Frustrated Random Walks: A Faster Algorithm to Evaluate Node Distances on Connected and Undirected Graphs

TL;DR

This paper introduces a faster algorithm for evaluating node distances in large connected, undirected graphs, significantly outperforming existing methods like DeepWalk through an analytical approach to expected hitting times.

Contribution

The paper presents an improved random walk-based algorithm with an analytical formula for quick expected hitting time calculation, reducing computation time over prior methods.

Findings

Achieves over ten times acceleration compared to DeepWalk

Robust results with respect to the parameter choice

Applicable to large-scale graph analysis tasks

Abstract

Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are, still they are either underperforming or too time-consuming to be applicable to huge graphs that we encounter daily in this big data era. To address these issues, here we propose a faster algorithm based on an improved version of random walks that can beat DeepWalk results with more than ten times acceleration. The reason for this significant acceleration is that we can derive an analytical formula to calculate the expected hitting times of this random walk quickly. There is only one parameter (the power expansion order) in our algorithm, and the results are robust with respect to its changes. Therefore, we can directly find the optimal solution without fine-tuning of model parameters. Our method can be widely used for fraud detection, targeted ads, recommendation systems, topic-sensitive search, etc.