Multi-label learning refers to the problems where an instance can be assigned to more than one category. In this paper, we present a novel Semi-supervised algorithm for Multi-label learning by solving a Sylvester Equation (SMSE). Two graphs are first constructed on instance level and category level respectively. For instance level, a graph is defined based on both labeled and unlabeled instances, where each node represents one instance and each edge weight reflects the similarity between corresponding pairwise instances. Similarly, for category level, a graph is also built based on all the categories, where each node represents one category and each edge weight reflects the similarity between corresponding pairwise categories. A regularization framework combining two regularization terms for the two graphs is suggested. The regularization term for instance graph measures the smoothness of the labels of instances, and the regularization term for category graph measures the smoothness of the labels of categories. We show that the labels of unlabeled data finally can be obtained by solving a Sylvester Equation. Experiments on RCV1 data set show that SMSE can make full use of the unlabeled data information as well as the correlations among categories and achieve good performance. In addition, we give a SMSE's extended application on collaborative filtering. Multi-label learning, Graph-based semi-supervised learning, Sylvester equation, Collaborative filtering 1 Introduction Many learning problems require each instance to be assigned to multiple different categories, which are generally called multi-label learning problems. Multi-label learning problems arise in many practical applications such as automatic image annotation and text categorization. For example, in automatic image annotation,
Chen et al. REF presented a graph regularized semi-supervised multi-label learning method that make use of input similarity matrix and category similarity matrix that captures the correlation information between the labels.
Semi-supervised Multi-label Learning by Solving a Sylvester Equation
SDM
Computer Science