Manifold regularization for structured outputs via the joint kernel

By utilizing the label dependencies among both the labeled and unlabeled data, semi-supervised learning often has better generalization performance than supervised learning. In this paper, we extend a popular graph-based semi-supervised learning method, namely, manifold regularization, to structured outputs. This is performed via the joint kernel directly and allows a unified manifold regularization framework for both unstructured and structured data. Experimental results on various data sets with inter-dependent outputs demonstrate the usefulness of manifold information in improving prediction performance.