A Recommender System Based on Local Random Walks and Spectral Methods

  • Zeinab Abbassi
  • Vahab S. Mirrokni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5439)


In this paper, we design recommender systems for blogs based on the link structure among them. We propose algorithms based on refined random walks and spectral methods. First, we observe the use of the personalized page rank vector to capture the relevance among nodes in a social network. We apply the local partitioning algorithms based on refined random walks to approximate the personalized page rank vector, and extend these ideas from undirected graphs to directed graphs. Moreover, inspired by ideas from spectral clustering, we design a similarity metric among nodes of a social network using the eigenvalues and eigenvectors of a normalized adjacency matrix of the social network graph. In order to evaluate these algorithms, we crawled a set of blogs and construct a blog graph. We expect that these algorithms based on the link structure perform very well for blogs, since the average degree of nodes in the blog graph is large. Finally, we compare the performance of our algorithms on this data set. In particular, the acceptable performance of our algorithms on this data set justifies the use of a link-based recommender system for social networks with large average degree.


Random Walk Directed Graph Recommender System Spectral Cluster Link Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1. (visited, December 2006)
  2. 2.
    Parsons, J., Ralph, P., Gallagher, K.: Using viewing time to infer user preference in recommender systems. In: AAAI Workshop in Semantic Web Personalization, San Jose, California (July 2004)Google Scholar
  3. 3.
    Resnick, P., Varian, H.: Recommender Systems. Communications of the ACM 40, 56–58 (1997)CrossRefGoogle Scholar
  4. 4.
    Andersen, R., Chung, F., Lang, K.: Local Graph Partitioning using PageRank Vectors. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), pp. 475–486 (2006)Google Scholar
  5. 5.
    Brin, S., Page, L., Motwani, R., Winograd, T.: The PageRank citation ranking: Bringing order to the web, Technical report, Stanford Digital Library Technologies Project (1998)Google Scholar
  6. 6.
    Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM Journal on Computing 1(2), 146–160 (1972)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Verma, D., Meila, M.: A comparison of spectral clustering algorithms. Technical report UW-cse-03-05-01, University of WashingtonGoogle Scholar
  8. 8.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)CrossRefGoogle Scholar
  9. 9.
    Kannan, R., Vempala, S., Vetta, A.: On clusterings- good, bad and spectral. In: Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS 2000), pp. 367–377 (2000)Google Scholar
  10. 10.
    Ng, A., Jordan, I., Weiss, Y.: On Spectral Clustering: Analysis and an algorithm. Advances in Neural Information Processing Systems 14, 849–856Google Scholar
  11. 11.
    Herlocker, J.L., Konstan, J.A., Terveen, L.G., Riedl, J.T.: Evaluating Collaborative Filtering Recommender Systems, ACM Transactions on Information Systems (TOIS) (2004)Google Scholar
  12. 12.
    Lovasz, L.: Random walks on graphs: A survey (January 1993)Google Scholar
  13. 13.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. (2001)Google Scholar
  14. 14.
    Spielman, D.A., Teng, S.: Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In: ACM STOC 2004, pp. 81–90. ACM Press, New York (2004)Google Scholar
  15. 15.
    Haveliwala, T.H.: Topic-sensitive PageRank: A context-sensitive ranking algorithm for web search. IEEE Trans. Knowl. Data Eng. 15(4), 784–796 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Zeinab Abbassi
    • 1
  • Vahab S. Mirrokni
    • 2
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  2. 2.Microsoft ResearchRedmondUSA

Personalised recommendations