An intuitive clustering algorithm for spherical data with application to extrasolar planets

Abstract

This paper proposes an intuitive clustering algorithm capable of automatically self-organizing data groups based on the original data structure. Comparisons between the propopsed algorithm and EM [1] and spherical k-means [7] algorithms are given. These numerical results show the effectiveness of the proposed algorithm, using the correct classification rate and the adjusted Rand index as evaluation criteria [5,6]. In 1995, Mayor and Queloz announced the detection of the first extrasolar planet (exoplanet) around a Sun-like star. Since then, observational efforts of astronomers have led to the detection of more than 1000 exoplanets. These discoveries may provide important information for understanding the formation and evolution of planetary systems. The proposed clustering algorithm is therefore used to study the data gathered on exoplanets. Two main implications are also suggested: (1) there are three major clusters, which correspond to the exoplanets in the regimes of disc, ongoing tidal and tidal interactions, respectively, and (2) the stellar metallicity does not play a key role in exoplanet migration.

Keywords:

• EM algorithm
• extrasolar planets
• mixtures of von mises distributions
• spherical data
• spherical k-means algorithm

Acknowledgments

The authors would like to thank the anonymous reviewers for their constructive comments to improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work is supported in part by the National Science Council, Taiwan, under Wen-Liang Hung's Grant: NSC 102-2118-M-134-001.