Ambiguities in recurrence-based complex network representations of time series

Area of Science:

• Complex Systems Science
• Time Series Analysis
• Network Science

Background:

• Recent advancements utilize complex network perspectives to analyze time series properties.
• Recurrence-based networks in phase space offer a promising approach for time series analysis.

Purpose of the Study:

• To investigate the potentials and limitations of phase space recurrence networks for time series analysis.
• To establish system-theoretic interpretations of network topology based on dynamic invariants.
• To propose rigorous interpretations of network metrics within this framework.

Main Methods:

• Analysis of phase space recurrence networks derived from time series data.
• Investigation of system-theoretic requirements for network interpretation.
• Systematic study of artifacts arising from disregarded requirements.
• Development of invariant-based interpretations for clustering coefficient and betweenness centrality.

Main Results:

• Identified key requirements for feasible system-theoretic interpretation of recurrence networks.
• Demonstrated potential artifacts from neglecting these requirements.
• Proposed rigorous, invariant-based definitions for clustering coefficient and betweenness centrality.

Conclusions:

• Phase space recurrence networks offer valuable insights into time series dynamics.
• Adherence to system-theoretic principles is crucial for accurate network interpretation.
• The proposed invariant-based metrics enhance the robustness and interpretability of network analysis for time series.