An M-Estimator for Robust Centroid Estimation on the Manifold of Covariance Matrices

This letter introduces a new robust estimation method for the central value of a set of N covariance matrices. This estimator, called Huber's centroid, is described starting from the expression of two well-known methods that are the center of mass and the median. In addition, a computation algorithm based on the gradient descent is proposed. Moreover, Huber's centroid performances are analyzed on simulated data to identify the impact of outliers on the estimation process. In the end, the algorithm is applied to brain decoding, based on magnetoencephalography data. For both simulated and real data, the covariance matrices are considered as realizations of Riemannian Gaussian distributions and the results are compared to those given by the center of mass and the median.