Multi-Label Learning with Weak Label

Multi-label learning deals with data associated with multiple labels simultaneously. Previous work on multi-label learning assumes that for each instance, the “full” label set associated with each training instance is given by users. In many applications, however, to get the full label set for each instance is difficult and only a “partial” set of labels is available. In such cases, the appearance of a label means that the instance is associated with this label, while the absence of a label does not imply that this label is not proper for the instance. We call this kind of problem “weak label” problem. In this paper, we propose the WELL (WEak Label Learning) method to solve the weak label problem. We consider that the classification boundary for each label should go across low density regions, and that each label generally has much smaller number of positive examples than negative examples. The objective is formulated as a convex optimization problem which can be solved efficiently. Moreover, we exploit the correlation between labels by assuming that there is a group of low-rank base similarities, and the appropriate similarities between instances for different labels can be derived from these base similarities. Experiments validate the performance of WELL.