Concise network models of memory dynamics reveal explainable patterns in path data.

Area of Science:

• Complex systems analysis
• Network science
• Data modeling

Background:

• Network methods model complex systems using random walks but struggle with path data memory effects.
• First-order Markov models are limited; higher-order models are data-intensive and prone to overfitting/underfitting.

Purpose of the Study:

• To develop concise networks that capture memory effects in path data.
• To balance model simplicity and accuracy for complex systems analysis.
• To improve the modeling of real-world systems with uneven data coverage.

Main Methods:

• Interpolating between first-order and second-order Markov models.
• Creating state nodes to capture prominent second-order effects.
• Proposing a transparent measure to balance model size and quality.

Main Results:

• Concise networks effectively reveal large-scale memory patterns in synthetic and real-world systems.
• The proposed models are significantly simpler than full second-order Markov models.
• The approach addresses limitations of existing network methods for path data with memory.

Conclusions:

• Concise networks offer a simplified yet effective approach to modeling complex systems with memory.
• This method enhances interpretability and reduces data requirements compared to higher-order models.
• The findings have implications for analyzing dynamic processes in various scientific domains.