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Entropy and Diversity Indices for Spatial and Temporal Data

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: 31 August 2024 | Viewed by 2187

Special Issue Editors


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Guest Editor
School of Mathematics and Statistics, University of Sheffield, Sheffield S10 2TN, UK
Interests: geographical information science; geocomputational statistics; spatial data science; scientific workflow; interoperability; data quality and uncertainty; spatio-temporal data structuring and analysis; descriptive analytics; data optimisation and simulation
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Guest Editor
Department of Statistical Sciences, University of Bologna, via Belle Arti, 41, 40126 Bologna, Italy
Interests: statistics; spatio-temporal statistics; stochastic processes; Bayesian inference; INLA; entropy; spatial entropy and entropy estimation; environmental data; capture–recapture data

Special Issue Information

Dear Colleagues,

Entropy, as a concept and a tool to measure heterogeneity in distributional properties, has been widely used in many disciplines, and is still of significant importance in geography, ecology and other fields dealing with discrete spatio-temporal data. The roots of entropy come from information theory, and it belongs to the set of diversity indices, together with other popular examples such as Simpson’s index and the general Hill’s number. They are known to evaluate alpha, beta and gamma diversity in biodiversity and ecological studies; however, synthetic measures of heterogeneity are of interest over a wide variety of natural phenomena, such as earthquakes, wildfires, polluting agent, meteorological events and epidemiological data. Other fields of application, though not traditionally open to entropy and diversity measures, may benefit from the flexibility and interpretability of such indices.

In the aforementioned studies, the spatio-temporal support of data constitutes a stimulating challenge. The definition of spatial and spatio-temporal entropy for categorical data in the literature has evolved from Shannon’s entropy to a more complex description taking into account unequal grid sizes, area partitions, co-occurrences of observations for contiguous areas or based on a certain distance range of interest; they are applied to both areal and point data, and ascribe to various approaches. When the goal expands from data description to inference, indices need to be complicated accordingly in order to deal with data dependence on available covariates and on temporal/spatial effects.

This Special Issue intends to explore some of these aspects. Papers are welcome which cover new challenges in entropy and other diversity indices, either from a pertinent data analysis perspective (e.g., compelling examples and best use) or from a more methodological focus (e.g., critical thinking, new approaches and novel concepts).

Dr. Didier G Leibovici
Dr. Linda Altieri
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • entropy
  • diversity indices
  • mutual information
  • conditional entropy
  • spatial data
  • spatio-temporal data
  • co-occurrences
  • observations
  • proximity of observations
  • information theory

Published Papers (2 papers)

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Research

25 pages, 931 KiB  
Article
Efficient Computation of Spatial Entropy Measures
by Linda Altieri, Daniela Cocchi and Giulia Roli
Entropy 2023, 25(12), 1634; https://doi.org/10.3390/e25121634 - 08 Dec 2023
Viewed by 904
Abstract
Entropy indices are commonly used to evaluate the heterogeneity of spatially arranged data by exploiting various approaches capable of including spatial information. Unfortunately, in practical studies, difficulties can arise regarding both the availability of computational tools for fast and easy implementation of these [...] Read more.
Entropy indices are commonly used to evaluate the heterogeneity of spatially arranged data by exploiting various approaches capable of including spatial information. Unfortunately, in practical studies, difficulties can arise regarding both the availability of computational tools for fast and easy implementation of these indices and guidelines supporting the correct interpretation of the results. The present work addresses such issues for the most known spatial entropy measures: the approach based on area partitions, the one based on distances between observations, and the decomposable spatial entropy. The newly released version of the R package SpatEntropy is introduced here and we show how it properly supports researchers in real case studies. This work also answers practical questions about the spatial distribution of nesting sites of an endangered species of gorillas in Cameroon. Such data present computational challenges, as they are marked points in continuous space over an irregularly shaped region, and covariates are available. Several aspects of the spatial heterogeneity of the nesting sites are addressed, using both the original point data and a discretised pixel dataset. We show how the diversity of the nesting habits is related to the environmental covariates, while seemingly not affected by the interpoint distances. The issue of scale dependence of the spatial measures is also discussed over these data. A motivating example shows the power of the SpatEntropy package, which allows for the derivation of results in seconds or minutes with minimum effort by users with basic programming abilities, confirming that spatial entropy indices are proper measures of diversity. Full article
(This article belongs to the Special Issue Entropy and Diversity Indices for Spatial and Temporal Data)
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16 pages, 8165 KiB  
Article
Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectra
by Meng Fu and Yanguang Chen
Entropy 2023, 25(8), 1126; https://doi.org/10.3390/e25081126 - 27 Jul 2023
Viewed by 662
Abstract
Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas that experience [...] Read more.
Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas that experience more active growth. However, effectively utilizing multifractal spectra to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension Dq is defined. This index takes the growth rate of Dq at extreme negative moment order as the numerator and that at extreme positive moment order as the denominator. During the stable stage of urban growth, the index demonstrates a consistent pattern over time, while during the active stage, the index may exhibit abnormal fluctuations or even jumps. This indicates that the index can reveal spatio-temporal information about urban evolution that cannot be directly observed through multifractal spectra alone. By integrating this index with multifractal spectra, we can more comprehensively characterize the evolutionary characteristics of urban spatial structure. Full article
(This article belongs to the Special Issue Entropy and Diversity Indices for Spatial and Temporal Data)
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