On the Geodesic Distance in Shapes K-means Clustering

Entropy (Basel). 2018 Aug 29;20(9):647. doi: 10.3390/e20090647.

Abstract

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.

Keywords: Fisher-Rao metric; K-means algorithm; Shape Analysis; clustering; wasserstein distance.