The Mean and Median Criterion for Automatic Kernel Bandwidth Selection for Support Vector Data Description

TL;DR

This paper introduces an automatic, unsupervised method for selecting the Gaussian kernel bandwidth in SVDD, improving anomaly detection by balancing overfitting and underfitting efficiently.

Contribution

The paper proposes a novel automatic bandwidth selection method based on the mean and median criterion, which is fast and competitive with existing approaches.

Findings

The method effectively balances overfitting and underfitting.

It is computationally efficient and easy to implement.

Performance is comparable to or better than existing methods.

Abstract

Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD classifier requires a kernel function, and the Gaussian kernel is a common choice for the kernel function. The Gaussian kernel has a bandwidth parameter, whose value is important for good results. A small bandwidth leads to overfitting, and the resulting SVDD classifier overestimates the number of anomalies. A large bandwidth leads to underfitting, and the classifier fails to detect many anomalies. In this paper we present a new automatic, unsupervised method for selecting the Gaussian kernel bandwidth. The selected value can be computed quickly, and it is competitive with existing bandwidth selection methods.