The Trace Criterion for Kernel Bandwidth Selection for Support Vector Data Description

Support vector data description (SVDD) is a popular anomaly detection technique. The SVDD classifier partitions the whole data space into an $\textit{inlier}$ region, which consists of the region $\textit{near}$ the training data, and an $\textit{outlier}$ region, which consists of points $\textit{away}$ from the training data. 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 for good results. A small bandwidth leads to overfitting such that 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, which exploits the low-rank representation of the kernel matrix to suggest a kernel bandwidth value, is competitive with existing bandwidth selection methods.