An electrostatics method for converting a time-series into a weighted complex network

Area of Science:

• Complex systems
• Network science
• Time-series analysis

Background:

• Time-series analysis often involves transforming data into networks for structural insights.
• Existing methods like the visibility graph offer valuable network representations.
• There is a need for novel, physics-inspired methods to capture complex time-series dynamics.

Purpose of the Study:

• To propose a novel method for converting time-series into weighted graphs using principles of electrostatics.
• To compare the effectiveness of the proposed electrostatic graph algorithm against the visibility graph in representing time-series structures.
• To establish a framework for evaluating the structural relevance between time-series and their graph transformations.

Main Methods:

• Conceptualizing time-series as charged particles to compute Coulomb-like forces.
• Generating electrostatic-like weighted and potentially disconnected graphs from time-series data.
• Analyzing structural similarities between time-series and their corresponding graphs using network measures.

Main Results:

• The electrostatic graph algorithm generates graphs whose node-measures are more representative of the source time-series structure than the visibility graph.
• The proposed method offers a more natural, physics-based approach compared to algebraic methods.
• Demonstrated superior representation of time-series characteristics like linearity, chaos, stationarity, periodicity, and cyclical patterns.

Conclusions:

• The electrostatic graph algorithm provides a more accurate and natural method for time-series to complex network transformation.
• This approach enhances the analysis of time-series structural properties through network science.
• The study offers a methodological framework for assessing the fidelity of time-series graph transformations.