Higher-Order Web Link Analysis Using Multilinear Algebra

Abstract

Linear algebra is a powerful and proven tool in Web search. Techniques, such as the PageRank algorithm of Brin and Page and the HITS algorithm of Kleinberg, score Web pages based on the principal eigenvector (or singular vector) of a particular non-negative matrix that captures the hyperlink structure of the Web graph. We propose and test a new methodology that uses multilinear algebra to elicit more information from a higher-order representation of the hyperlink graph. We start by labeling the edges in our graph with the anchor text of the hyperlinks so that the associated linear algebra representation is a sparse, three-way tensor. The first two dimensions of the tensor represent the Web pages while the third dimension adds the anchor text. We then use the rank-1 factors of a multilinear PARAFAC tensor decomposition, which are akin to singular vectors of the SVD, to automatically identify topics in the collection along with the associated authoritative Web pages.