Randomized low-rank nonlinear RXdetector

Anomaly detection is an important topic in various application areas including image analysis and network intrusion detection. The Reed–Xiaoli detector is an efficient and accurate anomaly detector that can be used if analyzed data is Gaussian distributed. However, in real-world data is rarely Gaussian distributed. For nonlinear data, kernel RX (KRX) is proposed and widely employed. The biggest issue with KRX method is its high computational complexity which prevents using it for big data or in real-time scenarios. As a remedy, in the literature, Random Fourier Features (RFF) approximation of the KRX method is proposed, namely RRX method. Another weakness of KRX is numerical issues, basically kernel matrix being bad-conditioned, which can be solved by regularization. This situation also applies to RRX method. In this study, we extend the RRX method with randomized SVD as an efficient solution owing to best low-rank approximation being Singular Value Decomposition (SVD). Proposed method, randomized low-rank RX (RLR-RX), provides better computational complexity and better detection performance compared to both RRX and KRX. Efficiency and detection performance of the proposed RLR-RX method is demonstrated using a synthetic dataset and real-world dataset. Keywords: Anomaly Detection, RX, Kernel RX, Random Fourier Features, Low-Rank, Randomized SVD