Geodesic Multi-Class SVM with Stiefel Manifold Embedding

Abstract

Manifold of geodesic plays an essential role in characterizing the intrinsic data geometry. However, the existing SVM methods have largely neglected the manifold structure. As such, functional degeneration may occur due to the potential polluted training. Even worse, the entire SVM model might collapse in the presence of excessive training contamination. To address these issues, this paper devises a manifold SVM method based on a novel ξ -measure geodesic, whose primary design objective is to extract and preserve the data manifold structure in the presence of training noises. To further cope with overly contaminated training data, we introduce Kullback-Leibler (KL) regularization with steerable sparsity constraint. In this way, each loss weight is adaptively obtained by obeying the prior distribution and sparse activation during model training for robust fitting. Moreover, the optimal scale for Stiefel manifold can be automatically learned to improve the model flexibility. Accordingly, extensive experiments verify and validate the superiority of the proposed method.