On the geodesic distance in shapes K-means clustering

Stefano Gattone; Angela de Sanctis; Stéphane Puechmorel; Florence Nicol

On the geodesic distance in shapes K-means clustering

Stefano Gattone ¹ Angela de Sanctis ¹ Stéphane Puechmorel ² Florence Nicol ²

1 Ud'A - Università degli studi "G. d'Annunzio" Chieti-Pescara [Chieti-Pescara]

2 ENAC - Ecole Nationale de l'Aviation Civile

Abstract : Using Information Geometry tools, we represent landmarks of a complex shape as probability densities in a statistical manifold. Then, in the setting of shapes clustering through a K-means algorithm, we evaluate the discriminative power of two different shapes distances. The first, derived from Fisher-Rao metric, is related with the minimization of information in the Fisher sense and the other is derived from the Wasserstein distance which measures the minimal transportation cost.

Keywords : K-means algorithm Shape Analysis Fisher-Rao metric Wasserstein distance 6 clustering wasserstein distance 9

Document type :

Journal articles

Domain :

Mathematics [math] / Differential Geometry [math.DG]

Mathematics [math] / Statistics [math.ST]

Statistics [stat] / Applications [stat.AP]

Statistics [stat] / Methodology [stat.ME]

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