High-dimensional data monitoring using support machines

Abstract

Dealing with high-dimensional data is a major challenge primary in statistics and consequently in statistical process control (SPC). “Shewhart-type” charts are control charts using rational subgrouping. Shewhart-type charts are effective in the detection of large shifts. In high-dimensional settings, where the number of variables is nearly as large as or larger than the number of observations, it will be very hard to use Shewhart-type charts based on rational subgroups. An alternative is to use Shewhart-type charts based on individual observations. Also, for most conventional control charts, the design of the control limits is commonly based on the assumption that the quality characteristics follow a multivariate normal distribution. However, this may not be reasonable in many real-world problems. This paper addresses these issues and suggests a monitoring methodology motivated by statistical learning theory. The proposed multivariate control chart uses tensor space model to represent a high-dimensional vector. This chart makes use of information extracted from in-control preliminary samples. Simulation studies demonstrate that the proposed control chart has very good performances.

Keywords:

• High-dimensional data
• Support Tensor Vector Data Description
• One-class classification
• Small sample size problem
• Tensor