Ranking on graph data

In ranking, one is given examples of order relationships among objects, and the goal is to learn from these examples a real-valued ranking function that induces a ranking or ordering over the object space. We consider the problem of learning such a ranking function when the data is represented as a graph, in which vertices correspond to objects and edges encode similarities between objects. Building on recent developments in regularization theory for graphs and corresponding Laplacian-based methods for classification, we develop an algorithmic framework for learning ranking functions on graph data. We provide generalization guarantees for our algorithms via recent results based on the notion of algorithmic stability, and give experimental evidence of the potential benefits of our framework.