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Practical Initialization of Recursive Mixture-Based Clustering for Non-negative Data

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Informatics in Control, Automation and Robotics (ICINCO 2017)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 495))

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Abstract

The paper provides a practical guide on initialization of the recursive mixture-based clustering of non-negative data. For modeling the non-negative data, mixtures of uniform, exponential, gamma and other distributions can be used. Initialization is known to be an important task for a start of the mixture estimation algorithm. Within the considered recursive approach, the key point of initialization is a choice of initial statistics of the involved prior distributions. The paper describes several initialization techniques for the mentioned types of components that can be beneficial primarily from a practical point of view.

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References

  1. Kárný, M., Kadlec, J., Sutanto, E.L.: Quasi-Bayes estimation applied to normal mixture. In: Rojíček, J., Valečková, M., Kárný, M., Warwick K. (eds.) Preprints of the 3rd European IEEE Workshop on Computer-Intensive Methods in Control and Data Processing, CMP’98 /3./, Prague, CZ, pp. 77–82 (1998)

    Google Scholar 

  2. Kárný, M., et al.: Optimized Bayesian Dynamic Advising: Theory and Algorithms. Springer, London (2006)

    Google Scholar 

  3. Nagy, I., Suzdaleva, E., Kárný, M., Mlynářová, T.: Bayesian estimation of dynamic finite mixtures. Int. J. Adapt. Control. Signal Process. 25(9), 765–787 (2011)

    Article  MathSciNet  Google Scholar 

  4. Nagy, I., Suzdaleva, E.: Algorithms and Programs of Dynamic Mixture Estimation. Unified Approach to Different Types of Components. SpringerBriefs in Statistics. Springer International Publishing, Cham (2017)

    Chapter  Google Scholar 

  5. Roy, A., Pal, A., Garain, U.: JCLMM: a finite mixture model for clustering of circular-linear data and its application to psoriatic plaque segmentation. Pattern Recognit. 66, (2017). https://doi.org/10.1016/j.patcog.2016.12.016

    Article  Google Scholar 

  6. Bouveyron, C., Brunet-Saumard, C.: Model-based clustering of high-dimensional data: a review. Comput. Stat. Data Anal. 71, 52–78 (2014)

    Article  MathSciNet  Google Scholar 

  7. Scrucca, L.: Genetic algorithms for subset selection in model-based clustering. Unsupervised Learning Algorithms, pp. 55–70. Springer International Publishing, Cham (2016)

    Google Scholar 

  8. Fernández, D., Arnold, R., Pledger, S.: Mixture-based clustering for the ordered stereotype model. Comput. Stat. Data Anal. 93, 46–75 (2016)

    Article  MathSciNet  Google Scholar 

  9. Suzdaleva, E., Nagy, I., Mlynářová, T.: Recursive estimation of mixtures of exponential and normal distributions. In: Proceedings of the 8th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, Warsaw, Poland, 24–26 Sept 2015, pp. 137–142 (2015)

    Google Scholar 

  10. Browne, R.P., McNicholas, P.D.: A mixture of generalized hyperbolic distributions. Can. J. Stat. 43(2), 176–198 (2015)

    Article  MathSciNet  Google Scholar 

  11. Morris, K., McNicholas, P.D.: Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures. Comput. Stat. Data Anal. 97, 133–150 (2016)

    Article  MathSciNet  Google Scholar 

  12. Malsiner-Walli, G., Frühwirth-Schnatter, S., Grün, B.: Model-based clustering based on sparse finite Gaussian mixtures. Stat. Comput. 26(1–2), 303–324 (2016)

    Article  MathSciNet  Google Scholar 

  13. Li, R., Wang, Z., Gu, C., Li, F., Wu, H.: A novel time-of-use tariff design based on Gaussian Mixture Model. Appl. Energy 162, 1530–1536 (2016)

    Article  Google Scholar 

  14. O’Hagan, A., Murphy, T.B., Gormley, I.C., McNicholas, P.D., Karlis, D.: Clustering with the multivariate normal inverse Gaussian distribution. Comput. Stat. Data Anal. 93, 18–30 (2016)

    Article  MathSciNet  Google Scholar 

  15. Suzdaleva, E., Nagy, I., Pecherková, P., Likhonina, R.: Initialization of recursive mixture-based clustering with uniform components. In: Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017), Madrid, Spain, 26–28 July 2017, pp. 449–458 (2017)

    Google Scholar 

  16. Scrucca, L., Raftery, A.E.: Improved initialisation of model-based clustering using Gaussian hierarchical partitions. Adv. Data Anal. Classif. 9(4), 447–460 (2015)

    Article  MathSciNet  Google Scholar 

  17. Melnykov, V., Melnykov, I.: Initializing the EM algorithm in Gaussian mixture models with an unknown number of components. Comput. Stat. Data Anal. 56(6), 1381–1395 (2012)

    Article  MathSciNet  Google Scholar 

  18. Kwedlo, W.: A new method for random initialization of the EM algorithm for multivariate Gaussian mixture learning. In: Burduk, R., Jackowski, K., Kurzynski, M., Wozniak, M., Zolnierek, A. (eds.) Proceedings of the 8th International Conference on Computer Recognition Systems CORES 2013, pp. 81–90. Springer International Publishing, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Shireman, E., Steinley, D., Brusco, M.J.: Examining the effect of initialization strategies on the performance of Gaussian mixture modeling. Behav. Res. Methods 1–12 (2015)

    Google Scholar 

  20. Maitra, R.: Initializing partition-optimization algorithms. IEEE/ACM Trans. Comput. Biol. Bioinform. (TCBB) 6(1), 144–157 (2009)

    Article  MathSciNet  Google Scholar 

  21. Gupta, M.R., Chen, Y.: Theory and use of the EM method. Found. Trends Signal Process. 4(3), 223–296 (2011)

    Google Scholar 

  22. Peterka, V.: Bayesian system identification. In: Eykhoff, P. (ed.) Trends and Progress in System Identification, pp. 239–304. Pergamon Press, Oxford (1981)

    Google Scholar 

  23. Nagy, I., Suzdaleva, E., Mlynářová, T.: Mixture-based clustering non-Gaussian data with fixed bounds. In: Proceedings of the IEEE International Conference Intelligent Systems IS’16, pp. 265–271 (2016)

    Google Scholar 

  24. Suzdaleva, E., Nagy, I., Mlynářová, T.: Expert-based initialization of recursive mixture estimation. In: Proceedings of the IEEE International Conference Intelligent Systems IS’16, pp. 308–315 (2016)

    Google Scholar 

  25. Kárný, M., Nedoma, P., Khailova, N., Pavelková, L.: Prior information in structure estimation. IEE Proc. Control. Theory Appl. 150(6), 643–653 (2003)

    Article  Google Scholar 

  26. Nagy, I., Suzdaleva, E., Pecherková, P.: Comparison of various definitions of proximity in mixture estimation. In: Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO), pp. 527–534 (2016)

    Google Scholar 

  27. Casella, G., Berger R.L.: Statistical Inference, 2nd edn. Duxbury Press (2001)

    Google Scholar 

  28. Jain, A.K.: Data clustering: 50 years beyond K-means. Pattern Recognit. Lett. 31(8), 651–666 (2010)

    Article  Google Scholar 

  29. DeGroot, M.: Optimal Statistical Decisions. McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  30. Spiegel, M.R.: Theory and Problems of Probability and Statistics. McGraw-Hill, New York (1992)

    Google Scholar 

  31. Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Pearson Prentice Hall, Upper Saddle River (2007)

    MATH  Google Scholar 

  32. Elfessi, A., Reineke, D.M.: A Bayesian look at classical estimation: the exponential distribution. J. Stat. Educ. 9(1) (2001)

    Google Scholar 

  33. Minka, T.P.: Estimating a gamma distribution. Microsoft Res. (2002)

    Google Scholar 

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Acknowledgements

The paper was supported by project GAČR GA15-03564S.

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Authors and Affiliations

  1. Department of Signal Processing, The Czech Academy of Sciences, Institute of Information Theory and Automation, Pod vodárenskou věží 4, 18208, Prague, Czech Republic

    Evženie Suzdaleva & Ivan Nagy

  2. Faculty of Transportation Sciences, Czech Technical University, Na Florenci 25, 11000, Prague, Czech Republic

    Ivan Nagy

Authors
  1. Evženie Suzdaleva
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  2. Ivan Nagy
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Corresponding author

Correspondence to Evženie Suzdaleva .

Editor information

Editors and Affiliations

  1. Ford Research and Advanced Engineering, Dearborn, MI, USA

    Oleg Gusikhin

  2. University of Paris-EST Créteil (UPEC), Vitry sur Seine, France

    Kurosh Madani

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Suzdaleva, E., Nagy, I. (2020). Practical Initialization of Recursive Mixture-Based Clustering for Non-negative Data. In: Gusikhin, O., Madani, K. (eds) Informatics in Control, Automation and Robotics . ICINCO 2017. Lecture Notes in Electrical Engineering, vol 495. Springer, Cham. https://doi.org/10.1007/978-3-030-11292-9_34

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