Density-based anomaly detection for functional data via archetypal analysis

Archetypal analysis (AA) is an interpretable, geometry-based unsupervised learning method that has been extended to functional data, where observations are represented as curves. In many industrial applications, such as manufacturing process monitoring, sensor measurements are inherently functional, making anomaly detection a critical task for monitoring and control. AA-based representations summarize functional observations using archetype coefficients, providing compact and interpretable features for functional anomaly detection. However, existing AA-based approaches often rely on heuristic and user-dependent criteria to identify anomalies, which can limit reproducibility and robustness. Motivated by characteristic distributional gaps observed in archetype coefficient spaces, we propose a density-based anomaly detection framework that identifies anomalies as observations located in low-density regions. Anomaly scores are defined using kernel density estimation, and decision thresholds are determined automatically by contamination-based quantiles. The proposed method is evaluated using simulation studies and an application to real semiconductor manufacturing process sensor data.

Archetypal analysis

Functional data

Manufacturing process

Anomaly detection

Density estimation

Decision threshold 

Korean International Statistical Society