Application of Partial Least Squares and Robust Approaches in Discriminant Analysis for High-Dimensional Data

Abstract

Classical discriminant analysis, namely linear discriminant analysis and quadratic discriminant analysis, is generally known to suffer from singularity problems when exprerienced with high-dimensional data and is not robust to outliers that make the data not multivariate normally distributed. This research focuses on investigating the classification performance of discriminant analysis on high-dimensional data by applying two approaches, namely the Partial Least Square (PLS) dimension reduction approach as a solution to high-dimensional data and a robust approach with the Minimum Covariance Determinant (MCD) estimator technique that is robust to outliers. The data used for this study is Lee Silverman Voice Treatment (LSVT) data. PLS forms five optimal latent variables that represent predictor variable information. Based on the assumption test of covariance homogeneity between groups, the test statistic value is greater than the chi-square table or the p-value is smaller than the significance level, which means that the assumption is unfulfilled, so quadratic discriminant analysis is applied. The evaluation results showed that the quadratic discriminant analysis analysis model with the MCD approach on the PLS transformed data was able to achieve 81% accuracy, 71% precision, 86% recall, and 77% F1-score. These values indicate that both approaches are able to maintain the efficiency of discriminant analysis classification performance on high-dimensional and multivariate non-normally distributed data.