Binary discrimination methods for high-dimensional data with a geometric representation

Four binary discrimination methods are studied in the context of high-dimension, low sample size data with an asymptotic geometric representation, when the dimension increases while the sample sizes of the classes are fixed. We show that the methods support vector machine, mean difference, distance-weighted discrimination, and maximal data piling have the same asymptotic behavior as the dimension increases. We study the consistent, inconsistent, and strongly inconsistent cases in terms of angles between the normal vectors of the separating hyperplanes of the methods and the optimal direction for classification. A simulation study is done to assess the theoretical results.