Quantifying Disorder in Data.

Area of Science:

• Complex Systems Science
• Data Analysis
• Dynamical Systems Theory

Background:

• Quantifying disorder in data is a persistent scientific challenge, especially with short datasets exhibiting complex behaviors.
• Distinguishing between chaotic, stochastic, and noisy processes is difficult due to indistinguishable characteristics in data.
• Existing methods struggle with short time series and identifying the nature of underlying processes.

Purpose of the Study:

• To introduce a novel method for directly quantifying disorder in data using recurrence microstate analysis.
• To develop a robust information entropy-based quantifier for differentiating signal types.
• To apply the method to analyze paleoclimatic data and identify drivers of past climate transitions.

Main Methods:

• Recurrence microstate analysis to quantify data disorder.
• Leveraging information entropy to create a robust disorder quantifier.
• Application to differentiate chaotic, correlated, and uncorrelated stochastic signals in small time series.
• Analysis of paleoclimatic data to identify disorder minima correlating with Cenozoic era stage transitions.

Main Results:

• The proposed method successfully quantifies disorder by maximizing recurrence microstates.
• The information entropy-based quantifier reliably distinguishes between chaotic, correlated, and uncorrelated stochastic signals.
• The method effectively characterizes corrupting noise in dynamical systems.
• Disorder minima in paleoclimatic data align with known Cenozoic era stage transitions.

Conclusions:

• Recurrence microstate analysis provides a robust framework for quantifying data disorder.
• The developed quantifier offers a reliable tool for signal characterization, even with limited data.
• The findings have implications for understanding dynamical systems, noise, and paleoclimatic change.