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Multi-label image classification, which can be categorized into label-dependency and region-based methods, is a challenging problem due to the complex underlying object layouts. Although region-based methods are less likely to encounter issues with model generalizability than label-dependency methods, they often generate hundreds of meaningless or noisy proposals with non-discriminative information, and the contextual dependency among the localized regions is often ignored or over-simplified. This paper builds a unified framework to perform effective noisy-proposal suppression and to interact between global and local features for robust feature learning. Specifically, we propose category-aware weak supervision to concentrate on non-existent categories so as to provide deterministic information for local feature learning, restricting the local branch to focus on more high-quality regions of interest. Moreover, we develop a cross-granularity attention module to explore the complementary information between global and local features, which can build the high-order feature correlation containing not only global-to-local, but also local-to-local relations. Both advantages guarantee a boost in the performance of the whole network. Extensive experiments on two large-scale datasets (MS-COCO and VOC 2007) demonstrate that our framework achieves superior performance over state-of-the-art methods.