Advertisement

Visualizing Very Large Graphs Using Clustering Neighborhoods

  • Dunja Mladenic
  • Marko Grobelnik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3539)

Abstract

This paper presents a method for visualization of large graphs in a two-dimensional space, such as a collection of Web pages. The main contribution here is in the representation change to enable better handling of the data. The idea of the method consists from three major steps: (1) First, we transform a graph into a sparse matrix, where for each vertex in the graph there is one sparse vector in the matrix. Sparse vectors have non-zero components for the vertices that are close to the vertex represented by the vector. (2) Next, we perform hierarchical clustering (eg., hierarchical K-Means) on the set of sparse vectors, resulting in the hierarchy of clusters. (3) In the last step, we map hierarchy of clusters into a two-dimensional space in the way that more similar clusters appear closely on the picture. The effect of the whole procedure is that we assign unique X and Y coordinates to each vertex, in a way those vertices or groups of vertices on several levels of hierarchy that are stronger connected in a graph are place closer in the picture. The method is particular useful for power distributed graphs. We show applications of the method on real-world examples of visualization of institution collaboration graph and cross-sell recommendation graph.

Keywords

Hierarchical Cluster Sparse Matrix Graph Transformation Cosine Similarity Original Graph 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley-Interscience, Hoboken (2000)Google Scholar
  2. 2.
    Fayyad, U., Grinstein, G.G., Wierse, A. (eds.): Information Visualization in Data Mining and Knowledge Discovery. Morgan Kaufmann, San Francisco (2001)Google Scholar
  3. 3.
    Grobelnik, M., Mladenić, D.: Efficient visualization of large text corpora. In: Proceedings of the seventh TELRI seminar, Dubrovnik, Croatia (2002)Google Scholar
  4. 4.
    Grobelnik, M., Mladenić, D.: Analysis of a database of research projects using text mining and link analysis. In: Mladenić, D., Lavrac, N., Bohanec, M., Moyle, S. (eds.) Data mining and decision support: integration and collaboration. The Kluwer international series in engineering and computer science, SECS 745, pp. 157–166. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  5. 5.
    Hand, D.J., Mannila, H., Smyth, P.: Principles of Data Mining. Adaptive Computation and Machine Learning. MIT Press, Cambridge (2001)Google Scholar
  6. 6.
    Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  7. 7.
    Mitchell, T.M.: Machine Learning. The McGraw-Hill Companies, Inc., New York (1997)zbMATHGoogle Scholar
  8. 8.
    Mutzel, P., Jünger, M., Leipert, S. (eds.): GD 2001. LNCS, vol. 2265. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  9. 9.
    North, S.C. (ed.): GD 1996. LNCS, vol. 1190. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  10. 10.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank citation ranking: bringing order to the web. Tech. Rept. SIDL-WP-1999-020, Stanford University (January 1998)Google Scholar
  11. 11.
    Robbins, K.S., Gorman, M.: Fast Visualization Methods for Comparing Dynamics: A Case Study in Combustion. In: Proceedings of the 11th IEEE Visualization 2000 Conference. IEEE Computer Society, Los Alamitos (2000)Google Scholar
  12. 12.
    Steinbach, M., Karypis, G., Kumar, V.: A comparison of document clustering techniques. In: Proceedings of KDD Workshop on Text Mining, pp. 109–110 (2000)Google Scholar
  13. 13.
    Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations. Morgan Kaufmann, San Francisco (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dunja Mladenic
    • 1
  • Marko Grobelnik
    • 1
  1. 1.Jozef Stefan InstituteLjubljanaSlovenia

Personalised recommendations