IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v94y2016icp20-32.html
   My bibliography  Save this article

A triplot for multiclass classification visualisation

Author

Listed:
  • Gardner-Lubbe, Sugnet

Abstract

Quadratic discriminant analysis is used when the assumption of equal covariance matrices for linear discrimination does not hold. The Canonical Variate Analysis biplot is used for graphical visualisation to accompany linear discriminant analysis. However, since class specific covariance matrix estimates are needed for quadratic discrimination the canonical transformation cannot be used. An alternative method of visually representing the discrimination and classification process is proposed: representing the sample points, classification regions based on quadratic discriminant analysis and including information on the variables. The methodology is further extended to other forms of multiclass classification and illustrated for support vector machines, classification trees, k-nearest neighbours and latent class analysis. In all these triplots three aspects are represented simultaneously, allowing for the representation of the relationships between samples and variables, relative to the classification regions.

Suggested Citation

  • Gardner-Lubbe, Sugnet, 2016. "A triplot for multiclass classification visualisation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 20-32.
    • Handle: RePEc:eee:csdana:v:94:y:2016:i:c:p:20-32
    DOI: 10.1016/j.csda.2015.07.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947315001711
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.07.014?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. 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. Linzer, Drew A. & Lewis, Jeffrey B., 2011. "poLCA: An R Package for Polytomous Variable Latent Class Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i10).
    3. John Aitchison & Michael Greenacre, 2002. "Biplots of compositional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 375-392, October.
    4. Lee, Yoonkyung & Lin, Yi & Wahba, Grace, 2004. "Multicategory Support Vector Machines: Theory and Application to the Classification of Microarray Data and Satellite Radiance Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 67-81, January.
    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. Adrian O’Hagan & Arthur White, 2019. "Improved model-based clustering performance using Bayesian initialization averaging," Computational Statistics, Springer, vol. 34(1), pages 201-231, March.
    2. B. Baris Alkan & Afsin Sahin, 2011. "Measuring inequalities in the distribution of health workers by bi-plot approach: The case of Turkey," Journal of Economics and Behavioral Studies, AMH International, vol. 2(2), pages 57-66.
    3. Aline Riboli Marasca & Maurício Scopel Hoffmann & Anelise Reis Gaya & Denise Ruschel Bandeira, 2021. "Subjective Well-Being and Psychopathology Symptoms: Mental Health Profiles and their Relations with Academic Achievement in Brazilian Children," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 14(3), pages 1121-1137, June.
    4. Lisa Blaydes, 2023. "Assessing the Labor Conditions of Migrant Domestic Workers in the Arab Gulf States," ILR Review, Cornell University, ILR School, vol. 76(4), pages 724-747, August.
    5. Yoonkyung Lee, 2014. "Comments on: Support vector machines maximizing geometric margins for multi-class classification," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 852-855, October.
    6. Michael Greenacre, 2016. "Selection and statistical analysis of compositional ratios," Economics Working Papers 1551, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Jindřich Špička & Zdeňka Náglová, 2022. "Consumer segmentation in the meat market - The case study of Czech Republic," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 68(2), pages 68-77.
    8. 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.
    9. Nicholas T. Davis & Kirby Goidel & Yikai Zhao, 2021. "The Meanings of Democracy among Mass Publics," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(3), pages 849-921, February.
    10. Javier Palarea-Albaladejo & Josep Martín-Fernández & Jesús Soto, 2012. "Dealing with Distances and Transformations for Fuzzy C-Means Clustering of Compositional Data," Journal of Classification, Springer;The Classification Society, vol. 29(2), pages 144-169, July.
    11. Carter, Virginia & Derudder, Ben & Henríquez, Cristián, 2021. "Assessing local governments’ perception of the potential implementation of biophilic urbanism in Chile: A latent class approach," Land Use Policy, Elsevier, vol. 101(C).
    12. Michael Greenacre & Paul Lewi, 2005. "Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data," Economics Working Papers 908, Department of Economics and Business, Universitat Pompeu Fabra, revised Aug 2007.
    13. Arjan S. Gosal & Janine A. McMahon & Katharine M. Bowgen & Catherine H. Hoppe & Guy Ziv, 2021. "Identifying and Mapping Groups of Protected Area Visitors by Environmental Awareness," Land, MDPI, vol. 10(6), pages 1-14, May.
    14. Crystal T. Nguyen & Daniel J. Luckett & Anna R. Kahkoska & Grace E. Shearrer & Donna Spruijt‐Metz & Jaimie N. Davis & Michael R. Kosorok, 2020. "Estimating individualized treatment regimes from crossover designs," Biometrics, The International Biometric Society, vol. 76(3), pages 778-788, September.
    15. Assem Abu Hatab & Padmaja Ravula & Swamikannu Nedumaran & Carl-Johan Lagerkvist, 2022. "Perceptions of the impacts of urban sprawl among urban and peri-urban dwellers of Hyderabad, India: a Latent class clustering analysis," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(11), pages 12787-12812, November.
    16. Anna Maria Fiori & Francesco Porro, 2023. "A compositional analysis of systemic risk in European financial institutions," Annals of Finance, Springer, vol. 19(3), pages 325-354, September.
    17. Martin Eling & David Pankoke, 2016. "Costs and Benefits of Financial Regulation: An Empirical Assessment for Insurance Companies," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 41(4), pages 529-554, October.
    18. Sunil Kumar & Zakir Husain & Diganta Mukherjee, 2015. "Assessing Consistency of Consumer Confidence Data using Dynamic Latent Class Analysis," Papers 1509.01215, arXiv.org.
    19. Lorena Charrier & Paola Berchialla & Paola Dalmasso & Alberto Borraccino & Patrizia Lemma & Franco Cavallo, 2019. "Cigarette Smoking and Multiple Health Risk Behaviors: A Latent Class Regression Model to Identify a Profile of Young Adolescents," Risk Analysis, John Wiley & Sons, vol. 39(8), pages 1771-1782, August.
    20. Germ`a Coenders & N'uria Arimany Serrat, 2023. "Accounting statement analysis at industry level. A gentle introduction to the compositional approach," Papers 2305.16842, arXiv.org, revised Feb 2024.

    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:94:y:2016:i:c:p:20-32. 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.