An efficient maximum entropy approach for categorical variable prediction

Allard, Denis; D’Or, Dimitri; Froidevaux, R.

doi:10.1111/j.1365-2389.2011.01362.x

Cited by 49 publications

(46 citation statements)

References 30 publications

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“…Bordley's formula has properties that are desirable in a geostatistical simulation framework. One of these properties is the 0/1 forcing property (Allard et al, 2011): if one probability term provides a null value (impossible event), then the aggregated result will be null; the same is valid for the value one (certain event). Other properties of Bordley's formula are external Bayesianity and nonconvexity (for more details see Comunian, 2011;Allard et al, in preparation).…”

Section: Bordley's Formulamentioning

confidence: 99%

3D multiple-point statistics simulation using 2D training images

Comunian¹,

Renard²,

Straubhaar³

2012

Computers & Geosciences

129

101

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a b s t r a c tOne of the main issues in the application of multiple-point statistics (MPS) to the simulation of threedimensional (3D) blocks is the lack of a suitable 3D training image. In this work, we compare three methods of overcoming this issue using information coming from bidimensional (2D) training images. One approach is based on the aggregation of probabilities. The other approaches are novel. One relies on merging the lists obtained using the impala algorithm from diverse 2D training images, creating a list of compatible data events that is then used for the MPS simulation. The other (s2Dcd) is based on sequential simulations of 2D slices constrained by the conditioning data computed at the previous simulation steps. These three methods are tested on the reproduction of two 3D images that are used as references, and on a real case study where two training images of sedimentary structures are considered. The tests show that it is possible to obtain 3D MPS simulations with at least two 2D training images. The simulations obtained, in particular those obtained with the s2Dcd method, are close to the references, according to a number of comparison criteria. The CPU time required to simulate with the method s2Dcd is from two to four orders of magnitude smaller than the one required by a MPS simulation performed using a 3D training image, while the results obtained are comparable. This computational efficiency and the possibility of using MPS for 3D simulation without the need for a 3D training image facilitates the inclusion of MPS in Monte Carlo, uncertainty evaluation, and stochastic inverse problems frameworks.

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Section: Bordley's Formulamentioning

confidence: 99%

3D multiple-point statistics simulation using 2D training images

Comunian¹,

Renard²,

Straubhaar³

2012

Computers & Geosciences

129

101

View full text Add to dashboard Cite

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“…Over the last decade, leaf spectral reflectance has been used successfully to discriminate plant species found in various habitat types/ecosystems [1][2][3][4]. In particular, in situ hyperspectral measurements greatly assist with the discrimination process by allowing contiguous spectral data to be analyzed statistically.…”

Section: Introductionmentioning

confidence: 99%

Plant Species Discrimination in a Tropical Wetland Using In Situ Hyperspectral Data

2014

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Abstract:We investigated the use of full-range (400-2,500 nm) hyperspectral data obtained by sampling foliar reflectances to discriminate 46 plant species in a tropical wetland in Jamaica. A total of 47 spectral variables, including derivative spectra, spectral vegetation indices, spectral position variables, normalized spectra and spectral absorption features, were used for classifying the 46 species. The Mann-Whitney U-test, paired oneway ANOVA, principal component analysis (PCA), random forest (RF) and a wrapper approach with a support vector machine were used as feature selection methods. Linear discriminant analysis (LDA), an artificial neural network (ANN) and a generalized linear model fitted with elastic net penalties (GLMnet) were then used for species separation. For comparison, the RF classifier (denoted as RFa) was also used to separate the species by using all reflectance spectra and spectral indices, respectively, without applying any feature selection. The RFa classifier was able to achieve 91.8% and 84.8% accuracy with importance-ranked spectral indices and reflectance spectra, respectively. The GLMnet classifier produced the lowest overall accuracies for feature-selected reflectance spectra data (52-77%) when compared with the LDA and ANN methods. However, when featureselected spectral indices were used, the GLMnet produced overall accuracies ranging from 79 to 88%, which were the highest among the three classifiers that used feature-selected data. A total of 12 species recorded a 100% producer accuracy, but with spectral indices, and an additional 8 species had perfect producer accuracies, regardless of the input features. The results of this study suggest that the GLMnet classifier can be used, OPEN ACCESSRemote Sens. 2014, 6 8495 particularly on feature-selected spectral indices, to discern vegetation in wetlands. However, it might be more efficient to use RFa without feature-selected variables, especially for spectral indices.

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“…Then, once an acceptable error on the proportions is defined (this choice will be application-specific), it is possible to find the parameters that yield the highest possible quality realizations (in terms of patterns reproduction) within this constraint. This 2-step parameterization approach was tested on a simple case, based on a training image which was obtained from an aerial photograph of sand dunes in the Gobi desert (Allard et al, 2011). The image, displayed in Fig.…”

Section: Optimal Parameters In the Case Of Global Proportions Constramentioning

confidence: 99%

Constraining distance-based multipoint simulations to proportions and trends

Mariethoz¹,

Straubhaar²,

Renard³

et al. 2015

Environmental Modelling & Software

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a b s t r a c tIn the last years, the use of training images to represent spatial variability has emerged as a viable concept. Among the possible algorithms dealing with training images, those using distances between patterns have been successful for applications to subsurface modeling and earth surface observation. However, one limitation of these algorithms is that they do not provide a precise control on the local proportion of each category in the output simulations. We present a distance perturbation strategy that addresses this issue. During the simulation, the distance to a candidate value is penalized if it does not result in proportions that tend to a target given by the user. The method is illustrated on applications to remote sensing and pore-scale modeling. These examples show that the approach offers increased user control on the simulation by allowing to easily impose trends or proportions that differ from the proportions in the training image.

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An efficient maximum entropy approach for categorical variable prediction

Cited by 49 publications

References 30 publications

3D multiple-point statistics simulation using 2D training images

3D multiple-point statistics simulation using 2D training images

Plant Species Discrimination in a Tropical Wetland Using In Situ Hyperspectral Data

Constraining distance-based multipoint simulations to proportions and trends

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