On the Anomaly Detection in Time SeriesData with Kernel PCA Algorithm

Abstract

Kernel Principal Component Analysis (Kernel PCA) is a non-linear extension of PCA. Kernel-based methods better model data produced by nonlinear processes by mapping data on higher-dimensional spaces using kernel functions. This feature enables kernel PCA to capture the complex, nonlinear relationships inherent in many observed real-world data. The goal of this study is to test and analyze the effectiveness of kernel Principal Component Analysis in detecting anomalous points for the time series data. We perform anomaly detection on select time series datasets with recorded anomalies and compare their classification performance with the regular PCA method. We demonstrate the competitive performance of the kernel PCA method in handling anomaly detection on three real-world datasets: circuit water, fluid leaks, and rotor imbalance. We also perform parameter search on a grid for both of considered methods to investigate how the number of anomalies present in time series impact the optimal values of PCA and Kernel PCA key parameters. Finally, we construct the ROC curves to evaluate the model performance in detecting anomalies in terms of the interplay of true positive and false positive rates.