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In the recent years there has been a surge of research activity in the area of information retrieval on the World Wide Web, using link analysis of the underlying hypertext graph topology. Most of the algorithms in the literature can be described as dynamical systems, that is, the repetitive application of a function on a set of weights. Algorithms that rely on eigenvector computations, such as HITS and PAGERANK, correspond to linear dynamical systems. In this work we consider two families of link analysis ranking algorithms that no longer enjoy the linearity property of the previous approaches. We study in depth an interesting special case of these two families. We prove that the corresponding non-linear dynamical system converges for any initialization, and we provide a rigorous characterization of the combinatorial properties of the stationary weights. The study of the weights provides a clear and insightful view of the mechanics of the algorithm. We also present extensive experimental results that demonstrate that our algorithm performs well in practice.

Using non-linear dynamical systems for web searching and ranking