Adaptive Pair-Weight Vector Projection Classifier for Semi-Supervised Classification

Manifold regularization is a popular technology based on graph theory and has been widely applied to nonparallel hyperplane classifiers for semi-supervised learning. However, these classifiers adopt the fixed similarity matrix that may be sensitive to noises and outliers. Thus, we propose a novel nonparallel hyperplane classifier, named the adaptive pair-weight vector projection (APVP) classifier, for semi-supervised classification tasks. The proposed APVP unifies projection learning and graph construction into a general framework. For projection learning, APVP achieves two projection vectors by solving the pair-wise optimization problems in which we need to simultaneously maximize the between-class scatter of data and minimize both the within-class scatter of data and the adaptive manifold regularization. For graph construction, the adaptive similarity matrix is constructed during the procedure of optimization. Thus, APVP can weaken the effect of noises and outliers by the adaptive similarity matrix and strengthen the discriminant capability by the Fisher criterion. To classify unseen data, we also design a new classification rule. Experimental results show that APVP has good performance in semi-supervised scene.