On transformation discriminant analysis

Multigroup discriminant analysis is an important supervised learning technique in the classification framework, with applications in various disciplines. Its objective is to approximate underlying class distributions based on data attributes or features. After the class distributions are estimated, the classification task can be readily carried out for data points with unknown labels. Linear discriminant analysis (LDA) as well as quadratic discriminant analysis (QDA) are statistical procedures widely utilized by practitioners due to their practicality and generally good performance. Both procedures rely on the assumption of normally distributed classes and can be affected by deviations from multivariate normality. To address this model deficiency, we propose an extension of LDA and QDA that relies on the idea of transformation and can readily accommodate asymmetry and skewness in data classes. Through the set of simulation studies and applications to real-life data sets, we demonstrate that the developed technique is promising as it demonstrates superior performance over competitors in a variety of cases.