Bidirectional Semi-supervised Learning with Graphs

We present a machine learning task, which we call bidirectional semi-supervised learning, where label-only samples are given as well as labeled and unlabeled samples. A label-only sample contains the label information of the sample but not the feature information. Then, we propose a simple and effective graph-based method for bidirectional semisupervised learning in multi-label classification. The proposed method assumes that correlated classes are likely to have the same labels among the similar samples. First, we construct a graph that represents similarities between samples using labeled and unlabeled samples in the same way with graph-based semi-supervised methods. Second, we construct another graph using labeled and label-only samples by connecting classes that are likely to co-occur, which represents correlations between classes. Then, we estimate labels of unlabeled samples by propagating labels over these two graphs. We can find a closed-form global solution for the label propagation by using matrix algebra. We demonstrate the effectiveness of the proposed method over supervised and semi-supervised learning methods with experiments using synthetic and multi-label text data sets.