Adaptive semi-supervised learning with discriminative least squares regression

Semi-supervised learning plays a significant role in multi-class classification, where a small number of labeled data are more deterministic while substantial unlabeled data might cause large uncertainties and potential threats. In this paper, we distinguish the label fitting of labeled and unlabeled training data through a probabilistic vector with an adaptive parameter, which always ensures the significant importance of labeled data and characterizes the contribution of unlabeled instance according to its uncertainty. Instead of using traditional least squares regression (LSR) for classification, we develop a new discriminative LSR by equipping each label with an adjustment vector. This strategy avoids incorrect penalization on samples that are far away from the boundary and simultaneously facilitates multi-class classification by enlarging the geometrical distance of instances belonging to different classes. An efficient alternative algorithm is exploited to solve the proposed model with closed form solution for each updating rule. We also analyze the convergence and complexity of the proposed algorithm theoretically. Experimental results on several benchmark datasets demonstrate the effectiveness and superiority of the proposed model for multi-class classification tasks.