The Trace Kernel Bandwidth Criterion for Support Vector Data Description

Abstract Support vector data description (SVDD) is a popular anomaly detection technique. The computation of the SVDD classifier requires a kernel function, for which the Gaussian kernel is a common choice. The Gaussian kernel has a bandwidth parameter, and it is important to set the value of this parameter correctly to ensure good results. A small bandwidth leads to overfitting, and the resulting SVDD classifier overestimates the number of anomalies, whereas a large bandwidth leads to underfitting and an inability to detect many anomalies. In this paper, we present a new, unsupervised method for selecting the Gaussian kernel bandwidth. Our method exploits a low-rank representation of the kernel matrix to suggest a kernel bandwidth value. Our new technique is competitive with the current state of the art for low-dimensional data and performs extremely well for many classes of high-dimensional data. This method is also applicable to one-class support vector machines (OCSVM).