Discovering Structural Regularities in Time Series via Gaussian Processes

Jan David Hüwel, Christian Beecks

Abstract: Time series are able to depict various kinds of real-world processes, which are frequently represented by the aggregation of multiple real-world components acting in parallel. Extracting these components and using them for discovering structural regularities is a major challenge in the domain of time series analytics. In this paper, we propose the CATGP+ algorithm for efficient Component Analysis in Time series with Gaussian Processes. For this purpose, we assume time series to be modelled by Gaussian processes, which are probabilistic machine learning models that are able to capture local linearity, trend, periodicity, etc. Based on these models, the proposed CATGP+ algorithm facilitates the determination of structural regularities, i.e. frequently occurring components, within Gaussian processes. By relating the components of the Gaussian processes, modelling the underlying time series data, with those appearing in real-world processes, we are able to gain further inside into behavior and dependencies on a structural and substructural level. Moreover, as our designed solution is compatible with the classical itemset mining problem, we are able to inherent the efficiency of existing algorithmic approaches. Our experimental evaluation indicates that the CATGP+ algorithm is able to efficiently discover frequent components hidden in the underlying time series data.