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Published on: June 27, 2013
Structural information in two-dimensional patterns: entropy convergence and excess entropy.
David P Feldman1, James P Crutchfield
1College of the Atlantic, Bar Harbor, Maine 04609, USA. dpf@santefe.edu
Summary
We introduce novel information-theoretic methods to measure spatial patterns in multidimensional systems. The convergence rate of entropy density provides a new way to quantify global correlation and structure.
Area of Science:
- Information theory
- Spatial statistics
- Complex systems analysis
Background:
- Spatial structure and patterns are fundamental in many scientific fields.
- Existing methods for quantifying spatial structure have limitations in higher dimensions.
- Entropy density estimation in 2D is well-established using conditional entropies.
Purpose of the Study:
- To develop new information-theoretic measures for spatial structure in any dimension.
- To establish the convergence of entropy density as a metric for global correlation.
- To compare this new method with existing techniques like mutual information and structure factors.
Main Methods:
- Developing information-theoretic measures based on entropy density convergence.
- Analyzing the rate of convergence of conditional entropies to their asymptotic values.
- Comparing the proposed method with mutual-information and structure-factor analyses.
Main Results:
- The convergence manner of conditional entropies quantifies global correlation and structure.
- This approach is applicable to spatial systems in any dimension.
- Entropy convergence offers a complementary perspective to mutual information and structure factors.
Conclusions:
- The rate of entropy convergence is a powerful new tool for analyzing multidimensional spatial systems.
- This method enhances the understanding of global correlation and structure.
- It provides a valuable alternative for spatial pattern quantification.
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