Spatial Data Analysis and Mapping Using Machine Learning Algorithms

Abstract

The Australian machine-learning workflows apply fusion, clustering, and estimation operations to hydrogeophysical data for deriving hydrostratigraphic units (HSUs). Data fusion is performed by training a self-organizing map (SOM) with these data. The application of Davies-Bouldin criteria to K-means clustering of SOM nodes determines the number and location of HSUs. Estimation is handled by iterative least-squares minimization of the SOM quantization and topographical errors. Two workflows provide 3D characterization of HSUs (and related attributes) from different hydrogeophysical data (measured, derived, interpolated, and estimated values) sets. In Workflow 1, the SOM learns to recognize relationships among a subset of borehole geophysical and hydrogeologic data. Using the data-fusion approach described above, the missing hydrological data are estimated using these learned relationships and HSUs determined at borehole sample locations resulting in a low lateral density and high vertical density spatial distribution. Variogram modeling of the regional field data and HSU estimates is undertaken to evaluate the spatial statistical structure of selected attributes. In workflow 2, the learned relationships between borehole data and the more spatially extensive AEM conductivity model are used to estimate the key attributes and HSUs at a number of locations away from the borehole. The AEM conductivity profile at a number of random locations are mapped to the SOM network and estimation performed to arrive at a set of continuous HSUs with high lateral density and medium vertical density (based on m-layer modelled structure). Performance metrics and validation are used to test each step of both workflows.

Primerjava metod prostorske interpolacije in večslojnih nevronskih mrež za različne geometrijske razporeditve točk na digitalnem modelu višin

“…In this study, six different training functions, namely trainlm (Levenberg-Marquardt) (More, 1978), traincgf (Fletcher-Powell Conjugate Gradient) (Scales, 1985), traingd (Gradient Descent), traingdx (Gradient descent with momentum and adaptive learning rule backpropagation) (Beale, 1972), trainrp (Resilient Backpropagation) (Riedmiller and Braun, 1993) and trainscg (Scaled Conjugate Gradient) (Moller, 1993) were used. (Ratle et al, 2008). …”

“…where w i are the weights corresponding to each neuron connection and w 0 is an additive bias corresponding to the entire hidden layer ( Figure 1); s is a sigmoid activation function which represents a nonlinear element in MLP: v i is a activation function steepness parameter (Ratle et al, 2008). The activation functions are log-sigmoid and tan-sigmoid are respectively given in equation 4.…”

“…Gradient optimization algorithms vary in performance efficiency and speed. Multiple results of the gradient optimization can be considered in order to reach the global minimum (or the lower local minimum) (Ratle et al, 2008). In this study, six different training functions, namely trainlm (Levenberg-Marquardt) (More, 1978), traincgf (Fletcher-Powell Conjugate Gradient) (Scales, 1985), traingd (Gradient Descent), traingdx (Gradient descent with momentum and adaptive learning rule backpropagation) (Beale, 1972), trainrp (Resilient Backpropagation) (Riedmiller and Braun, 1993) and trainscg (Scaled Conjugate Gradient) (Moller, 1993) were used.…”

“…Note that γ ij can be calculated for each data pair Z(x i ) and Z(x j ) (i,j=1,…, N(x 0 ) the number of data in the neighborhood of (x 0 )) whereas γ i0 is approximated by the fitted theoretical variogram model λ(h) with the separating vector h=x i -x 0 as an argument. An ordinary kriging variance (Ratle et al, 2008):…”

“…MLP or feed-forward back-propagation neural networks learn with supervision (with known expected outputs). Feed forward neural networks propagate information from the input to the output without recurrence and the error flow is propagated backwards from the output to the input modifying the ANN parameters according to captured dependencies from data (Ratle et al, 2008).…”