Comparison of discriminant analysis methods on the sphere

Abstract

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 first paper on maximum likelihood discriminant analysis with spherical data that considers non-rotationally symmetric distributions, while the k-nearest neighbors (k-NN) 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 flexible, computationally efficient, scalable to large sample sizes and suitable for big data, and on average is on par or outperforms the other methods.

Keywords:

• Discriminant analysis
• spherical data
• non-rotational symmetry

AMS CLASSIFICATION:

• 62H11
• 62H30