Abstract: Multi-label learning deals with the problems when each object can be assigned to multiple categories simultaneously, which is ubiquitous in many real world applications, such as text classification, image scene classification and bioinformatics, etc. In traditional multi-label learning methods, classifiers are usually required to utilize a large amount of fully labeled training data in order to obtain good performances for multi-label classifications. However, in many real world tasks, obtaining partially labeled (weak labeled) training data is often much easier and costs less efforts than obtaining a large amount of fully labeled training data. To alleviate the assumption of large amount fully labeled training data used by traditional multi-label learning methods, the authors propose a new multi-label learning method for weak labeling (TML-WL). By reweighting the error functions on positive and negative labels of weak labeled data, TML-WL method can effectively utilize the weak labeled training data to replenish the missing labels. TML-WL method can also use the weak labeled training data to improve the classification performances on unlabeled data. Empirical studies on the real-world application of image scene classification show that the proposed method can significantly improve the performance of multi-label learning when the training data are weak labeled.