ABSTRACT
A network represented as a graph, can be transformed to a sparser graph, if a threshold is applied to the relationship between its objects. The threshold can be used as an upper or lower limit or define a range based on which we can exclude connections from the graph, thus resulting to different views of a graph. We examine for various values of the threshold the effect it has on the task of community detection and we propose a method to validate the results of the corresponding clusterings against the clustering of the original graph. We transform the clusterings in comparable forms and we employ four known measures for clustering validation in order to examine their resemblance. We present some preliminary experiments to evaluate the effects of a threshold on the clustering task and we outline possible usage of the different views that are produced.
- A. Arenas, J. Duch, A. Fernandez, and S. Gomez. Size reduction of complex networks preserving modularity. New Journal of Physics, 9:176, June 2007.Google ScholarCross Ref
- V. D. Blondel, J. L. Guillaume, R. Lambiotte, and E. Lefebvre. Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 10 2008.Google Scholar
- F. Boutin, J. Thièvre, and M. Hascoët. Focus-based filtering + clustering technique for power law networks with small world phenomenon. In Proc. SPIE 6060, Visualization and Data Analysis 2006, 60600Q, pages 001--012, January 2006.Google Scholar
- Y. Chiricota, F. Jourdan, and G. Melançon. Software components capture using graph clustering. In Proceedings of the 11th IEEE International Workshop on Program Comprehension, IWPC '03, pages 217--226, Washington, DC, USA, 2003. IEEE Computer Society. Google ScholarDigital Library
- T. Cover and J. Thomas. Elements of Information Theory. Wiley, 1991. Google ScholarDigital Library
- M. De Choudhury, W. A. Mason, J. M. Hofman, and D. J. Watts. Inferring relevant social networks from interpersonal communication. In Proceedings of the 19th International Conference on World Wide Web (WWW '10), pages 301--310, New York, NY, USA, 2010. ACM. Google ScholarDigital Library
- S. Fortunato. Community detection in graphs. Physics Reports, 486:75--174, 2010.Google ScholarCross Ref
- A. L. Fred and A. K. Jain. Robust data clustering. In Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR, volume 3, pages 128--136, 2003.Google Scholar
- L. Hubert and P. Arabie. Comparing partitions. Journal of Classification, 2:193--218, 1985.Google ScholarCross Ref
- Y. Jia, J. Hoberock, M. Garland, and J. Hart. On the visualization of social and other scale-free networks. IEEE Transactions on Visualization and Computer Graphics, 14(6):1285--1292, Nov. 2008. Google ScholarDigital Library
- Y. Kim, S. W. Son, and H. Jeong. Linkrank: Finding communities in directed networks. Phys. Rev. E, 81, 2010.Google Scholar
- E. A. Leicht and M. E. Newman. Community structure in directed networks. Phys. Rev. Lett., 100, March 2008.Google ScholarCross Ref
- Y. Li, Z. L. Zhang, and J. Bao. Mutual or unrequited love: Identifying stable clusters in social networks with uni- and bi-directional links. CoRR, abs/1203.5474, 2012. Google ScholarDigital Library
- M. Meila. Comparing clusterings. Proc. of COLT 03, 2003.Google Scholar
- M. Newman. Modularity and community structure in networks. PNAS, 103:8577--8582, June 2006.Google ScholarCross Ref
- M. Newman and M. Girvan. Finding and evaluating community structure in networks. Phys. Rev. E, 69, 2004.Google Scholar
- M. E. Newman. Fast algorithm for detecting community structure in networks. Phys. Rev. E, 69, June 2004.Google Scholar
- A. Y. Ng, M. I. Jordan, and Y. Weiss. On spectral clustering: Analysis and an algorithm. In Neural Information Processing Systems - NIPS, pages 849--856, 2001.Google Scholar
- A. D. Perkins and M. A. Langston. Threshold selection in gene co-expression networks using spectral graph theory techniques. BMC Bioinformatics, 10(S-11), 2009.Google Scholar
- P. Pons and M. Latapy. Computing communities in large networks using random walks. J. of Graph Alg. and App. bf, 10(2):191--218, 2006.Google ScholarCross Ref
- W. M. Rand. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association (American Statistical Association), 66:846--850, 1971.Google Scholar
- M. Rosvall and C. T. Bergstrom. Maps of random walks on complex networks reveal community structure. In Proceedings of the National Academy of Sciences of the United States of America, volume 105, pages 1118--1123, 2008.Google ScholarCross Ref
- A. Strehl and J. Ghosh. Cluster ensembles - a knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research, 3:583--617, 2002. Google ScholarDigital Library
- S. van Dongen. Graph Clustering by Flow Simulation. PhD thesis, University of Utrecht, May 2000.Google Scholar
- N. X. Vinh, J. Epps, and J. Bailey. Information theoretic measures for clusterings comparison: is a correction for chance necessary? In ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning, pages 1073--1080, 2009. Google ScholarDigital Library
- N. X. Vinh, J. Epps, and J. Bailey. Information theoretic measures for clusterings comparison: variants, properties, normalization and correction for chance. Journal of Machine Learning Research, 11:2837--2854, 2010. Google ScholarDigital Library
- S. Wagner and D. Wagner. Comparing clusterings - an overview. Technical Report 2006-04, ITI Wagner, Informatics, Universitat Karlsruhe, 2007.Google Scholar
- S. White and P. Smyth. A spectral clustering approach to finding communities in graphs. In Proc. SIAM International Conference on Data Mining, 2005.Google ScholarCross Ref
Index Terms
- Alternate views of graph clusterings based on thresholds: a case study for a student forum
Recommendations
Graph Clustering by Maximizing Statistical Association Measures
IDA 2013: Proceedings of the 12th International Symposium on Advances in Intelligent Data Analysis XII - Volume 8207We are interested in objective functions for clustering undirected and unweighted graphs. Our goal is to define alternatives to the popular modularity measure. To this end, we propose to adapt statistical association coefficients, which traditionally ...
RoClust: Role discovery for graph clustering
Graph clustering, or community detection, is an important task of discovering the underlying structure in a network by clustering vertices in a graph into communities. In the past decades, non-overlapping methods such as normalized cuts and modularity-...
On the triangle clique cover and K t clique cover problems
AbstractAn edge clique cover of a graph is a set of cliques that covers all edges of the graph. We generalize this concept to K t clique cover, i.e. a set of cliques that covers all complete subgraphs on t vertices of the graph, ...
Comments