Analysis of Social Networks by Tensor Decomposition

  • Sergej Sizov
  • Steffen Staab
  • Thomas Franz


The Social Web fosters novel applications targeting a more efficient and satisfying user guidance in modern social networks, e.g., for identifying thematically focused communities, or finding users with similar interests. Large scale and high diversity of users in social networks poses the challenging question of appropriate relevance/authority ranking, for producing fine-grained and rich descriptions of available partners, e.g., to guide the user along most promising groups of interest. Existing methods for graph-based authority ranking lack support for fine-grained latent coherence between user relations and content (i.e., support for edge semantics in graph-based social network models). We present TweetRank, a novel approach for faceted authority ranking in the context of social networks. TweetRank captures the additional latent semantics of social networks by means of statistical methods in order to produce richer descriptions of user relations. We model the social network by a 3-dimensional tensor that enables the seamless representation of arbitrary semantic relations. For the analysis of that model, we apply the PARAFAC decomposition, which can be seen as a multi-modal counterpart to common Web authority ranking with HITS. The result are groupings of users and terms, characterized by authority and navigational (hub) scores with respect to the identified latent topics. Sample experiments with life data of the Twitter community demonstrate the ability of TweetRank to produce richer and more comprehensive contact recommendations than other existing methods for social authority ranking.


Singular Value Decomposition Authority Score User Relation Social Graph Tensor Decomposition 
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.


  1. 1.
    Boanerges Aleman-Meza, Christian Halaschek-Wiener, Ismailcem B. Arpinar, Cartic Ramakrishnan, and Amit P. Sheth. Ranking complex relationships on the semantic web. IEEE Internet Computing, 9(3):37–44, 2005CrossRefGoogle Scholar
  2. 2.
    Claus A. Andersson and Rasmus Bro. The n-way toolbox for matlab. Chemometrics and Intelligent Laboratory Systems, 52(1):1–4, 2000CrossRefGoogle Scholar
  3. 3.
    Kemafor Anyanwu and Amit P. Sheth. The p operator: Discovering and ranking associations on the semantic web. SIGMOD Record, 31(4):42–47, 2002CrossRefGoogle Scholar
  4. 4.
    Brett W. Bader and Tamara G. Kolda. Algorithm 862: MATLAB tensor classes for fast algorithm prototyping. ACM Transactions on Mathematical Software, 32(4):635–653, 2006CrossRefMathSciNetGoogle Scholar
  5. 5.
    Andrey Balmin, Vagelis Hristidis, and Yannis Papakonstantinou. Objectrank: Authority-based keyword search in databases. In VLDB, pages 564–575, 2004Google Scholar
  6. 6.
    Krishna Bharat and Monika Rauch Henzinger. Improved Algorithms for Topic Distillation in a Hyperlinked Environment. In 21st Annual International ACM SIGIR Conference, Melbourne, Australia, pages 104–111, 1998Google Scholar
  7. 7.
    S. Brin and L. Page. The anatomy of a large-scale hypertextual web search engine. In Seventh International World-Wide Web Conference (WWW 1998), 1998Google Scholar
  8. 8.
    Paul Alexandru Chirita, Stefania Ghita, Wolfgang Nejdl, and Raluca Paiu. Beagle\(++\) : Semantically enhanced searching and ranking on the desktop. In ESWC, 2006Google Scholar
  9. 9.
    David A. Cohn and Thomas Hofmann. The missing link – a probabilistic model of document content and hypertext connectivity. In 13th Conference on Advances in Neural Information Processing Systems (NIPS), Denver, USA, pages 430–436, 2000Google Scholar
  10. 10.
    Klaas Dellschaft and Steffen Staab. An epistemic dynamic model for tagging systems. In 19th ACM Conference on Hypertext and Hypermedia (Hypertext 2008), Pittsburgh, USA, pages 71–80, 2008Google Scholar
  11. 11.
    Michelangelo Diligenti, Marco Gori, and Marco Maggini. Web Page Scoring Systems for Horizontal and Vertical Search. In 11th International World Wide Web Conference (WWW), Honolulu, USA, pages 508–516, 2002Google Scholar
  12. 12.
    Chris H. Q. Ding, Xiaofeng He, Parry Husbands, Hongyuan Zha, and Horst D. Simon. PageRank, HITS and a Unified Framework for Link Analysis. In 25th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, Tampere, Finland, pages 353–354, 2002Google Scholar
  13. 13.
    Magdalini Eirinaki and Michalis Vazirgiannis. Usage-based pagerank for web personalization. Data Mining, IEEE International Conference on, pages 130–137, 2005Google Scholar
  14. 14.
    Richard A. Harshman and Margaret E. Lundy. Parafac: Parallel factor analysis. Computational Statistics and Data Analysis, 18(1):39–72, 1994MATHCrossRefGoogle Scholar
  15. 15.
    Taher H. Haveliwala. Topic-sensitive PageRank. In 11th International World Wide Web Conference (WWW), Honolulu, USA, pages 517–526, 2002Google Scholar
  16. 16.
    Glen Jeh and Jennifer Widom. Scaling Personalized Web Search. In 12th International World Wide Web Conference (WWW), Budapest, Hungary, pages 271–279, 2003Google Scholar
  17. 17.
    Jon M. Kleinberg. Authoritative sources in a hyperlinked environment. J. ACM, 46(5):604–632, 1999Google Scholar
  18. 18.
    Tamara G. Kolda and Brett W. Bader. Tensor decompositions and applications. SIAM Review, 51(3), 2009 (to appear)Google Scholar
  19. 19.
    Tamara G. Kolda, Brett W. Bader, and Joseph P. Kenny. Higher-Order Web Link Analysis Using Multilinear Algebra. In 5th IEEE International Conference on Data Mining (ICDM), Houston, USA, pages 242–249, 2005Google Scholar
  20. 20.
    Ronny Lempel and Shlomo Moran. SALSA: the Stochastic Approach for Link-Structure Analysis. ACM Transactions on Information Systems (TOIS), 19(2):131–160, 2001Google Scholar
  21. 21.
    Yu-Ting Liu, Bin Gao, Tie-Yan Liu, Ying Zhang, Zhiming Ma, Shuyuan He, and Hang Li. Browserank: letting web users vote for page importance. In SIGIR, pages 451–458, 2008Google Scholar
  22. 22.
    Davood Rafiei and Alberto O. Mendelzon. What is this Page known for? Computing Web Page Reputations. Computer Networks, 33(1–6):823–835, 2000CrossRefGoogle Scholar
  23. 23.
    Cartic Ramakrishnan, William H. Milnor, Matthew Perry, and Amit P. Sheth. Discovering informative connection subgraphs in multi-relational graphs. SIGKDD Explor. Newsl., 7(2):56–63, 2005Google Scholar
  24. 24.
    Matthew Richardson and Pedro Domingos. The Intelligent surfer: Probabilistic Combination of Link and Content Information in PageRank. In 14th Conference on Advances in Neural Information Processing Systems (NIPS), Vancouver, Canada, pages 1441–1448, 2001Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.WeST – Institute for Web Science and TechnologiesUniversity of Koblenz-LandauLandauGermany

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