Adaptive kernel density-based anomaly detection for nonlinear systems

This paper presents an unsupervised, density-based approach to anomaly detection. The purpose is to define a smooth yet effective measure of outlierness that can be used to detect anomalies in nonlinear systems. The approach assigns each sample a local outlier score indicating how much one sample deviates from others in its locality. Specifically, the local outlier score is defined as a relative measure of local density between a sample and a set of its neighboring samples. To achieve smoothness in the measure, we adopt the Gaussian kernel function. Further, to enhance its discriminating power, we use adaptive kernel width: in high-density regions, we apply wide kernel widths to smooth out the discrepancy between normal samples; in low-density regions, we use narrow kernel widths to intensify the abnormality of potentially anomalous samples. The approach is extended to an online mode with the purpose of detecting anomalies in stationary data streams. To validate the proposed approach, we compare it with several alternatives using synthetic datasets; the approach is found superior in terms of smoothness, effectiveness and robustness. A further experiment on a real-world dataset demonstrated the applicability of the proposed approach in fault detection tasks.