Multi-label learning focuses on the ambiguity at the label side, i.e., one instance is associated with multiple class labels, where the logical labels are always adopted to partition class labels into relevant labels and irrelevant labels rigidly. However, the relevance or irrelevance of each label corresponding to one instance is essentially relative in real-world tasks and the label distribution is more fine-grained than the logical labels by denoting one instance with a certain number of the description degrees of all class labels. As the label distribution is not explicitly available in most training sets, a process named label enhancement emerges to recover the label distributions in training datasets. By inducing the generative model of the label distribution and adopting the variational inference technique, the approximate posterior density of the label distributions should maximize the variational lower bound. Following the above consideration, LEVI is proposed to recover the label distributions from the training examples. In addition, the multi-label predictive model is induced for multi-label learning by leveraging the recovered label distributions along with a specialized objective function. The recovery experiments on fourteen label distribution datasets and the predictive experiments on fourteen multi-label learning datasets validate the advantage of our approach over the state-of-the-art approaches.

While most existing multilabel ranking methods assume the availability of a single objective label ranking for each instance in the training set, this paper deals with a more common case where only subjective inconsistent rankings from multiple rankers are associated with each instance. Two ranking methods are proposed from the perspective of instances and rankers, respectively. The first method, Instance-oriented Preference Distribution Learning (IPDL), is to learn a latent preference distribution for each instance. IPDL generates a common preference distribution that is most compatible to all the personal rankings, and then learns a mapping from the instances to the preference distributions. The second method, Ranker-oriented Preference Distribution Learning (RPDL), is proposed by leveraging interpersonal inconsistency among rankers, to learn a unified model from personal preference distribution models of all rankers. These two methods are applied to natural scene images dataset and 3D facial expression dataset BU_3DFE. Experimental results show that IPDL and RPDL can effectively incorporate the information given by the inconsistent rankers, and perform remarkably better than the compared state-of-the-art multilabel ranking algorithms.

Weakly supervised multi-label learning (WSML) concentrates on a more challenging multi-label classification problem, where some labels in the training set are missing. Existing approaches make multi-label prediction by exploiting the incomplete logical labels directly without considering the relative importance of each label to an instance. In this paper, a novel two-stage strategy named Weakly Supervised Multi-label Learning via Label Enhancement (WSMLLE) is proposed to learn from weakly supervised data via label enhancement. Firstly, the relative importance of each label, i.e., the description degrees are recovered by leveraging the structural information in the feature space and local correlations learned from the label space. Then, a tailored multi-label predictive model is induced by learning from the training instances with the recovered description degrees. To our best knowledge, it is the first attempt to unify the complement of the missing labels and the recovery of the description degrees into the same framework. Extensive experiments across a wide range of real-world datasets clearly validate the superiority of the proposed approach.