IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v12y2018i3d10.1007_s11634-017-0297-7.html
   My bibliography  Save this article

Archetypal shapes based on landmarks and extension to handle missing data

Author

Listed:
  • Irene Epifanio

    (Universitat Jaume I)

  • María Victoria Ibáñez

    (Universitat Jaume I)

  • Amelia Simó

    (Universitat Jaume I)

Abstract

Archetype and archetypoid analysis are extended to shapes. The objective is to find representative shapes. Archetypal shapes are pure (extreme) shapes. We focus on the case where the shape of an object is represented by a configuration matrix of landmarks. As shape space is not a vectorial space, we work in the tangent space, the linearized space about the mean shape. Then, each observation is approximated by a convex combination of actual observations (archetypoids) or archetypes, which are a convex combination of observations in the data set. These tools can contribute to the understanding of shapes, as in the usual multivariate case, since they lie somewhere between clustering and matrix factorization methods. A new simplex visualization tool is also proposed to provide a picture of the archetypal analysis results. We also propose new algorithms for performing archetypal analysis with missing data and its extension to incomplete shapes. A well-known data set is used to illustrate the methodologies developed. The proposed methodology is applied to an apparel design problem in children.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:12:y:2018:i:3:d:10.1007_s11634-017-0297-7
    DOI: 10.1007/s11634-017-0297-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-017-0297-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11634-017-0297-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Ian L. Dryden & András Zempléni, 2006. "Extreme shape analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(1), pages 103-121, January.
    2. Eugster, Manuel J.A. & Leisch, Friedrich, 2011. "Weighted and robust archetypal analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1215-1225, March.
    3. 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.
    4. 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).
    5. Ayala, G. & Epifanio, I. & Simo, A. & Zapater, V., 2006. "Clustering of spatial point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 1016-1032, February.
    6. Vincenzo Viscosi & Andrea Cardini, 2011. "Leaf Morphology, Taxonomy and Geometric Morphometrics: A Simplified Protocol for Beginners," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-20, October.
    7. Epifanio, Irene, 2016. "Functional archetype and archetypoid analysis," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 24-34.
    8. F. James Rohlf, 1999. "Shape Statistics: Procrustes Superimpositions and Tangent Spaces," Journal of Classification, Springer;The Classification Society, vol. 16(2), pages 197-223, July.
    9. Jiejun Du & Ian L. Dryden & Xianzheng Huang, 2015. "Size and Shape Analysis of Error-Prone Shape Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 368-379, 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. 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.
    2. Amelia Simó & M. Victoria Ibáñez & Irene Epifanio & Vicent Gimeno, 2020. "Generalized partially linear models on Riemannian manifolds," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 641-661, June.

    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. 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.
    2. Seiler, Christian & Wohlrabe, Klaus, 2013. "Archetypal scientists," Journal of Informetrics, Elsevier, vol. 7(2), pages 345-356.
    3. 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.
    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. Epifanio, Irene, 2016. "Functional archetype and archetypoid analysis," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 24-34.
    6. 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.
    7. 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.
    8. Brandon P Hedrick & Peter Dodson, 2013. "Lujiatun Psittacosaurids: Understanding Individual and Taphonomic Variation Using 3D Geometric Morphometrics," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-13, August.
    9. Katherine L Bell & Christopher A Hamm & Arthur M Shapiro & Chris C Nice, 2017. "Sympatric, temporally isolated populations of the pine white butterfly Neophasia menapia, are morphologically and genetically differentiated," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-17, May.
    10. Abdul Suleman, 2017. "On ill-conceived initialization in archetypal analysis," 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. 11(4), pages 785-808, December.
    11. 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.
    12. Levente Juhász & Adam Rousell & Jamal Jokar Arsanjani, 2016. "Technical Guidelines to Extract and Analyze VGI from Different Platforms," Data, MDPI, vol. 1(3), pages 1-22, September.
    13. Eugster, Manuel J.A. & Leisch, Friedrich, 2011. "Weighted and robust archetypal analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1215-1225, March.
    14. 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.
    15. Manuel Dehon & Denis Michez & André Nel & Michael S Engel & Thibaut De Meulemeester, 2014. "Wing Shape of Four New Bee Fossils (Hymenoptera: Anthophila) Provides Insights to Bee Evolution," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-16, October.
    16. Lea A I Vaas & Johannes Sikorski & Victoria Michael & Markus Göker & Hans-Peter Klenk, 2012. "Visualization and Curve-Parameter Estimation Strategies for Efficient Exploration of Phenotype Microarray Kinetics," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-18, April.
    17. 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.
    18. Sjoerd Beugelsdijk & Hester van Herk & Robbert Maseland, 2022. "The Nature of Societal Conflict in Europe; an Archetypal Analysis of the Postmodern Cosmopolitan, Rural Traditionalist and Urban Precariat," Journal of Common Market Studies, Wiley Blackwell, vol. 60(6), pages 1701-1722, November.
    19. Luis Gutiérrez & Ramsés H. Mena & Carlos Díaz-Avalos, 2020. "Linear models for statistical shape analysis based on parametrized closed curves," Statistical Papers, Springer, vol. 61(3), pages 1213-1229, June.
    20. Sean T. Osis & Blayne A. Hettinga & Shari L. Macdonald & Reed Ferber, 2015. "A novel method to evaluate error in anatomical marker placement using a modified generalized Procrustes analysis," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 18(10), pages 1108-1116, July.

    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:spr:advdac:v:12:y:2018:i:3:d:10.1007_s11634-017-0297-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.