Satterthwaite Approximation of the Distribution of SPE Scores: An R-Simulation-Based Improvement of the R-PCA-Based Outlier Detection Method

Outlier detection is a significant challenge in IoT-based systems, which encompass a multitude of sensor nodes deployed for diverse applications. Ensuring accurate data transmission from these nodes to base stations is crucial, as outliers (fault/event/intrusion) can adversely impact data processing accuracy and overall quality of service. The Principal Component Analysis (PCA) has gained popularity for outlier detection in IoT, with Recursive Principal Component Analysis (R-PCA) being a widely used method. In this paper, we explore popular PCA-based approaches and present an optimized, real-time, and reproducible enhancement to the existing R-PCA method. Our proposed improvement focuses on a data-driven approximation of the distribution of squared prediction error (SPE) scores, a fundamental component of PCA-based outlier detection. We address theoretical ambiguities in the assumptions underlying SPE scores in the existing R-PCA method. Through simulations, we demonstrate the inaccurate distributional assumption of SPE scores in the specified scheme. Additionally, we introduce a more suitable Satterthwaite-based approximation of the SPE score distribution, supported by Quantile-Quantile (Q-Q) plots. The effectiveness of the proposed approximation is validated through performance evaluation metrics, demonstrating its superiority over the Gaussian approximation used in R-PCA schemes. Furthermore, we provide an overview of our proposed scheme, which can be implemented in any PCA-based outlier detection system used by IoT practitioners and engineers. Our research contributes to advancing outlier detection methodologies in IoT-based systems, enabling more reliable anomaly detection and improved system performance.