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A triplot for multiclass classification visualisation

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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).
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