Abstract
In this paper we deal with data stated under the form of a binary relation between objects and properties. We propose an approach for clustering the objects and labeling them with characteristic subsets of properties. The approach is based on a parallel between formal concept analysis and graph clustering. The problem is made tricky due to the fact that generally there is no partitioning of the objects that can be associated with a partitioning of properties. Indeed a relevant partition of objects may exist, whereas it is not the case for properties. In order to obtain a conceptual clustering of the objects, we work with a bipartite graph relating objects with formal concepts. Experiments on artificial benchmarks and real examples show the effectiveness of the method, more particularly the fact that the results remain stable when an increasing number of properties are shared between objects of different clusters.
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.
Similar content being viewed by others
References
Bain, M.: Structured Features from Concept Lattices for Unsupervised Learning and Classification. In: McKay, B., Slaney, J.K. (eds.) Canadian AI 2002. LNCS (LNAI), vol. 2557, pp. 557–568. Springer, Heidelberg (2002)
Barber, M.J.: Modularity and community detection in bipartite networks. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 76(6) (December 2007)
Busygin, S., Prokopyev, O., Pardalos, P.M.: Biclustering in data mining. Computers and Operations Research 35(9), 2964–2987 (2008)
Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70(6) (December 2004)
Danon, L., Díaz-Guilera, A., Duch, J., Arenas, A.: Comparing community structure identification. Journal of Statistical Mechanics: Theory and Experiment 2005(09), P09008 (2005)
Delvenne, J.-C., Yaliraki, S.N., Barahona, M.: Stability of graph communities across time scales. Proc. of the National Academy of Sciences of the USA 107(29), 12755–12760 (2010)
Dhillon, I.S.: Co-clustering documents and words using bipartite spectral graph partitioning. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 269–274. ACM, San Francisco (2001)
Dubois, D., Dupin de Saint-Cyr, F., Prade, H.: A possibility theoretic view of formal concept analysis. Fundamenta Informaticae 75(1), 195–213 (2007)
Dubois, D., Prade, H.: Possibility theory and formal concept analysis: Characterizing independent sub-contexts. Fuzzy Sets and Systems 196, 4–16 (2012)
Fu, H., Nguifo, E.M.: A Parallel Algorithm to Generate Formal Concepts for Large Data. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 394–401. Springer, Heidelberg (2004)
Ganter, B., Wille, R.: Formal Concept Analysis. Springer (1999)
Gaume, B., Navarro, E., Prade, H.: A Parallel between Extended Formal Concept Analysis and Bipartite Graphs Analysis. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS (LNAI), vol. 6178, pp. 270–280. Springer, Heidelberg (2010)
Gaume, B., Navarro, E., Prade, H.: Clustering bipartite graphs in terms of approximate formal concepts and sub-contexts. IJCIS (to be published, 2012)
Gonçalves, T., Moura-Pires, F.: An Attribute Redundancy Measure for Clustering. In: Mercer, R.E. (ed.) Canadian AI 1998. LNCS, vol. 1418, pp. 273–284. Springer, Heidelberg (1998)
Hu, T., Qu, C., Lim, C., Yuan Sung, T.S., Zhou, W.: Preserving patterns in bipartite graph partitioning. In: 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2006), pp. 489–496. IEEE Computer Society, Washington, USA (2006)
Lancichinetti, A., Fortunato, S.: Community detection algorithms: A comparative analysis. Phys. Rev. E 80(5), 056117 (2009)
Liu, X., Murata, T.: Evaluating community structure in bipartite networks. In: Elmagarmid, A.K., Agrawal, D. (eds.) Proceedings of the 2010 IEEE Second International Conference on Social Computing, SocialCom / IEEE International Conference on Privacy, Security, Risk and Trust, PASSAT 2010, Minneapolis, USA, pp. 576–581. IEEE Computer Society (2010)
Rosvall, M., Bergstrom, C.T.: Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences 105(4), 1118–1123 (2008)
Schaeffer, S.E.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Navarro, E., Prade, H., Gaume, B. (2012). Clustering Sets of Objects Using Concepts-Objects Bipartite Graphs. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-33362-0_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33361-3
Online ISBN: 978-3-642-33362-0
eBook Packages: Computer ScienceComputer Science (R0)