Change detection using least squares one-class classification control chart

ABSTRACT

One-class classification can be thought as a special type of two-class classification problem, where data only from one class, the target class, are available for training the classifier (referred to as one-class classifier). The problem of classifying positive (or target) cases in the absence of appropriately characterized negative cases (or outliers) has gained increasing attention in recent years. Several methods are available to solve the one-class classification problem. Three methods are commonly used: density estimation, boundary methods, and reconstruction methods. This paper focuses on boundary methods which include k–center method, nearest neighbor method, one-class support vector machine (OCSVM), and support vector data description (SVDD). In statistical process control (SPC), practitioners successfully used SVDD to detect anomalies or outliers in the process. In this paper, we reformulate the standard OCSVM by a least squares version of the method. This least squares one-class support vector machine (LS-OCSVM) is used to design a control chart for monitoring the mean vector of processes. We compare the performance of the LS-OCSVM chart with the SVDD and $T^2$ chart. The experimental results indicate that the proposed control chart has very good performances.

KEYWORDS:

• Average run length (ARL)
• least squares support vector machines
• machine learning
• one-class classification
• proximity measure

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Edgard M. Maboudou-Tchao

Edgard M. Maboudou-Tchao received his MSc and PhD in Statistics from the School of Statistics at the University of Minnesota, Twin Cities.  He is currently an associate professor of Statistics at the Department of Statistics & Data Science at the University of Central Florida. His work has been published in a variety of journals, including Technometrics, Journal of Quality Technology, Computational Statistics and Data Analysis and Journal of Applied Statistics. His research interests include: Statistical Learning Theory, Machine Learning, Data Science, One-Class Classification, Tensors, Multivariate Statistics, and Multivariate Statistical Process Control.