IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v94y2005i2p344-365.html
   My bibliography  Save this article

Nonlinearity effects in multidimensional scaling

Author

Listed:
  • Gower, John C.
  • Ngouenet, Roger F.

Abstract

When multidimensional scaling of n cases is derived from dissimilarities that are functions of p basic continuous variables, the question arises of how to relate the values of the variables to the configuration of n points. We provide a methodology based on nonlinear biplots that expresses nonlinearity in two ways: (i) each variable is represented by a nonlinear trajectory and (ii) each trajectory is calibrated by an irregular scale. Methods for computing, calibrating and interpreting these trajectories are given and exemplified. Not only are the tools of immediate practical utility but the methodology established assists in a critical appraisal of the consequences of using nonlinear measures in a variety of multidimensional scaling methods.

Suggested Citation

  • Gower, John C. & Ngouenet, Roger F., 2005. "Nonlinearity effects in multidimensional scaling," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 344-365, June.
    • Handle: RePEc:eee:jmvana:v:94:y:2005:i:2:p:344-365
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00110-1
    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. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    2. J. Gower & P. Legendre, 1986. "Metric and Euclidean properties of dissimilarity coefficients," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 5-48, 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. Patrick Groenen & Niël Roux & Sugnet Gardner-Lubbe, 2015. "Spline-based nonlinear biplots," 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. 9(2), pages 219-238, June.
    2. repec:jss:jstsof:30:i12 is not listed on IDEAS
    3. John Gower & Niel Roux & Sugnet Gardner-Lubbe, 2014. "The Canonical Analysis of Distance," Journal of Classification, Springer;The Classification Society, vol. 31(1), pages 107-128, April.
    4. Vines, S.K., 2015. "Predictive nonlinear biplots: Maps and trajectories," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 47-59.
    5. Antonis A. Michis, 2021. "Wavelet Multidimensional Scaling Analysis of European Economic Sentiment Indicators," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 443-480, October.
    6. Fry, J.T. & Slifko, Matt & Leman, Scotland, 2018. "Generalized biplots for stress-based multidimensionally scaled projections," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 340-353.
    7. la Grange, Anthony & le Roux, Niël & Gardner-Lubbe, Sugnet, 2009. "BiplotGUI: Interactive Biplots in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 30(i12).

    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. Fry, J.T. & Slifko, Matt & Leman, Scotland, 2018. "Generalized biplots for stress-based multidimensionally scaled projections," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 340-353.
    2. Sewell, Daniel K., 2018. "Visualizing data through curvilinear representations of matrices," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 255-270.
    3. Guohuan Su & Adam Mertel & Sébastien Brosse & Justin M. Calabrese, 2023. "Species invasiveness and community invasibility of North American freshwater fish fauna revealed via trait-based analysis," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    4. Kohei Adachi & Nickolay T. Trendafilov, 2016. "Sparse principal component analysis subject to prespecified cardinality of loadings," Computational Statistics, Springer, vol. 31(4), pages 1403-1427, December.
    5. Norman Cliff, 1962. "Analytic rotation to a functional relationship," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 283-295, September.
    6. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    7. Adele Ravagnani & Fabrizio Lillo & Paola Deriu & Piero Mazzarisi & Francesca Medda & Antonio Russo, 2024. "Dimensionality reduction techniques to support insider trading detection," Papers 2403.00707, arXiv.org, revised May 2024.
    8. Alfredo García-Hiernaux & José Casals & Miguel Jerez, 2012. "Estimating the system order by subspace methods," Computational Statistics, Springer, vol. 27(3), pages 411-425, September.
    9. la Grange, Anthony & le Roux, Niël & Gardner-Lubbe, Sugnet, 2009. "BiplotGUI: Interactive Biplots in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 30(i12).
    10. Mitzi Cubilla‐Montilla & Ana‐Belén Nieto‐Librero & Ma Purificación Galindo‐Villardón & Ma Purificación Vicente Galindo & Isabel‐María Garcia‐Sanchez, 2019. "Are cultural values sufficient to improve stakeholder engagement human and labour rights issues?," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 26(4), pages 938-955, July.
    11. Michael Brusco & J Dennis Cradit & Douglas Steinley, 2021. "A comparison of 71 binary similarity coefficients: The effect of base rates," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-19, April.
    12. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
    13. Jos Berge & Henk Kiers, 1993. "An alternating least squares method for the weighted approximation of a symmetric matrix," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 115-118, March.
    14. Shimeng Huang & Henry Wolkowicz, 2018. "Low-rank matrix completion using nuclear norm minimization and facial reduction," Journal of Global Optimization, Springer, vol. 72(1), pages 5-26, September.
    15. Balepur, Prashant Narayan, 1998. "Impacts of Computer-Mediated Communication on Travel and Communication Patterns: The Davis Community Network Study," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt6cb1f85c, Institute of Transportation Studies, UC Berkeley.
    16. Niemann, Helen & Moehrle, Martin G. & Frischkorn, Jonas, 2017. "Use of a new patent text-mining and visualization method for identifying patenting patterns over time: Concept, method and test application," Technological Forecasting and Social Change, Elsevier, vol. 115(C), pages 210-220.
    17. Antti J. Tanskanen & Jani Lukkarinen & Kari Vatanen, 2016. "Random selection of factors preserves the correlation structure in a linear factor model to a high degree," Papers 1604.05896, arXiv.org, revised Dec 2018.
    18. Ali Habibnia & Esfandiar Maasoumi, 2021. "Forecasting in Big Data Environments: An Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet)," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 363-381, December.
    19. Michael J. Greenacre & Patrick J. F. Groenen, 2016. "Weighted Euclidean Biplots," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 442-459, October.
    20. Jin-Xing Liu & Yong Xu & Chun-Hou Zheng & Yi Wang & Jing-Yu Yang, 2012. "Characteristic Gene Selection via Weighting Principal Components by Singular Values," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-10, 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:eee:jmvana:v:94:y:2005:i:2:p:344-365. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.