[Paper Review] A Comparative Study of Matrix Factorization and Random Walk with Restart in Recommender Systems

Haekyu Park, Jinhong Jung+1 more|arXiv (Cornell University)|Aug 30, 2017

Recommender Systems and Techniques25 references3 citations

TL;DR

This paper compares matrix factorization (MF) and random walk with restart (RWR) in recommender systems, proposing a novel RWR variant with global bias terms to align with MF's bias modeling. Experiments show MF outperforms RWR on explicit feedback, while RWR excels on implicit feedback; biases improve both methods, but side information harms performance with implicit data.

ABSTRACT

Between matrix factorization or Random Walk with Restart (RWR), which method works better for recommender systems? Which method handles explicit or implicit feedback data better? Does additional information help recommendation? Recommender systems play an important role in many e-commerce services such as Amazon and Netflix to recommend new items to a user. Among various recommendation strategies, collaborative filtering has shown good performance by using rating patterns of users. Matrix factorization and random walk with restart are the most representative collaborative filtering methods. However, it is still unclear which method provides better recommendation performance despite their extensive utility. In this paper, we provide a comparative study of matrix factorization and RWR in recommender systems. We exactly formulate each correspondence of the two methods according to various tasks in recommendation. Especially, we newly devise an RWR method using global bias term which corresponds to a matrix factorization method using biases. We describe details of the two methods in various aspects of recommendation quality such as how those methods handle cold-start problem which typically happens in collaborative filtering. We extensively perform experiments over real-world datasets to evaluate the performance of each method in terms of various measures. We observe that matrix factorization performs better with explicit feedback ratings while RWR is better with implicit ones. We also observe that exploiting global popularities of items is advantageous in the performance and that side information produces positive synergy with explicit feedback but gives negative effects with implicit one.

Motivation & Objective

• To systematically compare matrix factorization (MF) and random walk with restart (RWR) in collaborative filtering for recommender systems.
• To investigate how each method performs under explicit versus implicit feedback settings.
• To evaluate the impact of global bias terms and side information on recommendation quality across both methods.
• To develop a new RWR variant with global bias terms that mirrors MF’s bias modeling for fairer comparison.
• To provide insights into the strengths and limitations of MF and RWR under different recommendation scenarios and data types.

Proposed method

• Proposes a new RWR-based method that incorporates global bias terms to model item popularity and user general tendencies, analogous to MF with bias.
• Uses a user-item bipartite graph to model interactions, where RWR computes personalized node proximity via random surfer simulation with restart probability.
• Applies matrix factorization to decompose the user-item rating matrix into low-rank user and item factors, including global bias terms.
• Integrates side information (e.g., user demographics, item categories) into both MF and RWR models via feature-based embedding or graph augmentation.
• Employs standard evaluation metrics including Spearman’s rho, precision@k, and RMSE across multiple real-world datasets (Movielens, FilmTrust, Epinions, Lastfm).
• Performs ablation studies to isolate the effects of bias terms and side information on performance across explicit and implicit feedback settings.

Experimental results

Research questions

• RQ1 Which method—matrix factorization or random walk with restart—performs better on explicit feedback data?
• RQ2 Which method performs better on implicit feedback data?
• RQ3 Do global bias terms improve recommendation performance in both MF and RWR?
• RQ4 How does side information affect recommendation performance in MF and RWR, especially under explicit versus implicit feedback?
• RQ5 What are the underlying reasons for the differing performance behaviors of MF and RWR across feedback types?

Key findings

• Matrix factorization outperforms random walk with restart on explicit feedback datasets, achieving higher precision@1, precision@2, precision@3, and Spearman’s rho across Movielens, FilmTrust, and Epinions.
• Random walk with restart performs better than matrix factorization on implicit feedback data, with RWR_Side achieving a Spearman’s rho of 0.440 on Lastfm compared to MF_Side’s 0.207.
• Global bias terms significantly improve recommendation performance in both MF and RWR, enhancing global ranking and top-k prediction accuracy.
• Side information improves performance in MF with explicit feedback (e.g., MF_Side outperforms MF on Movielens), but degrades performance in RWR with implicit feedback (e.g., RWR_Side underperforms RWR on Lastfm).
• The performance gap arises because implicit feedback is noisier, and side information amplifies noise in such settings, while explicit feedback is more robust to side information integration.
• The proposed RWR method with global bias terms (RWR_Bias) improves upon standard RWR, demonstrating that bias modeling is beneficial even in graph-based methods.