Perron-based algorithms for the multilinear pagerank
For researchers working on tensor-based ranking and network analysis, this provides more robust numerical methods for multilinear PageRank, though the improvement is incremental.
The authors prove properties of multilinear PageRank solutions, including existence of a minimal solution, and develop new fixed-point algorithms with homotopy continuation that solve more problems reliably than existing methods.
We consider the multilinear pagerank problem studied in [Gleich, Lim and Yu, Multilinear Pagerank, 2015], which is a system of quadratic equations with stochasticity and nonnegativity constraints. We use the theory of quadratic vector equations to prove several properties of its solutions and suggest new numerical algorithms. In particular, we prove the existence of a certain minimal solution, which does not always coincide with the stochastic one that is required by the problem. We use an interpretation of the solution as a Perron eigenvector to devise new fixed-point algorithms for its computation, and pair them with a homotopy continuation strategy. The resulting numerical method is more reliable than the existing alternatives, being able to solve a larger number of problems.