Perbandingan Performa Quadratic Discriminant Analysis Klasik dan Robust pada Data Hasil Principal Component Analysis untuk Klasifikasi Jenis Kaca

Abstract

This study aims to compare the performance of classical Quadratic Discriminant Analysis (QDA) and Robust Quadratic Discriminant Analysis (RQDA) after applying dimensionality reduction using Principal Component Analysis (PCA) on the Glass Identification Dataset. The dataset consists of eight chemical composition variables used to classify glass types based on their elemental characteristics. Prior to classification, discriminant analysis assumptions were examined, multivariate outliers were identified, and PCA was applied to address multicollinearity and enhance data stability. The PCA results indicate that the eight original variables can be reduced to five principal components, which collectively explain 93.20% of the total data variability. Classification was then performed using classical QDA and RQDA, where the latter incorporates the Minimum Covariance Determinant (MCD) estimator to obtain robust estimates of the mean vector and covariance matrix. Model performance was evaluated using a confusion matrix and the Apparent Error Rate (APER). The results show that both QDA and RQDA achieve the same classification accuracy of 63.7%, corresponding to an APER of 36.3%. These findings suggest that the application of PCA contributes to stabilizing the data structure and reducing the influence of outliers, thereby diminishing the advantage of robust estimation in this case. Nevertheless, RQDA remains a valuable alternative for classification tasks involving datasets with strong outliers or significant deviations from multivariate normality.