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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

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From time series to complex networks: the visibility graph.

Lucas Lacasa¹, Bartolo Luque, Fernando Ballesteros

¹Departmento Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain. lucas@dmae.upm.es

Proceedings of the National Academy of Sciences of the United States of America

|March 26, 2008

Summary

We introduce a visibility algorithm to transform time series data into graphs. This method reveals underlying data properties, linking fractal series to scale-free networks and aiding time series analysis.

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Area of Science:

Complex systems
Network theory
Data analysis

Background:

Time series analysis often relies on statistical methods.
Characterizing complex time series properties remains a challenge.
Network theory offers tools to analyze complex systems.

Purpose of the Study:

To present a novel computational method for converting time series into graphs.
To demonstrate how graph properties reflect time series characteristics.
To explore the relationship between fractal time series and network properties.

Main Methods:

The visibility algorithm is introduced as a computational tool.
Time series are converted into graph structures.
Properties of the resulting graphs are analyzed.

Main Results:

Periodic time series map to regular graphs.
Random time series map to random graphs.
Fractal time series map to scale-free networks, supporting the link between fractality and power-law distributions.

Conclusions:

The visibility algorithm provides a new perspective for time series characterization.
It connects time series analysis with complex network theory.
This approach allows the application of network measures to time series data.