Signature Isolation Forest
This work provides a more reliable anomaly detection method for complex functional datasets, though it is incremental as it builds on an existing algorithm.
The paper tackled the limitations of Functional Isolation Forest in anomaly detection for functional data by introducing Signature Isolation Forest, which uses the signature transform to address linearity and dictionary choice constraints, resulting in improved performance on benchmarks.
Functional Isolation Forest (FIF) is a recent state-of-the-art Anomaly Detection (AD) algorithm designed for functional data. It relies on a tree partition procedure where an abnormality score is computed by projecting each curve observation on a drawn dictionary through a linear inner product. Such linear inner product and the dictionary are a priori choices that highly influence the algorithm's performances and might lead to unreliable results, particularly with complex datasets. This work addresses these challenges by introducing \textit{Signature Isolation Forest}, a novel AD algorithm class leveraging the rough path theory's signature transform. Our objective is to remove the constraints imposed by FIF through the proposition of two algorithms which specifically target the linearity of the FIF inner product and the choice of the dictionary. We provide several numerical experiments, including a real-world applications benchmark showing the relevance of our methods.