## 4 Applied Methods
### Artificial Neural Networks  
Artificial neural network (ANN), as it is apparent from their name, are computational networks which are used for simulation of the network of brain neural cells in living creatures. Current knowledge of biologic scientists about the activity of neural neurons in the past few decades is the basis of designing such networks. Neural networks obtain their needed rules through teaching educational teaching. Neural networks use different algorithm for learning but without attention to applied method, learning is generally a repetitive operation during which a set of educational examples are shown to the  
Figure 7: Scatter plot of the predicted vs. actual iron ore price developing support vector regression (SVR) model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**10-Fold Model** & \(\varepsilon\) & \(\mathbf{c}\) & \(\mathbf{\gamma}\) & \(\mathbf{R^{2}}\) & **Ea** & **RMSE** \\ \hline
1 & 0.01 & 1 & 0.01 & 0.83 & 11.97 & 22.47 \\
2 & 0.01 & 10 & 0.01 & 0.90 & 8.54 & 16.15 \\
3 & 0.01 & 100 & 0.01 & 0.94 & 6.46 & 12.35 \\
4 & 0.01 & 500 & 0.01 & 0.97 & 4.95 & 8.88 \\
5 & 0.01 & 1000 & 0.01 & 0.97 & 4.69 & 8.18 \\
6 & 0.01 & 2000 & 0.01 & 0.98 & 4.38 & 7.68 \\
7 & 0.01 & 3000 & 0.01 & 0.98 & 4.26 & 7.48 \\
8 & 0.01 & 3000 & 0.06 & 0.98 & 3.88 & 6.65 \\
9 & 0.01 & 3000 & 0.08 & 0.98 & 3.84 & 6.63 \\
10 & 0.01 & 3000 & 0.10 & 0.98 & 3.94 & 6.75 \\ \hline \end{tabular}
\end{table}
Table 3: Results of ten-fold cross-validation and optimal values of C, \(\varepsilon\), and \(\gamma\) in predicting iron ore price.  
network so as to help it be thoroughly taught [99; 100; 101]. So, distribution is the most common learning algorithm of multi-layer neural networks with leading nutrition invented by [PERSON]. This method changes connection weights by slope reduction and minimizes error function [61; 62; 102; 103; 104; 105]. A neural network is composed of a number of neurons in consequent layers. Basically, three layers exist for such networks: an input layer, one or more middle layers in addition to existing neurons in each layer defined based on complexity of the issue through trial-and-error method. A simple network with leading nutrition of input R is presented in Figure 8[106].  
Each input, with suitable weight coefficient (W), is given a weight. Such weights are defined randomly and are corrected during the process of learning with reduction of network error. The sum of weight input and bias make up the input of function of stimulus F. In order to obtain the intended output, one can use a different transfer function. Tangent Sigmoid, logarithm sigmoid, linear and positive linear transfer functions are an example of such functions. In this model, trial-and-error method is used for the two intermediate hidden layers along with addition of logarithm sigmoid transfer function while its output shifts between zero and one. In output layer of leading multi-layer networks, positive linear transfer function was used [107; 108; 109; 110].  
Many researchers highlighted application of ANN in various fields of civil and mining works (e.g., [111; 112; 113]). A number of ANN models with different topology were built and among them, an ANN model with higher accuracy level was chosen. The most influential factors i.e., hidden layer No., No. of nodes in each hidden layer, and the applied transfer function were considered in modeling process. A network with architecture 12-6-1 with minimum error was found to be optimum. R\({}^{2}\) was determined between the predicted and the measured values as 0.977 for the optimum ANN model (see Figure 9) which shows capability of this model in predicting iron ore price.  
Figure 8: Structure of a simple neural cell with leading nutrition.