Time series clustering of dynamical systems via deterministic learning

A recent deterministic learning theory has achieved locally-accurate identification of unknown system dynamics. This article presents a novel application of deterministic learning theory to unsupervised learning for the first time. Specifically, a new time series clustering strategy with a dynamics-based similarity measure is proposed. Firstly, the dynamics knowledge learned from the time series is represented and stored in the form of constant weights through deterministic learning theory. Secondly, dynamical estimators constructed with the learned dynamics knowledge are used to generate recognition errors, forming a similarity measure matrix to characterize the dynamics-based similarity between time series. Finally, the clustering of time series data with different dynamical behaviors is achieved based on the K-medoids prototype according to the dynamics-based similarity measure matrix. To verify the effectiveness of the proposed method, a dynamical pattern dataset based on benchmark dynamical systems (e.g., Lorenz, Chen, and Lu systems) is also constructed. The experimental results on a synthetic dataset and two real datasets demonstrate that the proposed method is superior to other well-known clustering algorithms in the clustering task for dynamical systems.