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On the Geodesic Distance in Shapes K-means Clustering.

Stefano Antonio Gattone1, Angela De Sanctis2, Stéphane Puechmorel3

  • 1Department of Philosophical, Pedagogical and Economic-Quantitative Sciences, University "G. d'Annunzio" of Chieti-Pescara, 66100 Chieti, Italy.

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Summary

This study introduces a novel clustering method for rotationally invariant shapes using Information Geometry. It compares Fisher-Rao and Wasserstein distances, enhancing the K-means algorithm for shape analysis.

Keywords:
Fisher-Rao metricK-means algorithmShape Analysisclusteringwasserstein distance

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Area of Science:

  • Computational geometry
  • Information theory
  • Statistical analysis

Background:

  • Clustering rotationally invariant shapes presents challenges in pattern recognition.
  • Existing shape distance metrics may not optimally capture geometric properties.

Purpose of the Study:

  • To develop and evaluate a robust method for clustering rotationally invariant shapes.
  • To compare the efficacy of Information Geometry-based distances within a K-means framework.

Main Methods:

  • Defining shape landmarks as probability densities on a statistical manifold.
  • Applying and modifying the K-means algorithm for shape clustering.
  • Evaluating Fisher-Rao metric and Wasserstein distance for shape discrimination.

Main Results:

  • Information Geometry provides a powerful framework for shape clustering.
  • Both Fisher-Rao and Wasserstein distances show discriminative power.
  • The modified K-means algorithm with adaptive variances improves clustering performance.

Conclusions:

  • The proposed Information Geometry approach offers a principled way to cluster complex shapes.
  • The study highlights the utility of different distance metrics in shape analysis.
  • Adaptive variance in K-means enhances clustering accuracy for varying shape distributions.