A Hierarchical Piecewise Approximation Framework for Pattern-Based Sequence Learning

Several existing anomaly detection algorithms that work on sequence data employ similar pipelines that convert subsequences into piecewise approximations before aggregating these into a model. However, choices in sequence segmentation, representation, distance calculation, and modelling approaches affect detection performance across different anomaly types. We propose a framework that formalises these pipeline components and their parameters, enabling systematic evaluation of pipeline configurations across specific sequence learning tasks. Through this formalisation, we introduce a novel hierarchical piecewise approximation model based on nested words. Using the UCR Time Series Anomaly Archive, we demonstrate that specific framework configurations effectively identify subsequences corresponding to specific anomaly definitions, achieving performance comparable to state-of-the-art methods, including deep learning approaches.