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Abstract

Cluster ensembles are collections of individual solutions to a given clustering problem which are useful or necessary to consider in a wide range of applications. Aggregating these to a “common” solution amounts to finding a consensus clustering, which can be characterized in a general optimization framework. We discuss recent conceptual and computational advances in this area, and indicate how these can be used for analyzing the structure in cluster ensembles by clustering its elements.

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References

  • BEZDEK, J. C. (1974): Numerical taxonomy with fuzzy sets. Journal of Mathematical Biology, 1, 57–71.

    Article  MATH  MathSciNet  Google Scholar 

  • BREIMAN, L. (1996): Bagging predictors. Machine Learning, 24(2), 123–140.

    MATH  MathSciNet  Google Scholar 

  • DAY, W. H. E. (1986): Foreword: Comparison and consensus of classifications. Journal of Classification, 3, 183–185.

    Article  Google Scholar 

  • DIETTERICH, T. G. (2002): Ensemble learning. In: M. A. Arbib (Ed.): The Handbook of Brain Theory and Neural Networks. The MIT Press, Cambridge, MA, 405–408.

    Google Scholar 

  • DIMITRIADOU, E., WEINGESSEL, A. and HORNIK, K. (2001): Voting-merging: An ensemble method for clustering. In: G. Dorffner, H. Bischof and K. Hornik (Eds.): Artificial Neural Networks — ICANN 2001, volume 2130 of LNCS. Springer Verlag, 217–224.

    Google Scholar 

  • DIMITRIADOU, E., WEINGESSEL, A. and HORNIK, K. (2002): A combination scheme for fuzzy clustering. International Journal of Pattern Recognition and Artificial Intelligence, 16(7), 901–912.

    Article  Google Scholar 

  • DUDOIT, S. and FRIDLYAND, J. (2002): A prediction-based resampling method to estimate the number of clusters in a dataset. Genome Biology, 3(7), 0036.1–0036.21.

    Article  Google Scholar 

  • FRALEY, C. and RAFTERY, A. E. (2002): Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association, 97, 611–631. URL http://www.stat.washington.edu/mclust.

    Article  MathSciNet  Google Scholar 

  • FRED, A. L. N. and JAIN, A. K. (2002): Data clustering using evidence accumulation. In: Proceedings of the 16th International Conference on Pattern Recognition (ICPR 2002), 276–280.

    Google Scholar 

  • FRIEDMAN, J., HASTIE, T. and TIBSHIRANI, R. (2000): Additive logistic regression: A statistical view of boosting. The Annals of Statistics, 28(2), 337–407.

    Article  MathSciNet  Google Scholar 

  • GORDON, A. D. and VICHI, M. (1998): Partitions of partitions. Journal of Classification, 15, 265–285.

    Article  Google Scholar 

  • GORDON, A. D. and VICHI, M. (2001): Fuzzy partition models for fitting a set of partitions. Psychometrika, 66(2), 229–248.

    Article  MathSciNet  Google Scholar 

  • HOETING, J., MADIGAN, D., RAFTERY, A. and VOLINSKY, C. (1999): Bayesian model averaging: A tutorial. Statistical Science, 14, 382–401.

    Article  MathSciNet  Google Scholar 

  • HUBERT, L. and ARABIE, P. (1985): Comparing partitions. Journal of Classification, 2, 193–218.

    Article  Google Scholar 

  • JAIN, A. K. and DUBES, R. C. (1988): Algorithms for Clustering Data. Prentice Hall, New Jersey.

    Google Scholar 

  • KATZ, L. and POWELL, J. H. (1953): A proposed index of the conformity of one sociometric measurement to another. Psychometrika, 18, 149–256.

    Google Scholar 

  • KRIEGER, A. M. and GREEN, P. E. (1999): A generalized Rand-index method for consensus clustering of separate partitions of the same data base. Journal of Classification, 16, 63–89.

    Article  Google Scholar 

  • LEISCH, F. (1999): Bagged clustering. Working Paper 51, SFB “Adaptive Information Systems and Modeling in Economics and Management Science”. URL http://www.ci.tuwien.ac.at/~leisch/papers/wp51.ps.

    Google Scholar 

  • MESSATFA, H. (1992): An algorithm to maximize the agreement between partitions. Journal of Classification, 9, 5–15.

    MATH  MathSciNet  Google Scholar 

  • OLIVEIRA, C. A. S. and PARDALOS, P. M. (2004): Randomized parallel algorithms for the multidimensional assignment problem. Applied Numerical Mathematics, 49(1), 117–133.

    Article  MathSciNet  Google Scholar 

  • PAPADIMITRIOU, C. and STEIGLITZ, K. (1982): Combinatorial Optimization: Algorithms and Complexity. Prentice Hall, Englewood Cliffs.

    Google Scholar 

  • RAND, W. M. (1971): Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336).

    Google Scholar 

  • STREHL, A. and GHOSH, J. (2002): Cluster ensembles — a knowledge reuse framework for combining multiple partitions. Journal on Machine Learning Research, 3, 583–617.

    Article  MathSciNet  Google Scholar 

  • VICHI, M. (1999): One-mode classification of a three-way data matrix. Journal of Classification, 16, 27–44.

    Article  MATH  Google Scholar 

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© 2005 Springer-Verlag Berlin · Heidelberg

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Hornik, K. (2005). Cluster Ensembles. In: Weihs, C., Gaul, W. (eds) Classification — the Ubiquitous Challenge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28084-7_6

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