Comparison of discriminant analysis methods on the sphere

Discriminant analysis for spherical data (directional data in general) has not been studied to a great degree and most papers focus on one distribution, the rotationally symmetric (or isotropic) von Mises-Fisher. This is the rst paper on maximum likelihood discriminant analysis with spherical data that considers non rotationally symmetric distributions, while the k-Nearest Neighbours algorithm is included as a model-free alternative. Extensive Monte Carlo simulations and experiments with numerous real data yield multiple conclusions regarding the algorithms' predictive performance and computational cost. Maximum likelihood discriminant analysis using rotationally non-symmetric distributions performed satisfactorily and surprisingly enough, rotationally symmetric distributions performed well in some cases. Overall, the k-NN algorithm is suggested because it is non-parametric hence exible, computationally efficient,  calable to large sample sizes and suitable for big data, and on average is on par or outperforms the other methods.