2026-07-24T01:58:43Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20824 2024-09-09T09:21:19Z ddc:004 open_access

Probing the Information Theoretical Roots of Spatial Dependence Measures Wang, Zhangyu Janowicz, Krzysztof Mai, Gengchen Majic, Ivan Spatial Autocorrelation Moran’s I Information Theory Surprisal Self-Information 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Zhangyu Wang and Krzysztof Janowicz and Gengchen Mai and Ivan Majic 2024 Is Part Of LIPIcs, Volume 315, 16th International Conference on Spatial Information Theory (COSIT 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.COSIT.2024.9 urn:nbn:de:0030-drops-208247 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2024.9 eng https://creativecommons.org/licenses/by/4.0/legalcode