Mahalanobis Distance dan Principal Component Analysis Menggunakan Metode Robust Minimum Covariance Determinant (MCD) dan Minimum Volume Ellipsoid (MVE)

Abstract

In multivariate analysis, estimates of the mean and covariance matrix are used as the basis for calculations in the Mahalanobis Distance (MD) and Principal Component Analysis (PCA) statistical techniques. However, the presence of outliers significantly compromises the accuracy of the estimates and thus misleads the analysis results. Therefore, robust methods that are insensitive to outliers and produce representative estimates are required, commonly used robust methods are Minimum Covariance Determinant (MCD) and Minimum Volume Ellipsoid (MVE). This study aims to analyze the performance of MD to detect outliers and PCA to reduce data dimensionality, using estimates from the robust MCD and MVE methods. The results of the analysis showed that outlier detection with MD+MCD and MD+MVE resulted in 229 outliers and 158 outliers, respectively, while classical MD resulted in 87 outliers. Meanwhile, data dimension reduction with PCA+MCD and PCA+MVE resulted in 5 principal components with a cumulative variance of 88% while classical PCA only amounted to 81%. The process of outlier elimination from the dataset, data dimensionality reduction on MD clean data, increased the cumulative variance by 85% and remained 88% on MD+MCD and MD+MVE clean data. Based on the results of this study, it can be concluded that the robust MCD and MVE methods are able to improve the performance of MD to detect outliers and PCA to reduce the dimensionality of representative data. In addition, outlier detection and outlier elimination using non-robust methods can improve the representation of data structure, especially when using robust methods.