Manifold regularized matrix completion for multilabel classification

• Exploring the correlation among different labels via low rank minimization.
• Leveraging the requirement of large amount of training data via manifold regularization.
• Completing the missing labels via matrix completion automatically.

Multilabel learning is an important research problem arising in a number of practical applications from diverse fields. Recent studies on multilabel learning have suggested the approach of matrix completion as a novel and promising approach to transductive multilabel learning. Here the missing labels of test data are regarded as missing values from the construction matrix composed of feature-by-item and label-by-item matrices. With the assumption of the low rank of the construction matrix, by minimizing its rank under the constraints of observed data and labels, we can recover all the missing labels. Despite its success, however, naive matrix completion methods ignore the smoothness assumption of the large amount of unlabel data, i.e., similar data should share similar labels, which may under exploit the intrinsic structure of data. To this end, we propose to solve the multi-label learning problem as an enhanced matrix completion problem with manifold regularization, where the graph Laplacian is used to ensuring the label smoothness over the label space. The resulting nuclear norm minimization problem is solved with a modified fixed-point continuation method that is guaranteed to find the global optimum. Experiments on both synthetic and real-world data have shown the promising results of the proposed approach.