Outlier detection of clustered functional data with image and signal processing applications by archetype analysis

In this study, we introduce an innovative methodology for anomaly detection of curves, applicable to both multivariate and multi-argument functions. This approach distinguishes itself from prior methods by its capability to identify outliers within clustered functional data sets. We achieve this by extending the recent AA + kNN technique, originally designed for multivariate analysis, to functional data contexts. Our method demonstrates superior performance through a comprehensive comparative analysis against twelve state-of-the-art techniques, encompassing simulated scenarios with either a single functional cluster or multiple clusters. Additionally, we substantiate the effectiveness of our approach through its application in three distinct computer vision tasks and a signal processing problem. To facilitate transparency and replication of our results, we provide access to both the code and the datasets used in this research.