Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
Brandes, U., Erlebach, T.: Network Analysis: Methodological Foundations. LNCS. Springer, Heidelberg (March 2005)
Brandes, U., Gaertler, M., Wagner, D.: Engineering graph clustering: Models and experimental evaluation. ACM Journal of Experimental Algorithmics 12 (2007)
Corneil, D.G., Gotlieb, C.C.: An efficient algorithm for graph isomorphism. Journal of the ACM (JACM) 17, 51–64 (1970)
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)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 8271–8276 (2002)
Halkidi, M., Batistakis, Y., Vazirgiannis, M.: Cluster validity methods: Part i. ACM SIGMOD Record 31, 2002 (2002)
Halkidi, M., Vazirgiannis, M.: Clustering validity assessment: Finding the optimal partitioning of a data set (2001)
Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. 31(3), 264–323 (1999)
Kannan, R., Vempala, S., Vetta, A.: On clusterings good, bad and spectral. Journal of the ACM 51(3), 497–515 (2004)
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)
Maimon, O., Rokach, L.: Data Mining and Knowledge Discovery Handbook. Springer, Heidelberg (September 2005)
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)
Milligan, G.W.: A monte-carlo study of 30 internal criterion measures for cluster-analysis. Psychometrica 46, 187–195 (1981)
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)
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)
Newman, M.E.J.: Fast algorithm for detecting community structure in networks. Physical Review EÂ 69, 066133 (2004)
Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)Â 74(3) (2006)
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)
Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66(336), 846–850 (1971)
Rozenblat, C., Melançon, G., Koenig, P.-Y.: Continental integration in multilevel approach of world air transportation (2000-2004). Networks and Spatial Economics (2008)
Schaeffer, S.E.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)
Steinbach, M., Karypis, G., Kumar, V.: A comparison of document clustering techniques. Technical report, Departement of Computer Science and Engineering, University of Minnesota (2000)
Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zaidi, F., Archambault, D., Melançon, G. (2010). Evaluating the Quality of Clustering Algorithms Using Cluster Path Lengths. In: Perner, P. (eds) Advances in Data Mining. Applications and Theoretical Aspects. ICDM 2010. Lecture Notes in Computer Science(), vol 6171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14400-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-14400-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14399-1
Online ISBN: 978-3-642-14400-4
eBook Packages: Computer ScienceComputer Science (R0)