A two-group canonical variate analysis biplot for an optimal display of both means and cases

Niel Roux () and Sugnet Gardner-Lubbe
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Niel Roux: Stellenbosch University
Sugnet Gardner-Lubbe: Stellenbosch University

Advances in Data Analysis and Classification, 2025, vol. 19, issue 3, No 7, 748 pages

Abstract: Abstract Canonical variate analysis (CVA) entails a two-sided eigenvalue decomposition. When the number of groups, J, is less than the number of variables, p, at most $$J-1$$ J - 1 eigenvalues are not exactly zero. A CVA biplot is the simultaneous display of the two entities: group means as points and variables as calibrated biplot axes. It follows that with two groups the group means can be exactly represented in a one-dimensional biplot but the individual samples are approximated. We define a criterion to measure the quality of representing the individual samples in a CVA biplot. Then, for the two-group case we propose an additional dimension for constructing an optimal two-dimensional CVA biplot. The proposed novel CVA biplot maintains the exact display of group means and biplot axes, but the individual sample points satisfy the optimality criterion in a unique simultaneous display of group means, calibrated biplot axes for the variables, and within group samples. Although our primary aim is to address two-group CVA, our proposal extends immediately to an optimal three-dimensional biplot when encountering the equally important case of comparing three groups in practice.

Keywords: Biplot; Canonical variate analysis; Classification; Data visualization; Discriminant analysis; 62H30; 15A21; 93B60; 91C20; 97K80 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11634-024-00593-7

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