Learning The Optimal Discriminant SVM with Feature Extraction

Subspace learning and Support Vector Machine (SVM) are two critical techniques in pattern recognition, playing pivotal roles in feature extraction and classification. However, how to learn the optimal subspace such that the SVM classifier can perform the best is still a challenging problem due to the difficulty in optimization, computation, and algorithm convergence. To address these problems, this paper develops a novel method named Optimal Discriminant Support Vector Machine (ODSVM), which integrates support vector classification with discriminative subspace learning in a seamless framework. As a result, the most discriminative subspace and the corresponding optimal SVM are obtained simultaneously to pursue the best classification performance. The efficient optimization framework is designed for binary and multi-class ODSVM. Moreover, a fast sequential minimization optimization (SMO) algorithm with pruning is proposed to accelerate the computation in multi-class ODSVM. Unlike other related methods, ODSVM has a strong theoretical guarantee of global convergence, highlighting its superiority and stability. Numerical experiments are conducted on thirteen datasets and the results demonstrate that ODSVM outperforms existing methods with statistical significance.