A GEOMETRIC LEARNING APPROACH ON THE SPACE OF COMPLEX COVARIANCE MATRICES

Hatem Hajri (1) , Salem Said (1) , Lionel Bombrun (1) , Yannick Berthoumieu (1)

1 IMS - Laboratoire de l'intégration, du matériau au système

Many signal and image processing applications, including SAR polarimetry and texture analysis, require the classification of complex covariance matrices. The present paper introduces a geometric learning approach on the space of complex covariance matrices based on a new distribution called Riemannian Gaussian distribution. The proposed distribution has two parameters, the centre of mass $\bar{Y}$ and the dispersion parameter $\sigma$. After having derived its maximum likelihood estimator and its extension to mixture models, we propose an application to texture recognition on the VisTex database.

Mots clés: Classification; Hermitian matrices; Riemannian centre of mass; EM algorithm; Information geometry

Domaines: Mathématiques [math]; Statistiques [stat]

Hatem Hajri, Salem Said, Lionel Bombrun, Yannick Berthoumieu. A GEOMETRIC LEARNING APPROACH ON THE SPACE OF COMPLEX COVARIANCE MATRICES. 2017. ⟨hal-01483449⟩