Robust Eigenvector of a Stochastic Matrix with Application to PageRank

TL;DR

This paper introduces a robust eigenvector approach for stochastic matrices, offering a convex optimization-based method as a more resilient alternative to PageRank, along with a practical approximation algorithm.

Contribution

It presents a new robust eigenvector definition, formulates it as a convex optimization problem, and proposes an efficient approximation algorithm for ranking applications.

Findings

The robust eigenvector approach enhances ranking stability.

The convex optimization formulation enables reliable computation.

The proposed algorithm is simple and effective for practical use.

Abstract

We discuss a definition of robust dominant eigenvector of a family of stochastic matrices. Our focus is on application to ranking problems, where the proposed approach can be seen as a robust alternative to the standard PageRank technique. The robust eigenvector computation is reduced to a convex optimization problem. We also propose a simple algorithm for robust eigenvector approximation which can be viewed as a regularized power method with a special stopping rule.