Multi-label learning is more complicated than single-label learning since the semantics of the instances are usually overlapped and not identical. The effectiveness of many algorithms often fails when the correlations in the feature and label space are not fully exploited. To this end, we propose a novel non-negative matrix factorization (NMF) based modeling and training algorithm that learns from both the adjacencies of the instances and the labels of the training set. In the modeling process, a set of generators are constructed, and the associations among generators, instances, and labels are set up, with which the label prediction is conducted. In the training process, the parameters involved in the process of modeling are determined. Specifically, an NMF based algorithm is proposed to determine the associations between generators and instances, and a non-negative least square optimization algorithm is applied to determine the associations between generators and labels. The proposed algorithm fully takes the advantage of smoothness assumption, so that the labels are properly propagated. The experimentswere carried out on six set of benchmarks. The results demonstrate the effectiveness of the proposed algorithms.
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