An MM algorithm for multicategory vertex discriminant analysis

This article introduces a new method of supervised learning based on linear discrimination among the vertices of a regular simplex in Euclidean space. Each vertex represents a different category. Discrimination is phrased as a regression problem involving ϵ-insensitive residuals and a quadratic penalty on the coefficients of the linear predictors. The objective function can by minimized by a primal MM (majorization–minimization) algorithm that (a) relies on quadratic majorization and iteratively re-weighted least squares, (b) is simpler to program than algorithms that pass to the dual of the original optimization problem, and (c) can be accelerated by step doubling. Limited comparisons on real and simulated data suggest that the MM algorithm is competitive in statistical accuracy and computational speed with the best currently available algorithms for discriminant analysis.