Abstract
The Evidence Accumulation Clustering (EAC) paradigm is a clustering ensemble method which derives a consensus partition from a collection of base clusterings obtained using different algorithms. It collects from the partitions in the ensemble a set of pairwise observations about the co-occurrence of objects in a same cluster and it uses these co-occurrence statistics to derive a similarity matrix, referred to as co-association matrix. The Probabilistic Evidence Accumulation for Clustering Ensembles (PEACE) algorithm is a principled approach for the extraction of a consensus clustering from the observations encoded in the co-association matrix based on a probabilistic model for the co-association matrix parameterized by the unknown assignments of objects to clusters. In this paper we extend the PEACE algorithm by deriving a consensus solution according to a MAP approach with Dirichlet priors defined for the unknown probabilistic cluster assignments. In particular, we study the positive regularization effect of Dirichlet priors on the final consensus solution with both synthetic and real benchmark data.
An erratum to this chapter is available at 10.1007/978-3-319-12610-4_20
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-319-12610-4_20
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
Similar content being viewed by others
References
Fred, A.: Finding consistent clusters in data partitions. In: Kittler, J., Roli, F. (eds.) Multiple Classifier Systems, pp. 309–318. Springer, Heidelberg (2001)
Fred, A., Jain, A.: Data clustering using evidence accumulation. In: Proceedings of the 16th International Conference on Pattern Recognition, pp. 276–280 (2002)
Fred, A., Jain, A.: Combining multiple clustering using evidence accumulation. IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 835–850 (2005)
Rota Bulò, S., Lourenço, A., Fred, A., Pelillo, M.: Pairwise probabilistic clustering using evidence accumulation. In: Proceedings of 2010 International Conference on Structural, Syntactic, and Statistical Pattern Recognition. SSPR&SPR’10, pp. 395–404 (2010)
Lourenço, A., Rota Bulò, S., Rebagliati, N., Figueiredo, M.A.T., Fred, A.L.N., Pelillo, M.: Probabilistic evidence accumulation for clustering ensembles (2013)
Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming, 3rd edn. Springer, Heidelberg (2008)
Boyd, S., Vandenberghe, L.: Convex Optimization, 1st edn. Cambridge University, Cambridge (2004)
Kachurovskii, I.R.: On monotone operators and convex functionals. Uspekhi Mat. Nauk 15(4), 213–215 (1960)
Ghosh, J., Acharya, A.: Cluster ensembles. Wiley Interdisc. Rew. Data Min. Knowl. Disc. 1(4), 305–315 (2011)
Strehl, A., Ghosh, J.: Cluster ensembles—a knowledge reuse framework for combining multiple partitions. J. Mach. Learn. Res. 3, 583–617 (2002)
Topchy, A., Jain, A., Punch, W.: A mixture model of clustering ensembles. In: Proceedings of the SIAM Conference on Data Mining, April 2004
Dimitriadou, E., Weingessel, A., Hornik, K.: A combination scheme for fuzzy clustering. In: AFSS’02, pp. 332–338 (2002)
Ayad, H., Kamel, M.S.: Cumulative voting consensus method for partitions with variable number of clusters. IEEE Trans. Pattern Anal. Mach. Intell. 30(1), 160–173 (2008)
Fern, X.Z., Brodley, C.E.: Solving cluster ensemble problems by bipartite graph partitioning. In: Proc ICML’04 (2004)
Lourenço, A., Fred, A., Figueiredo, M.: A generative dyadic aspect model for evidence accumulation clustering. In: Proceedings of 1st International Conference Similarity-based Pattern Recognition. SIMBAD’11, pp. 104–116. Springer, Heidelberg (2011)
Topchy, A., Jain, A.K., Punch, W.: Clustering ensembles: models of consensus and weak partitions. IEEE Trans. Pattern Anal. Mach. Intell. 27(12), 1866–1881 (2005)
Wang, H., Shan, H., Banerjee, A.: Bayesian cluster ensembles. In: 9th SIAM International Conference on Data Mining (2009)
Griffiths, T.L., Steyvers, M.: Finding scientific topics. Proc. Nat. Acad. Sci. USA 101(Suppl 1), 5228–5235 (2004)
Steyvers, M., Griffiths, T.: Latent semantic analysis: a road to meaning. In: Probabilistic Topic Models. Laurence Erlbaum (2007)
Wang, P., Domeniconi, C., Laskey, K. B.: Nonparametric bayesian clustering ensembles. In: ECML PKDD’10, pp. 435–450 (2010)
Meila, M.: Comparing clusterings by the variation of information. In: Proceedings of the Sixteenth Annual Conference of Computational Learning Theory (COLT). Springer, Heidelberg (2003)
Lourenço, A., Fred, A., Jain, A.K.: On the scalability of evidence accumulation clustering. In: 20th International Conference on Pattern Recognition (ICPR), Istanbul Turkey, pp. 782–785, Aug 2010
Jain, A.K., Dubes, R.: Algorithms for Clustering Data. Prentice Hall, New Jersey (1988)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: NIPS, pp. 849–856. MIT, Cambridge (2001)
Manning, C.D., Raghavan, P., Schtze, H.: Introduction to Information Retrieval. Cambridge University, New York (2008)
Acknowledgments
This work was partially financed by an ERCIM “Alain Bensoussan” Fellowship Programme under the European Union Seventh Framework Programme (FP7/2007–2013), grant agreement n. 246016, by FCT under grants SFRH /PROTEC/49512/2009, PTDC/EEI-SII/2312/2012 (LearningS project) and PEst-OE/ EEI/LA0008/2011, and by the Área Departamental de Engenharia Electronica e Telecomunicações e de Computadores of Instituto Superior de Engenharia de Lisboa, whose support the authors gratefully acknowledge.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Lourenço, A., Rota Bulò, S., Rebagliati, N., Fred, A., Figueiredo, M., Pelillo, M. (2015). A MAP Approach to Evidence Accumulation Clustering. In: Fred, A., De Marsico, M. (eds) Pattern Recognition Applications and Methods. Advances in Intelligent Systems and Computing, vol 318. Springer, Cham. https://doi.org/10.1007/978-3-319-12610-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-12610-4_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12609-8
Online ISBN: 978-3-319-12610-4
eBook Packages: EngineeringEngineering (R0)