In this paper, we propose and compare multiple criteria for selecting ElectroEncephaloGraphic (EEG) channels over the Riemannian manifold, for EEG classification in Brain-Computer Interfaces (BCI). These criteria aim to promote EEG covariance matrix classifiers to generalize well by considering EEG data non-stationarity. Our approach consists of both increasing the discriminative information between classes over the manifold and reducing the dispersion within classes. We also reduce the influence of outliers in both discriminative and dispersion measures. Using the proposed criteria, channel selection is done automatically in a backward elimination process. The criteria are evaluated on EEG signals recorded from a tetraplegic subject and dataset IVa from BCI competition III. Experimental evidences confirm that considering the dispersion within each class as a measure for quantifying the effects of non-stationarity and removing the most affected channels can improve the performance of BCI by 5% on the tetraplegic subject and by 12 % on dataset IVa.