Simultaneous optimisation of clustering quality and approximation error for time series segmentation

Abstract

Time series segmentation is aimed at representing a time series by using a set of segments. Some researchers perform segmentation by approximating each segment with a simple model (e.g. a linear interpolation), while others focus their efforts on obtaining ho- mogeneous groups of segments, so that common patterns or behaviours can be detected. The main hypothesis of this paper is that both objectives are conflicting, so time series segmentation is proposed to be tackled from a multiobjective perspective, where both objec- tives are simultaneously considered, and the expert can choose the desired solution from a Pareto Front of different segmentations. A specific multiobjective evolutionary algorithm is designed for the purpose of deciding the cut points of the segments, integrating a cluster ing algorithm for fitness evaluation. The experimental validation of the methodology includes three synthetic time series and three time series from real-world problems. Nine clustering quality assessment metrics are experimentally compared to decide the most suitable one for the algorithm. The proposed algorithm shows good performance for both clustering quality and reconstruction error, improving the results of other mono-objective alternatives of the state-of-the-art and showing better results than a simple weighted linear combination of both corresponding fitness functions.