Efficient Nonlinear RX Anomaly Detectors

TL;DR

This paper introduces two efficient kernel-based anomaly detection methods that approximate the standard kernel RX algorithm, achieving similar or better accuracy with lower computational cost, suitable for real multi- and hyperspectral images.

Contribution

It proposes data-independent and data-dependent approximation techniques to enhance the efficiency of the kernel RX anomaly detector.

Findings

Proposed methods reduce computational cost.

Methods perform comparably or better than standard kernel RX.

Nyström approach improves detection power.

Abstract

Current anomaly detection algorithms are typically challenged by either accuracy or efficiency. More accurate nonlinear detectors are typically slow and not scalable. In this letter, we propose two families of techniques to improve the efficiency of the standard kernel Reed-Xiaoli (RX) method for anomaly detection by approximating the kernel function with either {\em data-independent} random Fourier features or {\em data-dependent} basis with the Nystr\"om approach. We compare all methods for both real multi- and hyperspectral images. We show that the proposed efficient methods have a lower computational cost and they perform similar (or outperform) the standard kernel RX algorithm thanks to their implicit regularization effect. Last but not least, the Nystr\"om approach has an improved power of detection.