Graph and Manifold Co-regularization

Classical foundations of Statistical Learning Theory rely on the assumption that the input patterns are independently and identically distributed. However, in many applications, the inputs, represented as feature vectors, are also embedded into a network of pair wise relations. Transductive approaches like graph regularization rely on the network topology without considering the feature vectors. Semi-supervised approaches like Manifold Regularization learn a function taking the feature vectors as input, while being smooth over the network connections. In this latter case, the connectivity information is processed at training time, but is still neglected during generalization, as the final classification decision takes only the feature vector representations as input. This paper presents and evaluates a model merging the advantages of graph regularization and kernel machines for transductive classification problems.