Outlier detection and classification in inhomogeneous voltage curves using functional depth

As a fundamental challenge in unsupervised learning, the identification of outliers in homogeneous populations has received considerable attention over the years. In practice, however, the data at hand stem from diverse processes, making it difficult to differentiate an anomaly from a valid signal. In the case of functional data, in particular, the definition of an outlier is no longer trivial. We propose a method using functional depth as an indicator of centrality, applied to a real industry problem in steel production. A set of potential outlier candidates is identified using functional depth, subsequently clustered and labeled. These labels are then used to expand to the entire dataset using semi-supervised learning techniques. Our method is rigorously compared to a manual labeling of the data as well as a classic functional clustering approach using scores and graphical investigation, showing that using functional depth to narrow down the set of potential outliers allows for more concise and easily identified anomaly categories.