The Mahalanobis-Taguchi Method Based on Graphical Modeling

Abstract

The Mahalanobis-Taguchi (MT) method is one of the Taguchi methods and a standard method of multivariate analysis for detecting anomalies or recognizing patterns. Particularly in recent years, some case studies have been reported that have used this method for monitoring the operating conditions of production equipment, whose data are acquired from sensors. However, it is difficult to estimate the essential correlation structure from the learning data, because the sensors might record noisy data.

To estimate the essential correlation structure from the data, we propose applying a regularization process based on Gaussian graphical modeling to the MT method. In our proposed procedure, we focus on the fact that the correlation structure estimated by the original procedure is based on the precision matrix. Then, by reducing the number of parameters by replacing the majority of the non-diagonal elements of the matrix to zeroes, we can estimate the essential correlation structure accurately. By analyzing the data from the UCI machine learning repository, and the Monte Carlo simulations, we show that even when the noisy data have been observed, the essential correlation structure can be estimated accurately in our proposed procedure.