Online Prediction on Large Diameter Graphs
Mark Herbster, Guy Lever and Massimiliano Pontil
In: NIPS 2008, 8-11 Dec 2008, Vancouver, Canada.
We continue our study of online prediction of the labelling of a graph. We show a
fundamental limitation of Laplacian-based algorithms: if the graph has a large diameter then the number of mistakes made by such algorithms may be proportional
to the square root of the number of vertices, even when tackling simple problems.
We overcome this drawback by means of an efficient algorithm which achieves
a logarithmic mistake bound. It is based on the notion of a spine, a path graph
which provides a linear embedding of the original graph. In practice, graphs may
exhibit cluster structure; thus in the last part, we present a modified algorithm
which achieves the “best of both worlds”: it performs well locally in the presence
of cluster structure, and globally on large diameter graphs.