Transductive Classification via Dual Regularization

Semi-supervised learning has witnessed increasing interest in the past decade. One common assumption behind semi-supervised learning is that the data labels should be sufficiently smooth with respect to the intrinsic data manifold. Recent research has shown that the features also lie on a manifold. Moreover, there is a duality between data points and features, that is, data points can be classified based on their distribution on features, while features can be classified based on their distribution on the data points. However, existing semi-supervised learning methods neglect these points. Based on the above observations, in this paper, we present a dual regularization, which consists of two graph regularizers and a co-clustering type regularizer. In detail, the two graph regularizers consider the geometric structure of the data points and the features respectively, while the co-clustering type regularizer takes into account the duality between data points and features. Furthermore, we propose a novel transductive classification framework based on dual regularization, which can be solved by alternating minimization algorithm and its convergence is theoretically guaranteed. Experiments on benchmark semi-supervised learning data sets demonstrate that the proposed methods outperform many state of the art transductive classification methods.