On the geodesic distance in shapes K-means clustering

Stefano Antonio 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

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.

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

Domaines: Géométrie différentielle [math.DG]; Statistiques [math.ST]; Applications [stat.AP]; Méthodologie [stat.ME]

Stefano Antonio Gattone, Angela de Sanctis, Stéphane Puechmorel, Florence Nicol. On the geodesic distance in shapes K-means clustering. Entropy, 2018, Special Issue Selected Papers from 4th International Electronic Conference on Entropy and Its Applications, 20 (9), pp 647. ⟨10.3390/e20090647⟩. ⟨hal-01852144v2⟩