Comparison of binary discrimination methods for high dimension low sample size data

A comparison of some binary discrimination methods is done in the high dimension low sample size context for Gaussian data with common diagonal covariance matrix. In particular we obtain results about the asymptotic behavior of the methods Support Vector Machine, Mean Difference (i.e. Centroid Rule), Distance Weighted Discrimination, Maximal Data Piling and Naive Bayes when the dimension d of the data sets tends to infinity and the sample sizes of the classes are fixed. It is concluded that, under appropriate conditions, the first four methods are asymptotically equivalent, but the Naive Bayes method can have a different asymptotic behavior when d tends to infinity.