Title: The Trace Criterion for Kernel Bandwidth Selection for Support Vector Data Description,
Abstract: 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.