Kernel methods for changes detection in covariance matrices

ABSTRACT Several methods have been proposed to solve the one-class classification problem for vectors. Three methods are mainly used: density estimation, boundary methods, and reconstruction methods. The focus here is on boundary methods. These methods include the k-center method, the nearest neighbor method, one-class support vector machine (OCSVM), and the support vector data description (SVDD). In industrial applications, like statistical process control (SPC), practitioners successfully used SVDD to detect anomalies or outliers in the process. However, when a multivariate process shifts, it occurs in either location or scale. This far, most of the research effort, like the OCSVM or SVDD, has focused on location (vectors or mean vectors). Several methods have been proposed recently to monitor the scale, i.e., the covariance matrix. Most of these methods deal with a full rank covariance matrix, i.e., a situation where the number of rational subgroups is larger than the number of variables. When the number of variables is nearly as large as, or larger than, the number of observations, most Shewhart-type charts are unable to solve this problem as the estimated covariance matrix is not full rank. This work will extend the one-class classification method using kernels to detect changes in the covariance matrix when the number of observations available is less than the number of variables.