Density-based anomaly detection for functional data via archetypal analysis

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Hee Su Lee (1), Min Ho Cho (1)

(1) N/A, N/A

Min Ho Cho  
N/A

Hee Su Lee  
N/A

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

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