An efficient approach for discriminant analysis based on adaptive feature augmentation

Effective discriminant analysis is of great practical importance, as demonstrated by economic and genetic applications. Feature augmentation via nonparametric and selection (FANS) is an efficient approach that has been widely used in classification. However, FANS may impair efficiency when a linear decision boundary separates data reasonably well. The available remedy is to use both the transformed features and original ones, which may increase computational cost and model complexity. Motivated by these concerns, this paper proposes an efficient nonparametric approach for binary discriminant analysis, called adaptive FANS, integrating augmentation and nonparametric tests. In this procedure, the original features or transformed ones are used selectively to keep the number of features constant. Thus, this procedure avoids the ergodic transformation and reduces error caused by nonparametric estimation and computational complexity. Simulation and real data analysis demonstrate its competitiveness and significant adaptability. Moreover, our approach can be easily extended to other linear frameworks.