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Weighted and robust archetypal analysis

Author

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  • Eugster, Manuel J.A.
  • Leisch, Friedrich

Abstract

Archetypal analysis represents observations in a multivariate data set as convex combinations of a few extremal points lying on the boundary of the convex hull. Data points which vary from the majority have great influence on the solution; in fact one outlier can break down the archetype solution. The original algorithm is adapted to be a robust M-estimator and an iteratively reweighted least squares fitting algorithm is presented. As a required first step, the weighted archetypal problem is formulated and solved. The algorithm is demonstrated using an artificial example, a real world example and a detailed simulation study.

Suggested Citation

  • Eugster, Manuel J.A. & Leisch, Friedrich, 2011. "Weighted and robust archetypal analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1215-1225, March.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1215-1225
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    References listed on IDEAS

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    1. Stephan Morgenthaler, 2007. "A survey of robust statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 271-293, February.
    2. Giovanni C. Porzio & Giancarlo Ragozini & Domenico Vistocco, 2008. "On the use of archetypes as benchmarks," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 419-437, September.
    3. Stephan Morgenthaler, 2007. "A survey of robust statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(1), pages 171-172, June.
    4. Stephan Morgenthaler, 2007. "A survey of robust statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 271-293, February.
    5. Sara Dolnicar & Friedrich Leisch, 2010. "Evaluation of structure and reproducibility of cluster solutions using the bootstrap," Marketing Letters, Springer, vol. 21(1), pages 83-101, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Seiler, Christian & Wohlrabe, Klaus, 2013. "Archetypal scientists," Journal of Informetrics, Elsevier, vol. 7(2), pages 345-356.
    2. Epifanio, Irene, 2016. "Functional archetype and archetypoid analysis," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 24-34.
    3. Moliner, Jesús & Epifanio, Irene, 2019. "Robust multivariate and functional archetypal analysis with application to financial time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 195-208.
    4. Firouzeh Noghrehchi & Jakub Stoklosa & Spiridon Penev, 2020. "Multiple imputation and functional methods in the presence of measurement error and missingness in explanatory variables," Computational Statistics, Springer, vol. 35(3), pages 1291-1317, September.
    5. Irene Epifanio & María Victoria Ibáñez & Amelia Simó, 2018. "Archetypal shapes based on landmarks and extension to handle missing data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 705-735, September.
    6. Vinué, Guillermo & Epifanio, Irene & Alemany, Sandra, 2015. "Archetypoids: A new approach to define representative archetypal data," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 102-115.
    7. Guillermo Vinue & Irene Epifanio, 2021. "Robust archetypoids for anomaly detection in big functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 437-462, June.

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