4. Built ANNs for soil properties

#### 4.1. ANNs for soil texture

A BP ANN was developed to estimate soil texture with three-layer structure in Figure 7 in Ref. [41]. The input layer had six nodes, including average clay and sand contents from coarse

Figure 7. ANN structure for predicting high-resolution clay content and sand content.

resolution soil data, and four DEM-generated topo-hydrologic variables. The output layer contained two nodes: predicted high-resolution clay and sand contents.

MSE <sup>¼</sup> <sup>1</sup> n Xn i¼1

was stopped.

3.3. ANN optimization

60 Advanced Applications for Artificial Neural Networks

nodes was too large, there was a potential over-fitting.

Figure 7. ANN structure for predicting high-resolution clay content and sand content.

4. Built ANNs for soil properties

4.1. ANNs for soil texture

ð Þ ti � oi

An early stopping method was used to avoid "over-fitting", which has the effect of decreasing prediction accuracy outside of the training data, and improving ANN generalization in Ref. [39, 40]. Through this method, in order to compute the gradient, update the network weights and estimate biases, a training set was used. Another data set, that is, the validation set, was applied to monitor the training process with the purpose of preventing "over-fitting". If training MSE decreased but the validating MSE increased, the training of the ANN model

The purpose of ANN optimization is adjusting networks structure and improving prediction accuracy of ANNs. It included two parts: (1) selecting the best combination of inputs. The schemes of combining inputs should follow one-variable, two-variable, three-variable, etc. (2) selecting the fittest number of hidden layer's nodes. When the number of hidden layer nodes was too small, prediction accuracy of the ANN was low. When the number of hidden layer

A BP ANN was developed to estimate soil texture with three-layer structure in Figure 7 in Ref. [41]. The input layer had six nodes, including average clay and sand contents from coarse

<sup>2</sup> (9)

The predictive capability of the ANN trained with LM and RP methods was assessed when the hidden layer nodes changed from 5 to 40, and training cycles changed from 25 to 250.

Accuracy of ANN models with the LM and RP training methods when 100 training cycles to various net structures is reported in Table 1. Results showed that the ANN models trained with the LM methods had much higher ROA 5% and lower MSE than the models trained with the RP methods when holding the same number of hidden layer nodes. The LM trained ANN models had better prediction capability. With increasing the number of hidden layer nodes, the MSE of ANNs trained by the LM method was decreasing, but the ROA 5% got the highest value with 25 hidden layer nodes. According to the results, the best ANN model of predicting clay and sand was a 6-25-2 ANN. Results also directed that when the number of hidden layer nodes was less than 25, the hidden layer scale was too small and the accuracy of model prediction was low. However, over-fitting happened when the number of hidden layer nodes exceeding 25. When the ANN model has been over-fitted, the training accuracy (MSE)


\* Relative overall accuracy (ROA) 5%, a parameter of assessing the relative accuracy of model predictions, was calculated by counting all predictions within a 5% range of the referenced clay and sand content.

Table 1. Prediction accuracy of ANNs trained with LM and RP algorithms with 100 epochs and nodes of hidden layer changing from 5 to 40 in ref. [41].

increased but the prediction accuracy decreased. In another word, over-fitted ANN models would have poor "generalization" and could lead to inaccurate prediction when using to other input data than the original training set. The same results were presented for the nets trained by the RP method, but the RP method had the highest value of prediction accuracy with 30 hidden layer nodes and the best net structure was 6-30-2.

Prediction accuracies of the 6-25-2 network using the LM training method with training cycles of 25–250 are showed in Table 2. As presented, the values of ROA 5% had the maximum value after 100 epochs. The results indicated that when the epochs of training was more than 100, the ANNs could be over-trained, which is another form of over-fitting.

It can be concluded that net structure, training algorithms, and training cycles would have significant impacts on performance of an ANN.
