A Classification Study in High-Dimensional Data of Linear Discriminant Analysis and Regularized Discriminant Analysis

Abstract

The objective of this work is to compare linear discriminant analysis (LDA) and regularized discriminant analysis (RDA) for classification in high-dimensional data. This dataset consists of the response variable as a binary or dichotomous variable and the explanatory as a continuous variable. The LDA and RDA methods are well-known in statistical and probabilistic learning classification. The LDA has created the decision boundary as a linear function where the covariance of two classes is equal. Then the RDA is extended from the LDA to resolve the estimated covariance when the number of observations exceeds the explanatory variables, or called high-dimensional data. The explanatory dataset is generated from the normal distribution, contaminated normal distribution, and uniform distribution. The binary of the response variables is computed from the logit function depending on the explanatory variable. The highest average accuracy percentage evaluates to propose the performance of the classification methods in several situations. Through simulation results, the LDA was successful when using large sample sizes, but the RDA performed when using the most sample sizes.