## 3 The Research Method Used
number of connections present in the network. In fact, the number of instances required also depends on the complexity of the functional dependency being modelled. However, this dependency generally has an unknown form, so it is difficult to come up with a truly exhaustive and accurate recipe for how many elements of a learning sequence are really indispensable. In smaller datasets, the network may not be sufficiently learned. In such a situation, simple models are preferred [25]. For such a small number of data as in the presented research, splitting the dataset into subsets of learning, test and validation data is not possible. The problem of a small number of cases is frequently encountered in research, and has therefore resulted in rich literature--e.g., [30; 31]. A comprehensive review of publications on this issue can be found in ref. [32]. In the case of this research, the results of which are presented herein, this problem was solved by limiting the number of subsets into which the considered set of mining plants was divided (Table 1). There is no universal algorithm to determine the number of similar groups, and thus the number of neurons in a Self-Organising Map network. Often, as a rule of thumb, we can assume that the SOM network should contain \(5\surd\)n neurons, where n is the number of datasets in the training set. This is usually a large enough number to capture the dominant patterns in the data. In the course of this study, the breakdowns of mines into 16, 8, 4 and 2 groups were analysed. The rejection of the division into 16 and 8 groups was due to the large number of groups with individual mines, while the grouping into only 2 sets was too general and did not allow generalisation of the information present in the dataset. By way of elimination, therefore, it was decided that grouping into 4 sets would be used for further research. The described course of action led to the following division of the analysed coal mines in Poland into four distinct groups:  
Group 1: 1 2 3 4 10 17 20 23 24 25 27 30 36
Group 2: 13 16 18 39
Group 3: 7 26 28 37
Group 4: 5 6 8 9 11 12 14 15 19 21 22 29 31 32 33 34 35 38  
Group 4 is the largest group, with 18 mines, followed by Group 1 with 13 mines. The other two concentrate 4 mines each (Figure 2). Tables 2-5 below present the resulting division into 4 groups of similar mines in Poland. Figure 2: Division of mines into similar sets (the colour scheme on the right is a scale of the distance of the cases from the winning neuron). \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**} & \multicolumn{2}{c}{**Intensity of**} & \multicolumn{2}{c}{**Number of Total**} & \multicolumn{2}{c}{**Average**} \\ \cline{2-5}  & **Output** & **Longwall Front** & **Pretary** & **Active Longwalls** & **Longwall Length** \\ \hline
7 & 14,595 & 1686 & 8.657 & 3.2 & 5.8 & 290.690 \\
26 & 24,382 & 1548 & 15.751 & 3 & 7.3 & 212.055 \\
28 & 16,098 & 1292 & 12.460 & 3.2 & 6 & 215.333 \\
37 & 14,690 & 1640 & 8.957 & 4 & 7.1 & 230.986 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Group 3 of mines.