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Archetypoids: A new approach to define representative archetypal data

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  • Vinué, Guillermo
  • Epifanio, Irene
  • Alemany, Sandra

Abstract

The new concept archetypoids is introduced. Archetypoid analysis represents each observation in a dataset as a mixture of actual observations in the dataset, which are pure type or archetypoids. Unlike archetype analysis, archetypoids are real observations, not a mixture of observations. This is relevant when existing archetypal observations are needed, rather than fictitious ones. An algorithm is proposed to find them and some of their theoretical properties are introduced. It is also shown how they can be obtained when only dissimilarities between observations are known (features are unavailable). Archetypoid analysis is illustrated in two design problems and several examples, comparing them with the archetypes, the nearest observations to them and other unsupervised methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:87:y:2015:i:c:p:102-115
    DOI: 10.1016/j.csda.2015.01.018
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    References listed on IDEAS

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    1. Eugster, Manuel J.A. & Leisch, Friedrich, 2011. "Weighted and robust archetypal analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1215-1225, March.
    2. Eugster, Manuel J. A. & Leisch, Friedrich, 2009. "From Spider-Man to Hero — Archetypal Analysis in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 30(i08).
    3. Manuel J. A. Eugster, 2012. "Performance Profiles based on Archetypal Athletes," International Journal of Performance Analysis in Sport, Taylor & Francis Journals, vol. 12(1), pages 166-187, April.
    4. Seiler, Christian & Wohlrabe, Klaus, 2013. "Archetypal scientists," Journal of Informetrics, Elsevier, vol. 7(2), pages 345-356.
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    Citations

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    Cited by:

    1. Aurea Grané & Alpha A. Sow-Barry, 2021. "Visualizing Profiles of Large Datasets of Weighted and Mixed Data," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    2. Sabine Gralka & Klaus Wohlrabe, 2022. "Classifying top economists using archetypoid analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 29(14), pages 1342-1346, August.
    3. Vinué, Guillermo, 2017. "Anthropometry: An R Package for Analysis of Anthropometric Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i06).
    4. Irene Epifanio & Vicent Gimeno & Ximo Gual-Arnau & M. Victoria Ibáñez-Gual, 2020. "A New Geometric Metric in the Shape and Size Space of Curves in R n," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    5. Aleix Alcacer & Irene Epifanio & M Victoria Ibáñez & Amelia Simó & Alfredo Ballester, 2020. "A data-driven classification of 3D foot types by archetypal shapes based on landmarks," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-19, January.
    6. Klaus Wohlrabe & Sabine Gralka, 2020. "Using archetypoid analysis to classify institutions and faculties of economics," Scientometrics, Springer;Akadémiai Kiadó, vol. 123(1), pages 159-179, April.
    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.
    8. Epifanio, Irene, 2016. "Functional archetype and archetypoid analysis," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 24-34.
    9. Kyunghee Han & Pantelis Z Hadjipantelis & Jane-Ling Wang & Michael S Kramer & Seungmi Yang & Richard M Martin & Hans-Georg Müller, 2018. "Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
    10. 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.

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