k-Means Algorithm in Statistical Shape Analysis

Abstract

In this work it is shown how the k-means method for clustering objects can be applied in the context of statistical shape analysis. Because the choice of the suitable distance measure is a key issue for shape analysis, the Hartigan and Wong k-means algorithm is adapted for this situation. Simulations on controlled artificial data sets demonstrate that distances on the pre-shape spaces are more appropriate than the Euclidean distance on the tangent space. Finally, results are presented of an application to a real problem of oceanography, which in fact motivated the current work.

Keywords:

• Geodesic distance
• Landmarks
• Non-Euclidean spaces

Mathematics Subject Classification:

• 62H11

Acknowledgments

We thank the anonymous referee for constructive criticism. Support of the Brazilian agencies CAPES and CNPQ is acknowledged. GJAA acknowledges support of the Brazilian agency FACEPE (APQ-0461-1.02/06).