Journal of Classification 22:59-86 (2005) DOI: 10.1007/s00357-005-0006-7 _______________ The authors would like to thank anonymous reviewers and the Editor for helpful comments and encouragement that enabled them to clarify and improve the paper. The financial support of the NRF of South Africa is gratefully acknowledged. Authors’ Address: Department of Statistics and Actuarial Science, University of Stellenbosch, Private Bag X1, Matieland, 7602, SOUTH AFRICA; e-mail: njlr@sun.ac.za. Extensions of Biplot Methodology to Discriminant Analysis Sugnet Gardner and Niël J. le Roux University of Stellenbosch, South Africa Abstract: In this paper we show how biplot methodology can be combined with various forms of discriminant analyses leading to highly informative visual displays of the respective class separations. It is demonstrated that the concept of distance as applied to discriminant analysis provides a unified approach to a wide variety of discriminant analysis procedures that can be accommodated by just changing to an appropriate distance metric. These changes in the distance metric are crucial for the construction of appropriate biplots. Several new types of biplots viz. quadratic discriminant analysis biplots for use with heteroscedastic stratified data, discriminant subspace biplots and flexible discriminant analysis biplots are derived and their use illustrated. Advantages of the proposed procedures are pointed out. Although biplot methodology is in particular well suited for complementing J > 2 classes discrimination problems its use in 2-class problems is also illustrated. Keywords: Biplot; CVA biplot; Data visualisation; Discrimination subspace model; Flexible discriminant analysis; Linear discriminant analysis; PCA biplot; Quadratic discriminant analysis; QDA biplot.