Quantitative Analysis of Similarity Measures of Distributions

Eric Bazán (PSL Research University - MINES ParisTech), Petr Dokládal ( PSL Research University - MINES ParisTech), Eva Dokládalová (Université Paris-Est, LIGM, UMR 8049, ESIEE Paris)

Abstract
There are many measures of dissimilarity that, depending on the application, do not always have optimal behavior. In this paper, we present a qualitative analysis of the similarity measures most used in the literature and the Earth Mover's Distance (EMD). The EMD is a metric based on the theory of optimal transport with interesting geometrical properties for the comparison of distributions. However, the use of this measure is limited in comparison with other similarity measures. The main reason was, until recently, the computational complexity. We show the superiority of the EMD through three different experiments. First, analyzing the response of the measures in the simplest of cases; one-dimension synthetic distributions. Second, with two image retrieval systems; using colour and texture features. Finally, using a dimensional reduction technique for a visual representation of the textures. We show that today the EMD is a measure that better reflects the similarity between two distributions.

DOI
10.5244/C.33.5
https://dx.doi.org/10.5244/C.33.5

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