We compared maximum likelihood and the k-NN algorithm in the context of discriminant analysis with spherical data.
We present new model for analyzing compositional data with structural zeros. Inspired by Butler and Glasbey (2008) who suggested a model in the presence of zero values in the data we propose a model that treats the zero values in a different manner.
Discriminant analysis for spherical data, or directional data in general, has not been extensively studied, and most papers focus on one distribution, the von Mises-Fisher. In this work, we study more distributions, escaping the rotational symmetry bound of the aforementioned distribution and also include a non parametric classier, the k-NN algorithm.
A folded type model is developed for analyzing compositional data based that provides a new and flexible class of distributions for modeling data defined on the simplex sample space. Despite its rather
seemingly complex structure, employment of the EM algorithm guarantees efficient parameter estimation.
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