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Communication Dans Un Congrès Année : 2022

ON THE USE OF GEODESIC TRIANGLES BETWEEN GAUSSIAN DISTRIBUTIONS FOR CLASSIFICATION PROBLEMS

Résumé

This paper presents a new classification framework for both first and second order statistics, i.e. mean/location and covariance matrix. In the last decade, several covariance matrix classification algorithms have been proposed. They often leverage the Riemannian geometry of symmetric positive definite matrices (SPD) with its affine invariant metric and have shown strong performance in many applications. However, this geometry assumes a zero mean. In practice, it is often estimated and then removed in a preprocessing step. This is of course damaging for applications where the mean is a discriminative feature. Unfortunately, the distance associated to the affine invariant metric for both mean and covariance matrix remains unknown. Leveraging previous works on geodesic triangles, we propose two affine invariant divergences that use both statistics. Then, we derive an algorithm to compute the associated Riemannian centers. Finally, a divergence based Nearest centroid, applied on the crop classification dataset Breizhcrops, shows the interest of the proposed framework.
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Dates et versions

hal-03752879 , version 1 (17-08-2022)

Identifiants

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Antoine Collas, Florent Bouchard, Guillaume Ginolhac, Arnaud Breloy, Chengfang Ren, et al.. ON THE USE OF GEODESIC TRIANGLES BETWEEN GAUSSIAN DISTRIBUTIONS FOR CLASSIFICATION PROBLEMS. 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022), May 2022, Singapour, Singapore. ⟨10.1109/ICASSP43922.2022.9747872⟩. ⟨hal-03752879⟩
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