Convex Bidirectional Large Margin Classifiers

Classification problems are commonly seen in practice. In this article, we aim to develop classifiers that can enjoy great interpretability as linear classifiers, and at the same time have model flexibility as nonlinear classifiers. We propose convex bidirectional large margin classifiers to fill the gap between linear and general nonlinear classifiers for high-dimensional data. Our method provides a new data visualization tool for classification of high-dimensional data. The obtained bilinear projection structure makes the proposed classifier very interpretable. Additional shrinkage to approximate variable selection is also considered. Through analysis of simulated and real data in high-dimensional settings, our method is shown to have superior prediction performance and interpretability when there are potential subpopulations in the data. The computer code of the proposed method is available as supplemental materials.