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Recursive Node Similarity in Networked Information Spaces

  • J. P. Grossman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2877)

Abstract

The link structure of a networked information space can be used to estimate similarity between nodes. A recursive definition of similarity arises naturally: two nodes are judged to be similar if they have similar neighbours. Quantifying similarity defined in this manner is challenging due to the tendency of the system to converge to a single point (i.e. all pairs of nodes are completely similar).

We present an embedding of undirected graphs into R n based on recursive node similarity which solves this problem by defining an iterative procedure that converges to a non-singular embedding. We use the spectral decomposition of the normalized adjacency matrix to find an explicit expression for this embedding, then show how to compute the embedding efficiently by solving a sparse system of linear equations.

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References

  1. 1.
    Chung, F.R.K.: Spectral Graph Theory. In: CBMS Lecture Notes, Regional Conference Series in Mathematics, vol. 92, p. 207. American Mathematical Society, Providence (1995)Google Scholar
  2. 2.
    Fasulo, D.: An Analysis of Recent Work on Clustering Algorithms, Technical Report #01-03-02, Department of Computer Science and Engineering, University of Washington, Seattle, WA, April 26 (1999)Google Scholar
  3. 3.
    Fraley, C., Raftery, A.E.: How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis. Computer Journal 41, 578–588 (1998)zbMATHCrossRefGoogle Scholar
  4. 4.
    Lee Giles, C., Bollacker, K.D., Lawrence, S.: Citeseer: An Automatic Citation Indexing System. In: Digital Libraries 1998 - Third ACM Conference on Digital Libraries 1998, pp. 89–98 (1998)Google Scholar
  5. 5.
    Lu, W., Janssen, J., Milios, E., Japkowicz, N.: Node Similarity in Networked Information Spaces. In: Proc. CASCON 2001, Toronto, Ontario, November 5-7 (2001)Google Scholar
  6. 6.
    Moody, J.: Peer influence groups: identifying dense clusters in large networks. Social Networks 23, 261–283 (2001)CrossRefGoogle Scholar
  7. 7.
    Richards Jr., W.D., Seary, A.J.: Convergence Analysis of Communication Networks, pp. 36 (1999), http://www.sfu.ca/~richards/Pages/converge.pdf
  8. 8.
    Salton, G., Yang, C.S.: On the specification of term values in automatic indexing. Journal of Documentation 29, 351–372 (1973)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • J. P. Grossman
    • 1
  1. 1.Department of Mathematics and StatisticsDalhousie UniversityHalifax, Nova ScotiaCanada

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