## 3 The Research Method Used
The learning factor \(L\) is modified according to the following relation (Equation (4)): \[L=L_{0}exp\left(-\frac{it-1}{\mu}\right)\] (4) where _it_--the number of iterations, \(L_{0}\)--the initial learning factor and \(\mu\)--a constant characterising the decrease in the learning factor as a function of the number of iterations. 7. There is a return to step 2 until the set number of iterations is reached. After a sufficiently large number of iterations, the algorithm makes it possible to obtain a map of stable zones. Ultimately, interpreting the results obtained can make it possible to find invisible patterns in the data. The essence of neural networks is that we have no information about how the division was carried out. This is also the method's strength--it does not use arbitrary division criteria, but finds them on its own. Once the Kohonen network has been taught to correctly recognise the structure of the data presented, it can be used as a tool to carry out data visualisation in order to gain a better understanding of the data. The problem arises of checking whether the network has been sufficiently trained. One way to do this is to analyse the frequency of wins (the number of wins of each neuron during the presentation of learning data). This number can be used to check whether sufficiently distinct clusters have already been formed in the Kohonen map [25]. In the studies conducted, network learning was stopped when a preset number of iterations was reached. The number of iterations was determined by performing multiple calculations. The maximum number of iterations was defined as the number beyond which the division of the considered set of cases into similar subsets no longer changed. The number of iterations was assumed to be 30,000 for all considered cases of calculation. The Data Characterising the Mines: The Adopted Structure of the SOM Network and the Results of the Calculations  
For the cluster analysis used, it was necessary to select an appropriate set of diagnostic data, which are the inputs to the algorithm. In this study, selection was carried out as suggested by [PERSON], that the input variables should have substantive properties and some of the formal properties analysed in the research [29]. Thus, with the above in mind, the following parameters of mining concentration in coal mines of year X were adopted for the cluster analysis (Table 1):  
\[ \begin{array}{l}\text{o}\quad\text{average daily output,}\\ \text{o}\quad\text{length of longwall front,}\\ \text{o}\quad\text{output per meter,}\\ \text{o}\quad\text{intensity of preparatory works,}\\ \text{o}\quad\text{number of total active longwalls,}\\ \text{o}\quad\text{average longwall length.}\end{array} \]  
The values given in Table 1 were used in the SOM network learning process, which was carried out using Statistica(tm). Networks of two, four (Figure 1), eight and sixteen neurons were considered. The number of similar sets determined was equal to the number of neurons in the SOM network. Determining the size of the learning set, i.e., the correct number of instances required to teach a neural network, poses significant problems in the general case. There are some heuristic rules that make the number of instances required dependent on the size of the network. One of the simplest states that the number of instances should be ten times the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mine**} & \multicolumn{2}{c}{**Average Daily**} & \multicolumn{2}{c}{**Length of**} & \multirow{2}{*}{**Output per Meter**} & \multirow{2}{*}{**Intensity of**} & \multicolumn{2}{c}{**Number of Total**} & \multicolumn{2}{c}{**Average**} \\  & **Output** & & **Longwall Front** & & & **Preparatory** & **Active Longwalls** & **Longwall Length** \\ \cline{2-7}  & **[t/d]** & **[m]** & **[t/m]** & **Works** & **[pcs.]** & **[m]** \\ \hline  
964 & 550 & 19.935 & 4.3 & 2.2 & 250 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mining concentration parameters in coal mines in year X.  
Figure 1: SOM network with four neurons.