Mendeteksi Outlier pada Data Multivariat dengan Metode Jarak Mahalanobis – Minimum Covariance Determinant (Mmcd)

Abstract

An outlier is data that is distant or remote from the data in the population, usually called an outlier, which is data that is separated from group data that is patterned or has a certain arrangement. The presence of outliers has important implications for data analysis, especially multivariate data. The presence of outliers can distort the classical estimators, i.e. the mean and covariance values which affect the significance results of parameter testing so that insensitive estimates are required when analyzing outlier data. This study aims to detect outliers in multivariate data using the Mahalanobis-Minimum Covariance Determinant (MMCD) distance method and then will be compared with the classic Mahalanobis distance method. In the MMCD Distance method, outlier detection is performed using MCD as an estimator to determine the data center and smallest covariance. Then identify with MMCD distance by replacing the data center with the median which is considered to be robust for outliers. Moreover, outlier detection is performed using the classic Mahalanobis distance method - Arithmetic Mean and Mahalanobis distance method – Median. Data is identified as outliers when the data has a distance of more than the specified cut off value. Based on this research, it is known that using the same data, the outlier data obtained in the MMCD distance method is smaller than the classic Mahalanobis distance method. The results of outlier detection using MMCD distance with MCD estimated mean and covariance are 34 wines and MMCD distance with MCD estimated covariance and median as data center 35 wines. Meanwhile, outliers detected using the classic Mahalanobis distance - Arithmetic Mean were 154 wines and the classic Mahalanobis distance - Median detected 188 wines as outliers. From these results it can be seen that MCD as an estimator of Mahalanobis distance works well to identify outlier data.