Signature Isolation Forest
Guillaume Staerman Marta Campi Gareth W. Peters
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.