Comparison theorems on large-margin learning

Classification is a very important research topic in statist ical machine learning. There are a large amount of literature on various classification methods, ran ging from the very classical distribution-based likelihood approaches such as Fisher linear discriminant analysis (LDA) and logistic regression [3], to the margin-based approaches such as the well-known s upport vector machine (SVM) [1, 2]. Each type of classifiers has their own merits. Recently, Liu a nd his coauthors proposed in [4] the so-called large-margin unified machines (LUMs) which es tablish a unique transition between these two types of classifiers. As noted in [5], SVM may suffer fr om data piling problems in the high-dimension low-sample size (HDLSS) settings, that is, the support vectors will pile up on top of each other at the margin boundaries when projected onto th e normal vector of the separating hyperplane.