Practical acceleration for computing the HITS ExpertRank vectors

A meaningful rank as well as efficient methods for computing such a rank are necessary in many areas of applications. Major methodologies for ranking often exploit principal eigenvectors. Kleinberg's HITS model is one of such methodologies. The standard approach for computing the HITS rank is the power method. Unlike the PageRank calculations where many acceleration schemes have been proposed, relatively few works on accelerating HITS rank calculation exist. This is mainly because the power method often works quite well in the HITS setting. However, there are cases where the power method is ineffective, moreover, a systematic acceleration over the power method is desirable even when the power method works well. We propose a practical acceleration scheme for HITS rank calculations based on the filtered power method by adaptive Chebyshev polynomials. For cases where the gap-ratio is below 0.85 for which the power method works well, our scheme is about twice faster than the power method. For cases where gap-ratio is unfavorable for the power method, our scheme can provide significant speedup. When the ranking problems are of very large scale, even a single matrix-vector product can be expensive, for which accelerations are highly necessary. The scheme we propose is desirable in that it provides consistent reduction in number of matrix-vector products as well as CPU time over the power method, with little memory overhead.