Evaluating the Quality of Clustering Algorithms Using Cluster Path Lengths

  • Faraz Zaidi
  • Daniel Archambault
  • Guy Melançon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6171)


Many real world systems can be modeled as networks or graphs. Clustering algorithms that help us to organize and understand these networks are usually referred to as, graph based clustering algorithms. Many algorithms exist in the literature for clustering network data. Evaluating the quality of these clustering algorithms is an important task addressed by different researchers. An important ingredient of evaluating these clustering techniques is the node-edge density of a cluster. In this paper, we argue that evaluation methods based on density are heavily biased to networks having dense components, such as social networks, but are not well suited for data sets with other network topologies where the nodes are not densely connected. Example of such data sets are the transportation and Internet networks. We justify our hypothesis by presenting examples from real world data sets.

We present a new metric to evaluate the quality of a clustering algorithm to overcome the limitations of existing cluster evaluation techniques. This new metric is based on the path length of the elements of a cluster and avoids judging the quality based on cluster density. We show the effectiveness of the proposed metric by comparing its results with other existing evaluation methods on artificially generated and real world data sets.


Evaluating Cluster Quality Cluster Path Length 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Auber, D., Chiricota, Y., Jourdan, F., Melancon, G.: Multiscale visualization of small world networks. In: INFOVIS 2003: Proceedings of the IEEE Symposium on Information Visualization, pp. 75–81 (2003)Google Scholar
  2. 2.
    Brandes, U., Erlebach, T.: Network Analysis: Methodological Foundations. LNCS. Springer, Heidelberg (March 2005)zbMATHGoogle Scholar
  3. 3.
    Brandes, U., Gaertler, M., Wagner, D.: Engineering graph clustering: Models and experimental evaluation. ACM Journal of Experimental Algorithmics 12 (2007)Google Scholar
  4. 4.
    Corneil, D.G., Gotlieb, C.C.: An efficient algorithm for graph isomorphism. Journal of the ACM (JACM) 17, 51–64 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gavin, A.-C., Bosche, M., Krause, R., Grandi, P., Marzioch, M., Bauer, A., Schultz, J., Rick, J.M., Michon, A.-M., Cruciat, C.-M., Remor, M., Hofert, C., Schelder, M., Brajenovic, M., Ruffner, H., Merino, A., Klein, K., Hudak, M., Dickson, D., Rudi, T., Gnau, V., Bauch, A., Bastuck, S., Huhse, B., Leutwein, C., Heurtier, M.-A., Copley, R.R., Edelmann, A., Querfurth, E., Rybin, V., Drewes, G., Raida, M., Bouwmeester, T., Bork, P., Seraphin, B., Kuster, B., Neubauer, G., Superti-Furga, G.: Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 415(6868), 141–147 (2002)CrossRefGoogle Scholar
  6. 6.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 8271–8276 (2002)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Halkidi, M., Batistakis, Y., Vazirgiannis, M.: Cluster validity methods: Part i. ACM SIGMOD Record 31, 2002 (2002)Google Scholar
  8. 8.
    Halkidi, M., Vazirgiannis, M.: Clustering validity assessment: Finding the optimal partitioning of a data set (2001)Google Scholar
  9. 9.
    Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. 31(3), 264–323 (1999)CrossRefGoogle Scholar
  10. 10.
    Kannan, R., Vempala, S., Vetta, A.: On clusterings good, bad and spectral. Journal of the ACM 51(3), 497–515 (2004)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Lacroix, V., Fernandes, C., Sagot, M.-F.: Motif search in graphs: Application to metabolic networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(4), 360–368 (2006)CrossRefGoogle Scholar
  12. 12.
    Maimon, O., Rokach, L.: Data Mining and Knowledge Discovery Handbook. Springer, Heidelberg (September 2005)Google Scholar
  13. 13.
    Mihail, M., Gkantsidis, C., Saberi, A., Zegura, E.: On the semantics of internet topologies, tech. rep. gitcc0207. Technical report, College of Computing, Georgia Institute of Technology, Atlanta, GA, USA (2002)Google Scholar
  14. 14.
    Milligan, G.W.: A monte-carlo study of 30 internal criterion measures for cluster-analysis. Psychometrica 46, 187–195 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Mitchell, B., Mancoridis, S., Yih-Farn, C., Gansner, E.: Bunch: A clustering tool for the recovery and maintenance of software system structures. In: International Conference on Software Maintenance, ICSM (1999)Google Scholar
  16. 16.
    Newman, M.E., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2 Pt. 2) (February 2004)Google Scholar
  17. 17.
    Newman, M.E.J.: Fast algorithm for detecting community structure in networks. Physical Review E 69, 066133 (2004)Google Scholar
  18. 18.
    Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 74(3) (2006)Google Scholar
  19. 19.
    Nguyen, Q.H., Rayward, Smith, V.J.: Internal quality measures for clustering in metric spaces. Int. J. Bus. Intell. Data Min. 3(1), 4–29 (2008)CrossRefGoogle Scholar
  20. 20.
    Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66(336), 846–850 (1971)CrossRefGoogle Scholar
  21. 21.
    Rozenblat, C., Melançon, G., Koenig, P.-Y.: Continental integration in multilevel approach of world air transportation (2000-2004). Networks and Spatial Economics (2008)Google Scholar
  22. 22.
    Schaeffer, S.E.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Steinbach, M., Karypis, G., Kumar, V.: A comparison of document clustering techniques. Technical report, Departement of Computer Science and Engineering, University of Minnesota (2000)Google Scholar
  24. 24.
    Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Faraz Zaidi
    • 1
  • Daniel Archambault
    • 1
  • Guy Melançon
    • 1
  1. 1.CNRS UMR 5800 LaBRI & INRIA Bordeaux - Sud OuestTalence cedexFrance

Personalised recommendations