Semi-supervised multiple empirical kernel learning with pseudo empirical loss and similarity regularization

Multiple empirical kernel learning (MEKL) is a scalable and efficient supervised algorithm based on labeled samples. However, there is still a huge amount of unlabeled samples in the real-world application, which are not applicable for the supervised algorithm. To fully utilize the spatial distribution information of the unlabeled samples, this paper proposes a novel semi-supervised multiple empirical kernel learning (SSMEKL). SSMEKL enables multiple empirical kernel learning to achieve better classification performance with a small number of labeled samples and a large number of unlabeled samples. First, SSMEKL uses the collaborative information of multiple kernels to provide a pseudo labels to some unlabeled samples in the optimization process of the model, and SSMEKL designs pseudo-empirical loss to transform learning process of the unlabeled samples into supervised learning. Second, SSMEKL designs the similarity regularization for unlabeled samples to make full use of the spatial information of unlabeled samples. It is required that the output of unlabeled samples should be similar to the neighboring labeled samples to improve the classification performance of the model. The proposed SSMEKL can improve the performance of the classifier by using a small number of labeled samples and numerous unlabeled samples to improve the classification performance of MEKL. In the experiment, the results on four real-world data sets and two multiview data sets validate the effectiveness and superiority of the proposed SSMEKL.