A Comparative Study of Matrix Factorization and Random Walk with Restart in Recommender System


Between matrix factorization (MF) or Random Walk with Restart (RWR), which method works better for recommender systems? Which method handles explicit or implicit feedback data better? Does additional side 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. MF and RWR 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 MF 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 MF 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.

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Explicit vs. Implicit feedback

MF performs better with explicit feedback. RWR is better when used with implicit feedback.

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Global bias terms

Global bias terms improve the overall quality of recommendation in both MF and RWR.

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Side information

Side information produces positive synergy when used with explicit feedback ratings but gives negative impact with implicit feedbacks.


A Comparative Study of Matrix Factorization and Random Walk with Restart
Haekyu Park, Jinhong Jung, and U Kang.
2017 IEEE International Conference on Big Data(Big Data 2017), Boston, MA, USA
[PDF] [Slides] [Bibtex]

  author    = {Haekyu Park and
	       Jinhong Jung and
	       U. Kang},
  title     = {A comparative study of matrix factorization and random walk with restart
	       in recommender systems},
  booktitle = {2017 {IEEE} International Conference on Big Data, BigData 2017, Boston,
	       MA, USA, December 11-14, 2017},
  pages     = {756--765},
  year      = {2017},


  • [Download Ver 1.0]
    The zip file includes codes of matrix factorization and random walk with restart methods for recommendation. We include four MF and four RWR implementations according to various recommendation scenarios.
  • More recent versions are in this repository.


Name #Users #Items #Ratings Rating type Side info. Processed data Source
Movielens 943 1,682 100,000 Explicit User demographic information [Download] [Link]
Filmtrust 1,642 2,071 35,494 Explicit Social links [Download] [Link]
Epinions 49,289 139,738 664,824 Explicit Social links [Download] [Link]
Lastfm 1,892 17,632 92,834 Implicit Social links [Download] [Link]
Audioscrobbler 148,111 1,631,028 24,296,858 Implicit N/A [Download] [Link]


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