 
Summary: Mach Learn (2010) 81: 333357
DOI 10.1007/s1099401051858
Learning to rank on graphs
Shivani Agarwal
Received: 31 July 2008 / Revised: 27 December 2009 / Accepted: 28 March 2010 /
Published online: 29 May 2010
© The Author(s) 2010
Abstract Graph representations of data are increasingly common. Such representations
arise in a variety of applications, including computational biology, social network analysis,
web applications, and many others. There has been much work in recent years on developing
learning algorithms for such graph data; in particular, graph learning algorithms have been
developed for both classification and regression on graphs. Here we consider graph learning
problems in which the goal is not to predict labels of objects in a graph, but rather to rank
the objects relative to one another; for example, one may want to rank genes in a biological
network by relevance to a disease, or customers in a social network by their likelihood of
being interested in a certain product. We develop algorithms for such problems of learning
to rank on graphs. Our algorithms build on the graph regularization ideas developed in the
context of other graph learning problems, and learn a ranking function in a reproducing ker
nel Hilbert space (RKHS) derived from the graph. This allows us to show attractive stability
and generalization properties. Experiments on several graph ranking tasks in computational
