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Unsupervised Initialization of Archetypal Analysis and Proportional Membership Fuzzy Clustering

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Intelligent Data Engineering and Automated Learning – IDEAL 2019 (IDEAL 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11872))

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Abstract

This paper further investigates and compares a method for fuzzy clustering which retrieves pure individual types from data, known as the fuzzy clustering with proportional membership (FCPM), with the FurthestSum Archetypal Analysis algorithm (FS-AA). The Anomalous Pattern (AP) initialization algorithm, an algorithm that sequentially extracts clusters one by one in a manner similar to principal component analysis, is shown to outperform the FurthestSum not only by improving the convergence of FCPM and AA algorithms but also to be able to model the number of clusters to extract from data.

A study comparing nine information-theoretic validity indices and the soft ARI has shown that the soft Normalized Mutual Information max (\(NMI_{sM}\)) and the Adjusted Mutual Information (AMI) indices are more adequate to access the quality of FCPM and AA partitions than soft internal validity indices. The experimental study was conducted exploring a collection of 99 synthetic data sets generated from a proper data generator, the FCPM-DG, covering various dimensionalities as well as 18 benchmark data sets from machine learning.

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References

  1. Bezdek, J.: A Primer on Cluster Analysis: 4 Basic Methods That (Usually) Work, 1st edn. Design Publishing (2017)

    Google Scholar 

  2. Chen, Y., Mairal, J., Harchaoui, Z.: Fast and robust archetypal analysis for representation learning. In: 2014 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1478–1485 (2014)

    Google Scholar 

  3. Cutler, A., Breiman, L.: Archetypal analysis. Technometrics 36(4), 338–347 (1994)

    Article  MathSciNet  Google Scholar 

  4. Eugster, M., Leisch, F.: From Spider-man to hero - archetypal analysis. R. J. Stat. Softw. 30(8), 1–23 (2009)

    Google Scholar 

  5. Eugster, M.: Performance profiles based on archetypal athletes. Int. J. Perform. Anal. Sport. 12(1), 166–187 (2012)

    Article  Google Scholar 

  6. Hannachi, A., Trendafilov, N.: Archetypal analysis: mining weather and climate extremes. J. Clim. 30(17), 6927–6944 (2017)

    Article  Google Scholar 

  7. Lei, Y., Bezdek, J., Chan, J., Vinh, N.X., Romano, S., Bailey, J.: Extending information-theoretic validity indices for fuzzy clustering. IEEE Trans. Fuzzy Syst. 25, 1013–1018 (2017)

    Article  Google Scholar 

  8. Mendes, G.S., Nascimento, S.: A study of fuzzy clustering to archetypal analysis. In: Yin, H., Camacho, D., Novais, P., Tallón-Ballesteros, A.J. (eds.) IDEAL 2018. LNCS, vol. 11315, pp. 250–261. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03496-2_28

    Chapter  Google Scholar 

  9. Mirkin, B.: Clustering for Data Mining: A Data Recovery Approach. Chapman & Hall /CRC Press, Boca Raton (2005)

    Google Scholar 

  10. Mirkin, B.: Core Data Analysis: Summarization, Correlation, and Visualization. Undergraduate Topics in Computer Science, 524 pp. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-00271-8

    Book  Google Scholar 

  11. Mørup, M., Hansen, L.: Archetypal analysis for machine learning and data mining. Neurocomputing 80, 54–63 (2012)

    Article  Google Scholar 

  12. Nascimento, S., Mirkin, B., Moura-Pires, F.: Modeling proportional membership in fuzzy clustering. IEEE Trans. Fuzzy Syst. 11(2), 173–186 (2003)

    Article  Google Scholar 

  13. Nascimento, S.: Fuzzy Clustering Via Proportional Membership Model, 178 pp. IOS Press, Amsterdam (2005)

    Google Scholar 

  14. Nascimento, S., Franco, P.: Segmentation of upwelling regions in sea surface temperature images via unsupervised fuzzy clustering. In: Corchado, E., Yin, H. (eds.) IDEAL 2009. LNCS, vol. 5788, pp. 543–553. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04394-9_66

    Chapter  Google Scholar 

  15. Porzio, C., Ragozini, G., Vistocco, D.: On the use of archetypes as benchmarks. Appl. Stoch. Model. Bus. Ind. 54(5), 419–437 (2008)

    Article  MathSciNet  Google Scholar 

  16. UCI Machine Learning Repository. http://archive.ics.uci.edu/ml. Accessed 27 July 2018

  17. Vinh, N.X., Epps, J., Bailey, J.: Information theoretic measures for clusterings comparison: variants, properties, normalization and correction for chance. J. Mach. Learn. Res. 11, 2837–2854 (2010)

    MathSciNet  MATH  Google Scholar 

  18. Wynen, D., Schmid, C., Mairal, J.: Unsupervised learning of artistic styles with archetypal style analysis. In: Proceedings of the 32nd Conference on Neural Information Processing Systems (NIPS 2018), pp. 6584–6593 (2018)

    Google Scholar 

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Acknowledgments

S.N. acknowledges the support by FCT/MCTES, NOVA LINCS (UID/CEC/04516/2019). The authors are thankful to the anonymous reviewers for their insightful and constructive comments that allowed to improve the paper.

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Authors and Affiliations

  1. Computer Science Department and NOVA LINCS, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisbon, Portugal

    Susana Nascimento & Nuno Madaleno

Authors
  1. Susana Nascimento
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  2. Nuno Madaleno
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Corresponding author

Correspondence to Susana Nascimento .

Editor information

Editors and Affiliations

  1. University of Manchester, Manchester, UK

    Hujun Yin

  2. Technical University of Madrid, Madrid, Spain

    David Camacho

  3. University of Birmingham, Birmingham, UK

    Peter Tino

  4. University of Huelva, Huelva, Spain

    Antonio J. Tallón-Ballesteros

  5. University of Exeter, Exeter, UK

    Ronaldo Menezes

  6. University of Manchester, Manchester, UK

    Richard Allmendinger

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Nascimento, S., Madaleno, N. (2019). Unsupervised Initialization of Archetypal Analysis and Proportional Membership Fuzzy Clustering. In: Yin, H., Camacho, D., Tino, P., Tallón-Ballesteros, A., Menezes, R., Allmendinger, R. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2019. IDEAL 2019. Lecture Notes in Computer Science(), vol 11872. Springer, Cham. https://doi.org/10.1007/978-3-030-33617-2_2

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  • DOI: https://doi.org/10.1007/978-3-030-33617-2_2

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