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Entropy and Geometric Objects
Article

On the Geodesic Distance in Shapes K-means Clustering

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Department of Philosophical, Pedagogical and Economic-Quantitative Sciences, University “G. d’Annunzio” of Chieti-Pescara, 66100 Chieti, Italy
2
Department of Business Economics, University "G. D'Annunzio" of Chieti-Pescara, 65127 Pescara, Italy
3
Ecole Nationale de l’aviation Civile (ENAC), Université Fédérale de Toulouse, FR-31055 Toulouse CEDEX, France
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(9), 647; https://doi.org/10.3390/e20090647
Received: 31 July 2018 / Revised: 22 August 2018 / Accepted: 27 August 2018 / Published: 29 August 2018
In this paper, the problem of clustering rotationally invariant shapes is studied and a solution using Information Geometry tools is provided. Landmarks of a complex shape are defined as probability densities in a statistical manifold. Then, in the setting of shapes clustering through a K-means algorithm, the discriminative power of two different shapes distances are evaluated. 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. A modification of the K-means algorithm is also proposed which allows the variances to vary not only among the landmarks but also among the clusters. View Full-Text
Keywords: Shape Analysis; clustering; K-means algorithm; Fisher-Rao metric; wasserstein distance Shape Analysis; clustering; K-means algorithm; Fisher-Rao metric; wasserstein distance
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MDPI and ACS Style

Gattone, S.A.; De Sanctis, A.; Puechmorel, S.; Nicol, F. On the Geodesic Distance in Shapes K-means Clustering. Entropy 2018, 20, 647. https://doi.org/10.3390/e20090647

AMA Style

Gattone SA, De Sanctis A, Puechmorel S, Nicol F. On the Geodesic Distance in Shapes K-means Clustering. Entropy. 2018; 20(9):647. https://doi.org/10.3390/e20090647

Chicago/Turabian Style

Gattone, Stefano A.; De Sanctis, Angela; Puechmorel, Stéphane; Nicol, Florence. 2018. "On the Geodesic Distance in Shapes K-means Clustering" Entropy 20, no. 9: 647. https://doi.org/10.3390/e20090647

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