Multi-View Semi-Supervised Label Distribution Learning with Local Structure Complementarity

Label distribution learning (LDL) is a paradigm that each sample is associated with a label distribution. At present, the existing approaches are proposed for the single-view LDL problem with labeled data, while the multi-view LDL problem with labeled and unlabeled data has not been considered. In this paper, we put forward the multi-view semi-supervised label distribution learning with local structure complementarity (MVSS-LDL) approach, which exploits the local nearest neighbor structure of each view and emphasizes the complementarity of local nearest neighbor structures in multiple views. Specifically speaking, we first explore the local structure of view $v$ by computing the $k$-nearest neighbors. As a result, the $k$-nearest neighbor set of each sample $\boldsymbol{x}_i$ in view $v$ is attained. Nevertheless, this $k$-nearest neighbor set describes only a part of the nearest neighbor information of sample $\boldsymbol{x}_i$. In order to obtain a more comprehensive description of sample $\boldsymbol{x}_i$'s nearest neighbors, we complement the nearest neighbor set in view $v$ by incorporating sample $\boldsymbol{x}_i$'s nearest neighbors in other views. Lastly, based on the complemented nearest neighbor set in each view, a graph learning-based multi-view semi-supervised LDL model is constructed. By considering the complementarity of local nearest neighbor structures, different views can mutually provide the local structural information to complement each other. To the best of our knowledge, this is the first attempt at multi-view LDL. Numerical studies have demonstrated that MVSS-LDL attains explicitly better classification performance than the existing single-view LDL methods.