Information and complexity analysis of spatial data

Angulo, J. M.; Esquivel, Francisco Javier; Madrid, Ana E.; Alonso, Francisco

doi:10.1016/j.spasta.2020.100462

Cited by 6 publications

(8 citation statements)

References 26 publications

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“…For the case of continuous probability distributions, Catalán et al [ 15 ] proposed a modified ‘exponential’ version of the LMC complexity (in the sense that Shannon entropy is replaced with its exponential), which was the basis for the formulation of a two-parameter generalized complexity measure, proposed later by López-Ruiz et al [ 18 ]. In fact, the latter is perfectly meaningful also in the discrete case (see [ 16 ], for instance, in relation to [ 17 ] diversity index), for which it takes the form

…”

Section: Preliminariesmentioning

confidence: 99%

“…For

tends to

(hence with the latter being also denoted as

). The exponential of Rényi divergence (in particular, Kullback–Leibler divergence) can be interpreted as a ‘relative diversity index of order

’ (see [ 16 ]).…”

Section: Preliminariesmentioning

confidence: 99%

“…A divergence-based formulation of a product-type generalized relative complexity measure was introduced for continuous distributions by Romera et al [ 19 ]. In the discrete case, it takes the form (see Angulo et al [ 16 ], in relation to a concept of ‘relative diversity’)

…”

Section: Preliminariesmentioning

confidence: 99%

“…A similar analysis can be performed in the context of complexity—for instance, with López-Ruiz, Mancini and Calbet (LMC) measure of complexity [ 14 ]. The exponential extension of LMC complexity proposed in [ 15 ], although originally introduced to solve the problems that arise for continuous distributions, is also appropriate in the discrete case as it can be interpreted in terms of diversity [ 16 , 17 ]. A related two-parameter generalization, in terms of Rényi entropies of different deformation orders, was formulated by López-Ruiz et al [ 18 ].…”

Section: Introductionmentioning

confidence: 99%

“…In the last few decades, since Papangelou’s [ 20 ] work defining the entropy rate for continuous point processes in the real line, many other studies have introduced theoretical concepts in the context of Information Theory and complexity for the analysis of point processes. Baratpour et al [ 21 ] assessed the properties of non-homogeneous Poisson processes in terms of entropy; Daley and Vere-Jones [ 22 ] extended the definition of entropy for a point process in a d -dimensional space, and more recently, Angulo et al [ 16 ] introduced approaches to the analysis of spatial point patterns regarding informational and complexity aspects and focusing on a multifractal context. However, to our knowledge, complexity and information transfer between the two phases of generation of log-Gaussian Cox processes has not been explored.…”

Section: Introductionmentioning

confidence: 99%

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Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes

Medialdea

Angulo

Mateu

2021

Entropy

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The doubly stochastic mechanism generating the realizations of spatial log-Gaussian Cox processes is empirically assessed in terms of generalized entropy, divergence and complexity measures. The aim is to characterize the contribution to stochasticity from the two phases involved, in relation to the transfer of information from the intensity field to the resulting point pattern, as well as regarding their marginal random structure. A number of scenarios are explored regarding the Matérn model for the covariance of the underlying log-intensity random field. Sensitivity with respect to varying values of the model parameters, as well as of the deformation parameters involved in the generalized informational measures, is analyzed on the basis of regular lattice partitionings. Both a marginal global assessment based on entropy and complexity measures, and a joint local assessment based on divergence and relative complexity measures, are addressed. A Poisson process and a log-Gaussian Cox process with white noise intensity, the first providing an upper bound for entropy, are considered as reference cases. Differences regarding the transfer of structural information from the intensity field to the subsequently generated point patterns, reflected by entropy, divergence and complexity estimates, are discussed according to the specifications considered. In particular, the magnitude of the decrease in marginal entropy estimates between the intensity random fields and the corresponding point patterns quantitatively discriminates the global effect of the additional source of variability involved in the second phase of the double stochasticity.

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…”

Section: Preliminariesmentioning

confidence: 99%

“…For

tends to

(hence with the latter being also denoted as

). The exponential of Rényi divergence (in particular, Kullback–Leibler divergence) can be interpreted as a ‘relative diversity index of order

’ (see [ 16 ]).…”

Section: Preliminariesmentioning

confidence: 99%

…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes

Medialdea

Angulo

Mateu

2021

Entropy

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Infinite–Dimensional Divergence Information Analysis

Angulo

Ruiz-Medina

2022

Studies in Systems, Decision and Control

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Informational assessment of large scale self-similarity in nonlinear random field models

Angulo,

Ruiz-Medina

2023

Stoch Environ Res Risk Assess

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Large-scale behavior of a wide class of spatial and spatiotemporal processes is characterized in terms of informational measures. Specifically, subordinated random fields defined by nonlinear transformations on the family of homogeneous and isotropic Lancaster–Sarmanov random fields are studied under long-range dependence (LRD) assumptions. In the spatial case, it is shown that Shannon mutual information between random field components for infinitely increasing distance, which can be properly interpreted as a measure of large scale structural complexity and diversity, has an asymptotic power law decay that depends on the underlying LRD parameter scaled by the subordinating function rank. Sensitivity with respect to distortion induced by the deformation parameter under the generalized form given by divergence-based Rényi mutual information is also analyzed. In the spatiotemporal framework, a spatial infinite-dimensional random field approach is adopted. The study of the large-scale asymptotic behavior is then extended under the proposal of a functional formulation of the Lancaster–Sarmanov random field class, as well as of divergence-based mutual information. Results are illustrated, in the context of geometrical analysis of sample paths, considering some scenarios based on Gaussian and Chi-Square subordinated spatial and spatiotemporal random fields.

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Information and complexity analysis of spatial data

Cited by 6 publications

References 26 publications

Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes

Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes

Infinite–Dimensional Divergence Information Analysis

Informational assessment of large scale self-similarity in nonlinear random field models

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