Inference of a Hidden Spatial Tessellation from Multivariate Data: Application to the Delineation of Homogeneous Regions in an Agricultural Field

Guillot, Gilles; Kan-King-Yu, Denis; Michelin, Joël; Huet, Philippe

doi:10.1111/j.1467-9876.2006.00544.x

Cited by 15 publications

(17 citation statements)

References 36 publications

(40 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this case a statistical model may be invoked for how the boundary uncertainty affects predictions from the model. Examples of this are given by Lillah and Boisvert (2013), SilanCárdenas et al (2009) and Guillot et al (2006) and an interesting stochastic model for uncertainty in geographical polygons is offered by Heuvelink et al (2007). However, in the case of conventional geological survey, boundaries do not emerge from a statistical model for a response variable, but are the result of expert interpretation.…”

Section: Past Work On the Uncertainty Of Geological Boundariesmentioning

confidence: 99%

Uncertainty in mapped geological boundaries held by a national geological survey:eliciting the geologists' tacit error model

et al. 2015

View full text Add to dashboard Cite

Abstract. It is generally accepted that geological line work, such as mapped boundaries, are uncertain for various reasons. It is difficult to quantify this uncertainty directly, because the investigation of error in a boundary at a single location may be costly and time consuming, and many such observations are needed to estimate an uncertainty model with confidence. However, it is recognized across many disciplines that experts generally have a tacit model of the uncertainty of information that they produce (interpretations, diagnoses, etc.) and formal methods exist to extract this model in usable form by elicitation. In this paper we report a trial in which uncertainty models for geological boundaries mapped by geologists of the British Geological Survey (BGS) in six geological scenarios were elicited from a group of five experienced BGS geologists. In five cases a consensus distribution was obtained, which reflected both the initial individually elicited distribution and a structured process of group discussion in which individuals revised their opinions. In a sixth case a consensus was not reached. This concerned a boundary between superficial deposits where the geometry of the contact is hard to visualize. The trial showed that the geologists' tacit model of uncertainty in mapped boundaries reflects factors in addition to the cartographic error usually treated by buffering line work or in written guidance on its application. It suggests that further application of elicitation, to scenarios at an appropriate level of generalization, could be useful to provide working error models for the application and interpretation of line work.

show abstract

Section: Past Work On the Uncertainty Of Geological Boundariesmentioning

confidence: 99%

Uncertainty in mapped geological boundaries held by a national geological survey:eliciting the geologists' tacit error model

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Guillot et al (2006) propose a method to infer an underlying PVT in a data set, which allows them to generate spatial predictions which include a component which is uniform within Voronoi polygons. The inference is complex, and undertaken by Monte Carlo Markov Chain methods.…”

Section: Stochastic Geometry 715mentioning

confidence: 99%

“…The inference is complex, and undertaken by Monte Carlo Markov Chain methods. While Guillot et al (2006) compute variograms of their data for exploratory purposes, they do not make a link between these and the PVT that they set out to estimate. It would be interesting to explore whether fitting a variogram model, with a nested PVT component, to the empirical variogram could improve the efficiency of this approach by providing prior estimates of the intensity parameter, l, and the between-polygon variance.…”

Section: Stochastic Geometry 715mentioning

confidence: 99%

A stochastic‐geometric model of soil variation

Lark

2009

European J Soil Science

View full text Add to dashboard Cite

Stochastic models of soil variation are used in geostatistical analysis, but in general they bear no relation to our mechanistic understanding of the processes in soil that cause its properties to vary spatially. It is proposed that we require a suitable stochastic model in which space is partitioned into discrete domains as a first step towards random spatial models that incorporate our understanding of processes in soil. Even though the soil is essentially continuous in its spatial variation, there are components of soil variation (e.g. differences between parent materials) which are discontinuous. This paper shows how variogram models can be derived directly from the Poisson Voronoi Tessellation (PVT), a stochastic-geometric partition of d-dimensional space. The PVT variogram models, for d = 2 and 3, were fitted to variograms estimated from data over disparate scales, including computerized tomographic images of soil aggregates (pixels of a few tens of micrometres long) and the land systems of Swaziland. In all cases, PVT variogram models fitted better than the conventional geostatistical ones. The good performance of PVT variogram models at these disparate scales encourages further work on tessellation models for soil variation. In principle such models could incorporate information on underlying factors of soil formation such as the spatial distribution of individual plants, the origin and growth of microbial colonies, spatial processes in soil chemistry (such as reaction-diffusion processes) and geometrical information on boundaries between geological strata or contrasting plant communities. PVT models may therefore be one component of a random model of soil variation which reflects our understanding of soil-forming processes, and so have a stronger scientific basis than the models that are now in standard use.

show abstract

“…The third group enforces the spatial contiguity during the clustering process [38,39]. The latest group relies on the assumption that observations are drawn from a particular distribution like a mixture of Gaussian or Markov random fields [1][2][3][4]14,21].…”

Section: Introductionmentioning

confidence: 99%

A spectral clustering approach for multivariate geostatistical data

Fouedjio

2017

Int J Data Sci Anal

View full text Add to dashboard Cite

Spectral clustering has recently become one of the most popular modern clustering methods for conventional data. However, applied to geostatistical data, the general spectral clustering method produces clusters that are spatially non-contiguous which is certainly undesirable for many geoscience applications. In this paper, a spectral clustering approach is proposed, allowing to discover spatially contiguous and meaningful clusters in multivariate geostatistical data, in which spatial dependence plays an important role. The proposed spectral clustering approach relies on a similarity measure built from a nonparametric kernel estimator of the multivariate spatial dependence structure of the data, emphasizing the spatial correlation among data locations. It integrates existing methods to find the relevant number of clusters and to assess the contribution of variables in the formation of the clusters. The results from both synthetic and real-world datasets demonstrate that the proposed spectral clustering approach can effectively provide spatially contiguous and meaningful clusters.

show abstract

Inference of a Hidden Spatial Tessellation from Multivariate Data: Application to the Delineation of Homogeneous Regions in an Agricultural Field

Cited by 15 publications

References 36 publications

Uncertainty in mapped geological boundaries held by a national geological survey:eliciting the geologists' tacit error model

Uncertainty in mapped geological boundaries held by a national geological survey:eliciting the geologists' tacit error model

A stochastic‐geometric model of soil variation

A spectral clustering approach for multivariate geostatistical data

Contact Info

Product

Resources

About