A Modified Mahalanobis Distance Metric Used to Optimize Mahalanobis Space and Improve Classification Performance of MTS

The Mahalanobis–Taguchi system (MTS) is a diagnostic and forecasting technique in a multidimensional system that integrates the Mahalanobis distance (MD) and robust engineering of Taguchi. To implement MTS, a set of observations from a normal group is selected to construct the Mahalanobis space (MS). With this MS as a reference, new observations from an unknown group can be judged to be normal or abnormal, and the degree of abnormality can be determined. MD is very sensitive to data changes, so the data quality of normal samples used to construct the MS directly affects the accuracy of classification. In practical applications, the selection of normal samples depends on the experience and subjective judgment of experts and lacks an objective selection mechanism. In this paper, a modified MD metric is proposed, which is combined with the individual control chart to obtain a robust MS. First, the initial MS is constructed according to the normal samples selected by experts, and the MD of each normal sample is calculated by the initial MS. Then, the MD of each normal sample in the corresponding reduced MS is computed, and the incremental MD is used as the new distance metric to establish the individual control charts. The stability rules of the control chart are employed to eliminate abnormal points, and the MS of the stable state is obtained. To evaluate the effectiveness of the modified MD metric, a numerical simulation experiment is implemented, and the results show that the proposed method is effective and improves the classification performance of MTS. Finally, the improved MTS method is applied to a real medical diagnosis case.