Abstract
Detecting the community structure exhibited by real networks is a crucial step toward an understanding of complex systems beyond the local organization of their constituents. Many algorithms proposed so far, especially the group of methods in the k-means formulation, can lead to a high degree of efficiency and accuracy. Here we test three k-means methods, based on optimal prediction, diffusion distance and dissimilarity index, respectively, on two artificial networks, including the widely known ad hoc network with same community size and a recently introduced LFR benchmark graphs with heterogeneous distributions of degree and community size. All of them display an excellent performance, with the additional advantage of low computational complexity, which enables the analysis of large systems. Moreover, successful applications to several real world networks confirm the capability of the methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–97 (2002)
Newman, M., Barabási, A.L., Watts, D.J.: The structure and dynamics of networks. Princeton University Press, Princeton (2005)
Girvan, M., Newman, M.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99(12), 7821–7826 (2002)
Newman, M., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. EÂ 69(2), 026113 (2004)
Newman, M.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. USA 103(23), 8577–8582 (2006)
Zhou, H.: Distance, dissimilarity index, and network community structure. Phys. Rev. EÂ 67(6), 061901 (2003)
Lafon, S., Lee, A.: Diffusion Maps and Coarse-Graining: A Unified Framework for Dimensionality Reduction, Graph Partitioning, and Data Set Parameterization. IEEE Trans. Pattern. Anal. Mach. Intel. 28, 1393–1403 (2006)
Duch, J., Arenas, A.: Community detection in complex networks using extremal optimization. Phys. Rev. EÂ 72, 027104 (2005)
Danon, L., Diaz-Guilera, A., Duch, J., Arenas, A.: Comparing community structure identification. J. Stat. Mech. 9, P09008 (2005)
Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. EÂ 78(4), 046110 (2008)
Weinan, E., Li, T., Vanden-Eijnden, E.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys. Rev. EÂ 80(1), 016118 (2009)
Li, T., Liu, J., Weinan, E.: Community detection algorithms: a comparative analysis. Phys. Rev. EÂ 80(5), 056117 (2009)
Weinan, E., Li, T., Vanden-Eijnden, E.: Optimal partition and effective dynamics of complex networks. Proc. Natl. Acad. Sci. USA 105(23), 7907–7912 (2008)
Li, T., Liu, J., Weinan, E.: Probabilistic Framework for Network Partition. Phys. Rev. EÂ 80, 026106 (2009)
Liu, J.: Detecting the fuzzy clusters of complex networks. Patten Recognition 43, 1334–1345 (2010)
Liu, J., Liu, T.: Detecting community structure in complex networks using simulated annealing with k-means algorithms. Physica A 389, 2300–2309 (2010)
Liu, J.: An extended validity index for identifying community structure in networks. In: Zhang, L., Lu, B.-L., Kwok, J. (eds.) ISNN 2010. LNCS, vol. 6064, pp. 258–267. Springer, Heidelberg (2010)
Liu, J.: Finding and evaluating fuzzy clusters in networks. In: Tan, Y., Shi, Y., Tan, K.C. (eds.) Advances in Swarm Intelligence. LNCS, vol. 6146, pp. 17–26. Springer, Heidelberg (2010)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intel. 22(8), 888–905 (2000)
Meilǎ, M., Shi, J.: A random walks view of spectral segmentation. In: Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics, pp. 92–97 (2001)
Chorin, A.J., Kast, A.P., Kupferman, R.: Unresolved computation and optimal predictions. Comm. Pure Appl. Math. 52(10), 1231–1254 (1999)
Chorin, A.J.: Conditional expectations and renormalization. Multi. Model. Simul. 1, 105–118 (2003)
Lovasz, L.: Random walks on graphs: A survey. Combinatorics, Paul Erdos is Eighty 2, 1–46 (1993)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York (2001)
Chung, F.: Spectral Graph Theory. American Mathematical Society, Rhode Island (1997)
Zachary, W.: An information flow model for conflict and fission in small groups. J. Anthrop. Res. 33(4), 452–473 (1977)
Lusseau, D.: The emergent properties of a dolphin social network. Proceedings of the Royal Society B: Biological Sciences 270, 186–188 (2003)
Lusseau, D., Schneider, K., Boisseau, O., Haase, P., Slooten, E., Dawson, S.: The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations. Behavioral Ecology and Sociobiology 54(4), 396–405 (2003)
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
Liu, J. (2010). Comparative Analysis for k-Means Algorithms in Network Community Detection. In: Cai, Z., Hu, C., Kang, Z., Liu, Y. (eds) Advances in Computation and Intelligence. ISICA 2010. Lecture Notes in Computer Science, vol 6382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16493-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-16493-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16492-7
Online ISBN: 978-3-642-16493-4
eBook Packages: Computer ScienceComputer Science (R0)