K-Means and Gaussian Mixture Models on Lie Groups: Application to Geometrical Clustering
Résumé
In this article, we derive and implement two new clustering algorithms dedicated to Lie groups, adapted from the well known K-Means algorithm and Gaussian mixture models. More precisely, the K-Means algorithm is reformalized by taking into account the fact that observations belong to a Lie group (LG) with an appropriate intrinsic metric and Gaussian mixture model are defined for data living in LGs. The consistency and the performance of the resulting are numerically validated for data lying on the LG SE(2), by comparison with state-of-the-art methods for synthetic data and pseudo-real data generated using an ultra-sound sensor model.
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