[Paper Review] Supervised and Extended Restart in Random Walks for Ranking and Link Prediction in Networks

Woojeong Jin, Jinhong Jung+1 more|arXiv (Cornell University)|Oct 18, 2017

Complex Network Analysis Techniques24 references3 citations

TL;DR

This paper proposes Random Walk with Extended Restart (RWER), a personalized relevance scoring method that assigns unique restart probabilities to each node to enhance expressiveness in ranking and link prediction. It introduces SuRe, a supervised learning algorithm that automatically learns optimal restart probabilities from data, achieving up to 15.8% higher MAP than the best competitor in link prediction tasks.

ABSTRACT

Given a real-world graph, how can we measure relevance scores for ranking and link prediction? Random walk with restart (RWR) provides an excellent measure for this and has been applied to various applications such as friend recommendation, community detection, anomaly detection, etc. However, RWR suffers from two problems: 1) using the same restart probability for all the nodes limits the expressiveness of random walk, and 2) the restart probability needs to be manually chosen for each application without theoretical justification. We have two main contributions in this paper. First, we propose Random Walk with Extended Restart (RWER), a random walk based measure which improves the expressiveness of random walks by using a distinct restart probability for each node. The improved expressiveness leads to superior accuracy for ranking and link prediction. Second, we propose SuRe (Supervised Restart for RWER), an algorithm for learning the restart probabilities of RWER from a given graph. SuRe eliminates the need to heuristically and manually select the restart parameter for RWER. Extensive experiments show that our proposed method provides the best performance for ranking and link prediction tasks, improving the MAP (Mean Average Precision) by up to 15.8% on the best competitor.

Motivation & Objective

• Address the limitation of fixed restart probabilities in traditional Random Walk with Restart (RWR), which restricts expressiveness in measuring node relevance.
• Overcome the need for heuristic, manual selection of restart probabilities in RWR by developing a data-driven learning approach.
• Improve ranking and link prediction accuracy by enabling query nodes to express preferences through distinct restart probabilities.
• Design a scalable and robust learning algorithm that avoids overfitting while maintaining high performance on real-world graphs.

Proposed method

• Propose RWER, a generalization of RWR where each node has a unique restart probability, allowing finer control over random walk behavior based on node-specific preferences.
• Formulate the relevance score computation as a system of linear equations involving a personalized transition matrix with node-specific restart probabilities.
• Introduce SuRe, a supervised learning framework that optimizes restart probabilities using a differentiable objective function based on ground-truth links or rankings.
• Incorporate an origin vector as a regularizer in SuRe to prevent overfitting and improve generalization, especially in low-data regimes.
• Use stochastic optimization with mini-batch sampling to scale SuRe to large graphs, ensuring near-linear time complexity with respect to the number of edges.
• Leverage the power of personalized random walks by learning restart probabilities that maximize prediction accuracy on downstream tasks.

Experimental results

Research questions

• RQ1 Can assigning distinct restart probabilities to each node improve the expressiveness and accuracy of random walk-based relevance scoring in graphs?
• RQ2 How can restart probabilities be automatically learned from data without modifying the graph structure, to outperform heuristic or fixed-parameter approaches?
• RQ3 Does the proposed SuRe method generalize well across diverse graph types and tasks, such as link prediction and node ranking?
• RQ4 What is the impact of the origin vector regularization in SuRe on model stability and generalization performance?
• RQ5 How does the scalability of SuRe compare to existing learning-based and traditional RWR methods on large-scale networks?

Key findings

• SuRe improves Mean Average Precision (MAP) by up to 15.8% compared to the best existing method in link prediction tasks.
• SuRe boosts Precision@20 by up to 10.1% on the best competitor, demonstrating superior performance in top-k ranking.
• The inclusion of the origin vector in SuRe significantly improves performance and reduces overfitting, especially in low-data regimes.
• SuRe scales near-linearly with the number of edges, with a slope of 0.76, outperforming other learning-based methods like SRW and QUINT in terms of efficiency.
• RWER with learned restart probabilities consistently outperforms standard RWR and other supervised methods across all evaluated datasets and tasks.
• The method is robust to parameter choices and shows stable performance across different datasets, including Polblogs, HepTh, and Wikipedia.