Anomaly detection in high-dimensional data with the Mahalanobis–Taguchi system

Abstract

The Mahalanobis–Taguchi (MT) system is a typical Taguchi method and plays an important role in several fields. This study aims at improving the statistical procedure employed for anomaly detection in high-dimensional data with the MT system. The proposed study focuses on estimating the eigenvalues and eigenvectors of the covariance matrix and introduces an estimation procedure based on sparse principal component analysis (SPCA) in the MT system. By incorporating SPCA, eigenvalues and eigenvectors can be accurately estimated for high-dimensional data. In addition, the interpretation of the principal components can become simplified with decreasing number of nonzero elements in the estimated eigenvectors. Numerical experiments have confirmed that the proposed procedure is beneficial for both anomaly detection performance and investigating the cause of anomalies in high-dimensional data. Furthermore, a limitation of the proposed study is its emphasis on improving anomaly detection procedures founded on the first principal component and its residual component. However, the scope of such an anomaly detection procedure can be easily expanded for further improvement.

Keywords:

• Mahalanobis distance
• Mahalanobis–Taguchi system
• sparse principal component analysis
• Taguchi method

Acknowledgement

We would like to thank the anonymous referees for their valuable comments. This work was partly supported by the Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research Grant Number JP15K00056 and the Waseda University Grant for Special Research Projects Number 2017B-168.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partly supported by the Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research grant number [JP15K00056] and the Waseda University grant for special research projects number [2017B-168].