Projection Pursuit Multivariate Transform

Barnett, Ryan M.; Manchuk, John G.; Deutsch, Clayton V.

doi:10.1007/s11004-013-9497-7

Cited by 77 publications

(48 citation statements)

References 19 publications

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“…For instance, the scatter diagram between any two transformed variables does not have an elliptical shape, which indicates that these transformed variables do not correspond to jointly Gaussian random fields. To avoid this inconvenience, a joint normal scores transformation can be used, such as stepwise conditional transformation (SCT) [27], flow transformation (FT) [28], or projection pursuit multivariate transformation (PPMT) [29][30][31]. All these methods require all the variables to be known at all the data locations (isotopic sampling), which is the case in the present case study; otherwise, the data set should be completed by multivariate imputation techniques [32] before joint normal scores transformation.…”

Section: Projection Pursuit Multivariate Transformationmentioning

confidence: 99%

“…In practice, the first two approaches are still limited to few variables (SCT) or to small data sets (FT), and for this reason we chose the third approach (PPMT) here. The PPMT transformation is based on an iterative algorithm and allows the complex dependence relationships (such as nonlinearities and heteroscedasticities) between cross-correlated variables to be removed, providing a set of new variables that are normally distributed and uncorrelated at collocated locations [29][30][31]. The transformation uses declustering weights to account for the uneven positions of the drill hole data in space.…”

Section: Projection Pursuit Multivariate Transformationmentioning

confidence: 99%

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Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

2017

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This paper proposes a geostatistical approach for geological modelling and for validating an interpreted geological model, by identifying the areas of an ore deposit with a high probability of being misinterpreted, based on quantitative coregionalised covariates correlated with the geological categories. This proposal is presented through a case study of an iron ore deposit at a stage where the only available data are from exploration drill holes. This study consists of jointly simulating the quantitative covariates with no previous geological domaining. A change of variables is used to account for stoichiometric closure, followed by projection pursuit multivariate transformation, multivariate Gaussian simulation, and conditioning to the drill hole data. Subsequently, a decision tree classification algorithm is used to convert the simulated values into a geological category for each target block and realisation. The determination of the prior (ignoring drill hole data) and posterior (conditioned to drill hole data) probabilities of categories provides a means of identifying the blocks for which the interpreted category disagrees with the simulated quantitative covariates.

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Section: Projection Pursuit Multivariate Transformationmentioning

confidence: 99%

Section: Projection Pursuit Multivariate Transformationmentioning

confidence: 99%

Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

2017

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“…Although this guarantees only marginal normality and not joint normality, until recently there were no practical alternative methods that deliver a multivariate jointly normal data-set. Stepwise conditional transformation (Leuangthong and Deutsch, 2003) is not practical for high-dimensional data-sets, and the projection pursuit multivariate transform (Barnett et al, 2014), a recent approach that promises to remedy this shortfall, could not be implemented here as it appeared only during the review process.…”

Section: Regionalized Compositionsmentioning

confidence: 99%

Improving processing by adaption to conditional geostatistical simulation of block compositions

Tolosana‐Delgado

Mueller

Boogaart

et al. 2015

J. S. Afr. Inst. Min. Metall.

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“…Once the data are transformed to normal scores, the experimental variograms are computed from normal scores, and a variogram model is fitted to the experimental points. More sophisticated transformation may be required for correlated variables of complex relationship (Leuangthong and Deutsch 2003; Barnett et al 2014). The variables should be presented by data sampled homotopically (at same locations), otherwise experimental variograms will not be stable.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Multivariate grid-free geostatistical simulation with point or block scale secondary data

Zagayevskiy

Deutsch

2015

Stoch Environ Res Risk Assess

Self Cite

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A novel grid-free geostatistical simulation method (GFS) allows representing coregionalized variables as an analytical function of the coordinates of the simulation locations. Simulation on unstructured grids, regridding and refinement of available realizations of natural phenomena including, but not limited to, environmental systems are possible with GFS in a consistent manner. The unconditional realizations are generated by utilizing the linear model of coregionalization and Fourier series-based decomposition of the covariance function. The conditioning to data is performed by kriging. The data can be measured at scattered point-scale locations or sampled at a block scale. Secondary data are usually used in conjunction with primary data for the improved modeling. Satellite imaging is an example of exhaustively sampled secondary data. Improvements and recommendations are made to the implementation of GFS to properly assimilate secondary exhaustive data sets in a grid-free manner. Intrinsic cokriging (ICK) is utilized to reduce computational time and preserve the overall quality of the simulation. To further reduce the computational cost of ICK, a block matrix inversion is implemented in the calculation of the kriging weights. A projection approach to ICK is proposed to avoid artifacts in the realizations around the edges of the exhaustive data region when the data do not cover the entire modeling domain. The point-scale block value representation of the block-scale data is developed as an alternative to block cokriging to integrate block-scale data into realizations within the GFS framework. Several case studies support the proposed enhancements.

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Projection Pursuit Multivariate Transform

Cited by 77 publications

References 19 publications

Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

Improving processing by adaption to conditional geostatistical simulation of block compositions

Multivariate grid-free geostatistical simulation with point or block scale secondary data

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