Multi-class semi-supervised SVMs with Positiveness Exclusive Regularization

In this work, we address the problem of multi-class classification problem in semi-supervised setting. A regularized multi-task learning approach is presented to train multiple binary-class Semi-Supervised Support Vector Machines (S3VMs) using the one-vs-rest strategy within a joint framework. A novel type of regularization, namely Positiveness Exclusive Regularization (PER), is introduced to induce the following prior: if an unlabeled sample receives significant positive response from one of the classifiers, it is less likely for this sample to receive positive responses from the other classifiers. That is, we expect an exclusive relationship among different S3VMs for evaluating the same unlabeled sample. We propose to use an ℓ1,2-norm regularizer as an implementation of PER. The objective of our approach is to minimize an empirical risk regularized by a PER term and a manifold regularization term. An efficient Nesterov-type smoothing approximation based method is developed for optimization. Evaluations with comparisons are conducted on several benchmarks for visual classification to demonstrate the advantages of the proposed method.