IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i3p1215-1225.html
   My bibliography  Save this article

Weighted and robust archetypal analysis

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00405-6
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Seiler, Christian & Wohlrabe, Klaus, 2013. "Archetypal scientists," Journal of Informetrics, Elsevier, vol. 7(2), pages 345-356.
    4. 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.
    5. 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.
    6. Epifanio, Irene, 2016. "Functional archetype and archetypoid analysis," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 24-34.
    7. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roland Fried & Herold Dehling, 2011. "Robust nonparametric tests for the two-sample location problem," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(4), pages 409-422, November.
    2. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    3. Leonid Hanin, 2021. "Cavalier Use of Inferential Statistics Is a Major Source of False and Irreproducible Scientific Findings," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    4. Youssef Allouah & Rachid Guerraoui & L^e-Nguy^en Hoang & Oscar Villemaud, 2022. "Robust Sparse Voting," Papers 2202.08656, arXiv.org, revised Jan 2024.
    5. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    6. Alfons, A. & Ates, N.Y. & Groenen, P.J.F., 2018. "A Robust Bootstrap Test for Mediation Analysis," ERIM Report Series Research in Management ERS-2018-005-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. repec:jss:jstsof:32:i03 is not listed on IDEAS
    8. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
    9. George Djolov, 2014. "Business concentration through the eyes of the HHI," International Journal of Business and Economic Sciences Applied Research (IJBESAR), International Hellenic University (IHU), Kavala Campus, Greece (formerly Eastern Macedonia and Thrace Institute of Technology - EMaTTech), vol. 7(2), pages 105-127, September.
    10. A van Giessen & K G M Moons & G A de Wit & W M M Verschuren & J M A Boer & H Koffijberg, 2015. "Tailoring the Implementation of New Biomarkers Based on Their Added Predictive Value in Subgroups of Individuals," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-14, January.
    11. Paola Costantini & Marielle Linting & Giovanni C. Porzio, 2010. "Mining performance data through nonlinear PCA with optimal scaling," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(1), pages 85-101, January.
    12. Hajibaba, Homa & Gretzel, Ulrike & Leisch, Friedrich & Dolnicar, Sara, 2015. "Crisis-resistant tourists," Annals of Tourism Research, Elsevier, vol. 53(C), pages 46-60.
    13. Ana Alina Tudoran, 2022. "A machine learning approach to identifying decision-making styles for managing customer relationships," Electronic Markets, Springer;IIM University of St. Gallen, vol. 32(1), pages 351-374, March.
    14. Amaro, Suzanne & Duarte, Paulo & Henriques, Carla, 2016. "Travelers’ use of social media: A clustering approach," Annals of Tourism Research, Elsevier, vol. 59(C), pages 1-15.
    15. 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.
    16. Maik Dehnert & Josephine Schumann, 2022. "Uncovering the digitalization impact on consumer decision-making for checking accounts in banking," Electronic Markets, Springer;IIM University of St. Gallen, vol. 32(3), pages 1503-1528, September.
    17. Seiler, Christian & Wohlrabe, Klaus, 2013. "Archetypal scientists," Journal of Informetrics, Elsevier, vol. 7(2), pages 345-356.
    18. Sara Dolnicar & Friedrich Leisch, 2017. "Using segment level stability to select target segments in data-driven market segmentation studies," Marketing Letters, Springer, vol. 28(3), pages 423-436, September.
    19. Pierpaolo D'Urso & Girish Prayag & Marta Disegna & Riccardo Massari, 2013. "Market Segmentation using Bagged Fuzzy C–Means (BFCM): Destination Image of Western Europe among Chinese Travellers," BEMPS - Bozen Economics & Management Paper Series BEMPS13, Faculty of Economics and Management at the Free University of Bozen.
    20. Dolnicar, Sara & Grün, Bettina & Leisch, Friedrich, 2016. "Increasing sample size compensates for data problems in segmentation studies," Journal of Business Research, Elsevier, vol. 69(2), pages 992-999.
    21. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1215-1225. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.