Adaptation of the Mahalanobis–Taguchi Method to Ordinal Scale

Abstract

The Mahalanobis–Taguchi (MT) method is a multivariate analysis method that addresses problems such as pattern recognition and anomaly detection wherein outliers from data groups are detected. The MT method is applied to various other fields (e.g., medical examination, corporate bankruptcy discrimination, and employee turnover discrimination). At the time of application, the effectiveness of the MT method for scale data, other than continuous variables, has not been clarified. The MT method using the polyserial and polychoric correlation (MTP) method, which is an MT method using the Mahalanobis distance calculated by Pearson, polyserial and polychoric correlation coefficients, is proposed. Correlations between continuous variables are calculated using Pearson’s correlation coefficient, continuous and ordinal-scale variables are calculated using the polyserial correlation coefficient, and ordinal-scale variables are calculated using the polychoric correlation coefficient. Through simulation with artificial data, it was confirmed that the anomaly detection accuracy of the MT method decreased with respect to the ordinal scale and the correlation weakening by ordinal scaling can be eliminated using the polyserial and polychoric correlation coefficients. The results of this study indicate that the abnormality discrimination accuracy of the MTP method exceeds that of the MT method, although in a limited environment.