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Label-specific features learning is a multi-label learning framework that utilizes label feature extraction to solve a single example where multiple class labels exist simultaneously. As an essential multi-label learning method, label correlation learning has been widely used in multi-label classification learning. However, in the existing label-specific features learning, the label correlation measurement often assumes that the label correlations are a global structure or that the label correlations only have a local smoothness. In actual application scenarios, the two situations may occur together. This paper proposes a multi-label classification method by joint Label-Specific features and Global and Local label correlation learning, named LSGL. Firstly, we obtain the weight of the label-specific features of each class label utilizing the l 1 -norm and then learn high-order global label correlation and label local smoothness. By adding manifold regularization terms, we fully utilize the structural relationship between features and labels and mine global and local label association information. These processes are carried out in a unified optimization model, and each part learns and promotes each other. Finally, in the low-dimensional label-specific features representation learning is to carry out multi-label classification learning through the support vector machine and the extreme learning machine, respectively. A comparative study with state-of-the-art approaches and statistical hypothesis testing manifests the validity of the LSGL method and the features learned from label-specific features learning. [ABSTRACT FROM AUTHOR]