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Classification is an important topic in statistics and machine learning withgreat potential in many real applications. In this paper, we investigate twopopular large margin classification methods, Support Vector Machine (SVM) andDistance Weighted Discrimination (DWD), under two contexts: thehigh-dimensional, low-sample size data and the imbalanced data. A unifiedfamily of classification machines, the FLexible Assortment MachinE (FLAME) isproposed, within which DWD and SVM are special cases. The FLAME family helps toidentify the similarities and differences between SVM and DWD. It is well knownthat many classifiers overfit the data in the high-dimensional setting; andothers are sensitive to the imbalanced data, that is, the class with a largersample size overly influences the classifier and pushes the decision boundarytowards the minority class. SVM is resistant to the imbalanced data issue, butit overfits high-dimensional data sets by showing the undesired data-pilingphenomena. The DWD method was proposed to improve SVM in the high-dimensionalsetting, but its decision boundary is sensitive to the imbalanced ratio ofsample sizes. Our FLAME family helps to understand an intrinsic connectionbetween SVM and DWD, and improves both methods by providing a better trade-offbetween sensitivity to the imbalanced data and overfitting the high-dimensionaldata. Several asymptotic properties of the FLAME classifiers are studied.Simulations and real data applications are investigated to illustrate theusefulness of the FLAME classifiers.

Flexible High-dimensional Classification Machines and Their Asymptotic Properties