Discriminant Analysis with High Dimensional von Mises - Fisher Distributions
Mario Romanazzi · Athens Journal of Sciences · 2014
This paper extends previous work in discriminant analysis with von Mises-Fisher distributions (e. g., Morris and Laycock, Biometrika, 1974) to general dimension, allowing computation of misclassification probabilities.The main result is the probability distribution of the cosine transformation of a von Mises-Fisher distribution, that is, the random variable , where , satisfying , is a random direction with von Mises-Fisher distribution and , satisfying , is a fixed non-random direction.This transformation is of general interest in multivariate analysis, in particular it underlies discriminant analysis in both two-group and multiple group problem.