Towards a probabilistic semi-supervised Kernel Minimum Squared Error algorithm

Recently, semi-supervised learning has received much attention in data mining and machine learning, and a number of algorithms are proposed to discuss how to make good use of the unlabeled data. Some algorithms deal with the unlabeled data in an exact way, in which each unlabeled sample is assigned to one single class and then treated as a labeled sample. Other algorithms use the unlabeled data to regularize the objective function but do not explicitly model the influence of the unlabeled data towards different classes. In many applications, however, the unlabeled data may be ambiguous and belong to multiple classes with different probabilities. Based on this assumption, this paper presents a Probabilistic Laplacian-regularized Kernel Minimum Squared Error algorithm (named PrLapKMSE), in which the probabilities of the unlabeled data belonging to different classes are adaptively generated. “Adaptively” means that these probabilities are recalculated iteratively along with the reformulated objective function so that the unlabeled data may have increasingly accurate effects on the semi-supervised learning procedure. Experimental results on several simulated and real-world datasets illustrate the effectiveness of our algorithm.