Flexible multi-view semi-supervised learning with unified graph

At present, the diversity of data acquisition boosts the growth of multi-view data and the lack of label information. Since manually labeling is expensive and impractical, it is practical to enhance learning performance with a small amount of labeled data and a large amount of unlabeled data. In this study, we propose a novel multi-view semi-supervised learning (MSEL) framework termed flexible MSEL (FMSEL) with unified graph. In this framework, two flexible regression residual terms are introduced. One is a linear penalty term, which adaptively weighs the diverse contributions of different views and properly learns a well structured unified graph. The other is a relaxation regularization term, which finds the optimal prediction and the linear regression function. Both the prediction of samples in the database and new-coming data are supported. Moreover, during the process, the unified graph learns depending on the data structure and dynamically updated label information. Further, we provide an alternating optimization algorithm to iteratively solve the resultant objective problem and theoretically analyze the corresponding complexities. Extensive experiments conducted on synthetic and public datasets demonstrate the superiority of FMSEL.