This work focuses on the problem of multi-label learning with missing labels (MLML), which aims to label each test instance with multiple class labels given training instances that have an incomplete/partial set of these labels (i.e. some of their labels are missing). To handle missing labels, we propose a unified model of label dependencies by constructing a mixed graph, which jointly incorporates (i) instance-level similarity and class co-occurrence as undirected edges and (ii) semantic label hierarchy as directed edges. Unlike most MLML methods, We formulate this learning problem transductively as a convex quadratic matrix optimization problem that encourages training label consistency and encodes both types of label dependencies (i.e. undirected and directed edges) using quadratic terms and hard linear constraints. The alternating direction method of multipliers (ADMM) can be used to exactly and efficiently solve this problem. To evaluate our proposed method, we consider two popular applications (image and video annotation), where the label hierarchy can be derived from Wordnet. Experimental results show that our method achieves a significant improvement over state-of-the-art methods in performance and robustness to missing labels.
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