IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v128y2018icp340-353.html
   My bibliography  Save this article

Generalized biplots for stress-based multidimensionally scaled projections

Author

Listed:
  • Fry, J.T.
  • Slifko, Matt
  • Leman, Scotland

Abstract

Dimension reduction and visualization are staples of data analytics. Methods such as Principal Component Analysis (PCA) and Multidimensional Scaling (MDS) provide low dimensional (LD) projections of high dimensional (HD) data while preserving an HD relationship between observations. Traditional biplots assign meaning to the LD space of a PCA projection by displaying LD axes for the attributes. These axes, however, are specific to the linear projection used in PCA. Stress-based MDS (s-MDS) projections, which allow for arbitrary stress and dissimilarity functions, require special care when labeling the LD space. An iterative scheme is developed to plot an LD axis for each attribute based on the user-specified stress and dissimilarity metrics. The resulting plot, which contains both the LD projection of observations and attributes, is referred to as the Generalized s-MDS Biplot. The details of the Generalized s-MDS Biplot methodology, its relationship with PCA-derived biplots, and an application to a real dataset are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:340-353
    DOI: 10.1016/j.csda.2018.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301865
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.08.003?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. Gower, John C. & Ngouenet, Roger F., 2005. "Nonlinearity effects in multidimensional scaling," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 344-365, June.
    2. 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.
    3. 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.
    4. Warren Torgerson, 1952. "Multidimensional scaling: I. Theory and method," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 401-419, December.
    5. 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)

    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. repec:jss:jstsof:30:i12 is not listed on IDEAS
    2. 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).
    3. Vines, S.K., 2015. "Predictive nonlinear biplots: Maps and trajectories," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 47-59.
    4. 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.
    5. Gower, John C. & Ngouenet, Roger F., 2005. "Nonlinearity effects in multidimensional scaling," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 344-365, June.
    6. W. J. Krzanowski, 2006. "Sensitivity in Metric Scaling and Analysis of Distance," Biometrics, The International Biometric Society, vol. 62(1), pages 239-244, March.
    7. 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.
    8. C. Horan, 1969. "Multidimensional scaling: Combining observations when individuals have different perceptual structures," Psychometrika, Springer;The Psychometric Society, vol. 34(2), pages 139-165, June.
    9. Alexander Strehl & Joydeep Ghosh, 2003. "Relationship-Based Clustering and Visualization for High-Dimensional Data Mining," INFORMS Journal on Computing, INFORMS, vol. 15(2), pages 208-230, May.
    10. Sewell, Daniel K., 2018. "Visualizing data through curvilinear representations of matrices," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 255-270.
    11. 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.
    12. 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.
    13. Norman Cliff, 1962. "Analytic rotation to a functional relationship," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 283-295, September.
    14. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Venera Tomaselli, 1996. "Multivariate statistical techniques and sociological research," Quality & Quantity: International Journal of Methodology, Springer, vol. 30(3), pages 253-276, August.
    21. 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.

    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:128:y:2018:i:c:p:340-353. 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.