Graph-regularized semi-supervised learning has been used effectively for classification when (i) instances are connected through a graph, and (ii) labeled data is scarce. If available, using multiple relations (or graphs) between the instances can improve the prediction performance. On the other hand, when these relations have varying levels of veracity and exhibit varying relevance for the task, very noisy and or irrelevant relations may deteriorate the performance. As a result, an effective weighing scheme needs to be put in place. In this work, we propose a robust and scalable approach for multi-relational graph-regularized semi-supervised classification. Under a convex optimization scheme, we simultaneously infer weights for the multiple graphs as well as a solution. We provide a careful analysis of the inferred weights, based on which we devise an algorithm that filters out irrelevant and noisy graphs and produces weights proportional to the informativeness of the remaining graphs. Moreover, the proposed method is linearly scalable w.r.t. the number of edges in the union of the multiple graphs. Through extensive experiments we show that our method yields superior results under different noise models, and under increasing number of noisy graphs and intensity of noise, as compared to a list of baselines and state-of-the-art approaches.
A number of real-world networks are heterogeneous information networks, which are composed of different types of nodes and links. Numerical prediction in heterogeneous information networks is a challenging but significant area because network based information for unlabeled objects is usually limited to make precise estimations. In this paper, we consider a graph regularized meta-path based transductive regression model (Grempt), which combines the principal philosophies of typical graph-based transductive classification methods and transductive regression models designed for homogeneous networks. The computation of our method is time and space efficient and the precision of our model can be verified by numerical experiments. Transductive inference on graphs such as label propagation algorithms is receiving a lot of attention. In this paper, we address a label propagation problem on multiple networks and present a new algorithm that automatically integrates structure information brought in by multiple networks. The proposed method is robust in that irrelevant networks are automatically deemphasized, which is an advantage over Tsuda's approach (2005). We also show that the proposed algorithm can be interpreted as an expectation-maximization (EM) algorithm with a student-t prior. Finally, we demonstrate the usefulness of our method in protein function prediction and digit classification, and show analytically and experimentally that our algorithm is much more efficient than existing algorithms. 