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Probing the Information Theoretical Roots of Spatial Dependence Measures

Authors Zhangyu Wang , Krzysztof Janowicz, Gengchen Mai , Ivan Majic

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Author Details

Zhangyu Wang
  • University of California Santa Barbara, CA, USA
Krzysztof Janowicz
  • Faculty of Geosciences, Geography and Astronomy, University of Vienna, Austria
  • University of California Santa Barbara, CA, USA
Gengchen Mai
  • SEAI Lab, Department of Geography and the Environment, University of Texas at Austin, TX, USA
  • Department of Geography, University of Georgia, Atlanta, GA, USA
Ivan Majic
  • University of Vienna, Austria

Funding

  • Wang, Zhangyu: This work was supported by the National Science Foundation under Grant No. 2033521 A1 – KnowWhereGraph: Enriching and Linking Cross-Domain Knowledge Graphs using Spatially-Explicit AI Technologies.

Cite AsGet BibTex

Zhangyu Wang, Krzysztof Janowicz, Gengchen Mai, and Ivan Majic. Probing the Information Theoretical Roots of Spatial Dependence Measures. In 16th International Conference on Spatial Information Theory (COSIT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 315, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.COSIT.2024.9

Abstract

Intuitively, there is a relation between measures of spatial dependence and information theoretical measures of entropy. For instance, we can provide an intuition of why spatial data is special by stating that, on average, spatial data samples contain less than expected information. Similarly, spatial data, e.g., remotely sensed imagery, that is easy to compress is also likely to show significant spatial autocorrelation. Formulating our (highly specific) core concepts of spatial information theory in the widely used language of information theory opens new perspectives on their differences and similarities and also fosters cross-disciplinary collaboration, e.g., with the broader AI/ML communities. Interestingly, however, this intuitive relation is challenging to formalize and generalize, leading prior work to rely mostly on experimental results, e.g., for describing landscape patterns. In this work, we will explore the information theoretical roots of spatial autocorrelation, more specifically Moran’s I, through the lens of self-information (also known as surprisal) and provide both formal proofs and experiments.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Information theory
  • Information systems → Geographic information systems
  • Computing methodologies → Philosophical/theoretical foundations of artificial intelligence
Keywords
  • Spatial Autocorrelation
  • Moran’s I
  • Information Theory
  • Surprisal
  • Self-Information

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