A novel framework for time series recognition and classification based on dispersion transition networks

The use of complex network for nonlinear analysis of time series has attracted increasing attention, among which, ordinal networks have been widely studied for their simplicity and computational efficiency. However, existing ordinal network methodologies exhibit two limitations: 1) inadequate handling of equal values in time series discretization, 2) neglect of some amplitude information. They potentially compromising the characterization of complex systems. To address these limitations, this paper proposes a dispersion transition network framework, which includes node-wise entropy and Wasserstein entropy curve based on the dynamic transition information and Wasserstein distance, to identify the properties of systems. The introduction of Wasserstein distance improves the stability and comprehensiveness of the information extracted from the probability distribution. The node-wise entropy and entropy curve are local metric and global metric, respectively. Numerical results show that the framework have a strong ability to distinguish signals with different dynamics and can show the variation of system properties with parameters. In the empirical application, the proposed methods can be applied to financial data classification without complex preprocessing. We also apply these methods to railway corrugation detection and compare them with other nine dimensionality reduction methods. The most satisfactory classification results are obtained by the proposed methods. The entropy curve can also be combined with multidimensional scaling for physiological time series classification.