Effective Methods for Quantifying Complexity Based on Improved Ordinal Partition Networks: Topological Dispersion Entropy and Weighted Topological Dispersion Entropy

Topological permutation entropy is based on ordinal partition networks (OPNs) to approximate topological entropy of low-dimensional chaotic systems. But the ordinal patterns of OPN ignore the magnitude of the amplitude value. To solve the problem, we propose topological dispersion entropy (TDE) and weighted topological dispersion entropy (WTDE) based on dispersion patterns to characterize the complexity of a system. Furthermore, WTDE strengthens the topological structure analysis of complex networks by weighting the adjacency matrix of the improved ordinal partition networks, thereby more accurately capturing the dynamic evolution of time series. The proposed methods are comprehensively evaluated by numerical experiments. The results show that the performance of both TDE and WTDE is significantly better than TPE. Especially, WTDE has good stability to parameters, data length, and noise. Finally, combining support vector machines and K-Nearest Neighbor, TDE and WTDE are applied to the classification of physiological data and mechanical failure data.