists. Here we describe the distance by assessing its main statistical properties and we show extensions to partial ranked lists. We conclude providing two examples of use in functional genomics.