Comparing histogram data using a Mahalanobis-Wasserstein distance

In this paper, we present a new distance for comparing data described by histograms. The distance is a generalization of the classical Mahalanobis distance for data described by correlated variables. We define a way to extend the classical concept of inertia and codeviance from a set of points to a set of data described by histograms. The same results are also presented for data described by continuous density functions (empiric or estimated). An application to real data is performed to illustrate the effects of the new distance using dynamic clustering.