Distributed online semi-supervised support vector machine

Recently, the research on semi-supervised support vector machine ((SVM)-V-3) has received much attention, and many (SVM)-V-3 algorithms have been proposed. Existing studies have shown that (SVM)-V-3 is effective especially in the situations where labeled data is scarce. Nevertheless, most of existing (SVM)-V-3 algorithms belong to centralized learning, that is, all the data is stored and processed at a fusion center. In many real-world applications, data may be horizontally or vertically distributed over multiple nodes (parties). Besides, from the concerns of privacy and security, each node would not like to share its original data with the others. On the other hand, considering that the data is usually sequentially generated, online processing is preferred. In this paper, we propose two online distributed (SVM)-V-3 (dS(3)VM) algorithms, which are respectively used for horizontally and vertically partitioned data classification. In these two algorithms, to get a fully decentralized implementation, we propose a new form of manifold regularization defined on some anchor points that are adaptively selected by an online strategy. Besides, we use the sparse random feature map to approximate the kernel feature map. In this manner, the model parameters can be collaboratively estimated without transmitting the original data between neighbors. The convergence performances of the proposed algorithms are analyzed. Simulations on several data sets are performed. Results show that the proposed dS(3)VM algorithms achieve good classification performance even when there is only a small portion of labeled data. (C) 2018 Elsevier Inc. All rights reserved.