Adjusting PageRank parameters and Comparing results

TL;DR

This paper investigates how adjusting damping factor and tolerance affects PageRank computation efficiency, comparing convergence norms and ratios, revealing key relationships and optimal configurations for large graphs.

Contribution

It provides a detailed analysis of the impact of damping factor and tolerance adjustments on PageRank convergence speed and stability across different norms and mean ratios.

Findings

Increasing damping factor linearly increases iterations needed.

Decreasing tolerance exponentially decreases iterations needed.

L-infinity norm yields the fastest convergence.

Abstract

The effect of adjusting damping factor {\alpha} and tolerance {\tau} on iterations needed for PageRank computation is studied here. Relative performance of PageRank computation with L1, L2, and L{\infty} norms used as convergence check, are also compared with six possible mean ratios. It is observed that increasing the damping factor {\alpha} linearly increases the iterations needed almost exponentially. On the other hand, decreasing the tolerance {\tau} exponentially decreases the iterations needed almost exponentially. On average, PageRank with L{\infty} norm as convergence check is the fastest, quickly followed by L2 norm, and then L1 norm. For large graphs, above certain tolerance {\tau} values, convergence can occur in a single iteration. On the contrary, below certain tolerance {\tau} values, sensitivity issues can begin to appear, causing computation to halt at maximum iteration limit without convergence. The six mean ratios for relative performance comparison are based on arithmetic, geometric, and harmonic mean, as well as the order of ratio calculation. Among them GM-RATIO, geometric mean followed by ratio calculation, is found to be most stable, followed by AM-RATIO.