Abstract. We consider the problem of labeling a partially labeled graph. This setting may arise in a number of situations from survey sampling to information retrieval to pattern recognition in manifold settings. It is also of potential practical importance, when the data is abundant, but labeling is expensive or requires human assistance. Our approach develops a framework for regularization on such graphs. The algorithms are very simple and involve solving a single, usually sparse, system of linear equations. Using the notion of algorithmic stability, we derive bounds on the generalization error and relate it to structural invariants of the graph. Some experimental results testing the performance of the regularization algorithm and the usefulness of the generalization bound are presented. 1

A modified version for semi-supervised learning algorithm with local and global consistency was proposed in this paper. The new method adds the label information, and adopts the geodesic distance rather than Euclidean distance as the measure of the difference between two data points when conducting calculation. In addition we add class prior knowledge. It was found that the effect of class prior knowledge was different between under high label rate and low label rate. The experimental results show that the changes attain the satisfying classification performance better than the original algorithms. 1.