LAUSR

In this paper we study multi-label learning with weakly labeled data, i.e., labels of training examples are incomplete, which commonly occurs in real applications, e.g., image classification, document categorization. This setting includes, e.g., (i) semi-supervised multi-label learning where completely labeled examples are partially known; (ii) weak label learning where relevant labels of examples are partially known; (iii) extended weak label learning where relevant and irrelevant labels of examples are partially known. Previous studies often expect that the learning method with the use of weakly labeled data will improve the performance, as more data are employed. This, however, is not always the cases in reality, i.e., weakly labeled data may sometimes degenerate the learning performance. It is desirable to learn safe multi-label prediction that will not hurt performance when weakly labeled data is involved in the learning procedure. In this work we optimize multi-label evaluation metrics ($$\hbox {F}_1$$F1 score and Top-k precision) given that the ground-truth label assignment is realized by a convex combination of base multi-label learners. To cope with the infinite number of possible ground-truth label assignments, cutting-plane strategy is adopted to iteratively generate the most helpful label assignments. The whole optimization is cast as a series of simple linear programs in an efficient manner. Extensive experiments on three weakly labeled learning tasks, namely, (i) semi-supervised multi-label learning; (ii) weak label learning and (iii) extended weak label learning, clearly show that our proposal improves the safeness of using weakly labeled data compared with many state-of-the-art methods.