Is There a Best Quality Metric for Graph Clusters?
Graph clustering, the process of discovering groups of similar vertices in a graph, is a very interesting area of study, with applications in many different scenarios. One of the most important aspects of graph clustering is the evaluation of cluster quality, which is important not only to measure the effectiveness of clustering algorithms, but also to give insights on the dynamics of relationships in a given network. Many quality evaluation metrics for graph clustering have been proposed in the literature, but there is no consensus on how do they compare to each other and how well they perform on different kinds of graphs. In this work we study five major graph clustering quality metrics in terms of their formal biases and their behavior when applied to clusters found by four implementations of classic graph clustering algorithms on five large, real world graphs. Our results show that those popular quality metrics have strong biases toward incorrectly awarding good scores to some kinds of clusters, especially seen in larger networks. They also indicate that currently used clustering algorithms and quality metrics do not behave as expected when cluster structures are different from the more traditional, clique-like ones.
KeywordsCluster Algorithm Quality Metrics Spectral Cluster Good Cluster Graph Cluster
Unable to display preview. Download preview PDF.
- 2.Danon, L., Díaz-Guilera, A., Duch, J., Arenas, A.: Comparing community structure identification. Journal of Statistical Mechanics: Theory and Experiment 2005(09), P09008 (2005)Google Scholar
- 10.Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Statistical properties of community structure in large social and information networks. In: WWW 2008: Proceeding of the 17th International Conference on World Wide Web, pp. 695–704. ACM, New York (2008)Google Scholar
- 11.Leskovec, J., Lang, K.J., Mahoney, M.: Empirical comparison of algorithms for network community detection. In: Proceedings of the 19th International Conference on World Wide Web, WWW 2010, pp. 631–640. ACM, New York (2010)Google Scholar
- 12.Nepusz, T., Bazso, F.: Likelihood-based clustering of directed graphs, pp. 189–194 (March 2007)Google Scholar
- 14.Newman, M.E., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E 69(2) (February 2004)Google Scholar
- 19.Steinbach, M., Karypis, G., Kumar, V.: A comparison of document clustering techniques. In: Grobelnik, M., Mladenic, D., Milic-Frayling, N. (eds.) KDD-2000 Workshop on Text Mining, Boston, MA, August 20, pp. 109–111 (2000)Google Scholar
- 20.Tan, P.-N., Kumar, V., Srivastava, J.: Selecting the right interestingness measure for association patterns. In: KDD 2002: Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 32–41. ACM, New York (2002)Google Scholar
- 21.Tan, P.-N., Steinbach, M., Kumar, V.: Introduction to Data Mining. Addison-Wesley Longman Publishing Co., Inc., Boston (2005)Google Scholar
- 22.van Dongen, S.M.: Graph Clustering by Flow Simulation. PhD thesis, University of Utrecht, The Netherlands (2000)Google Scholar