## 2 Methods of Grouping Objects into Sets of Similar Objects  
Clustering is one of the most popular exploratory data analysis techniques. It involves dividing a dataset into subsets such that data points in the same subset (cluster) are similar to each other, while data points in different clusters are different. Different measures of similarity can be used, such as Euclidean distance or the strength of correlational relationships. Mining companies in Poland are an interesting testing ground. They are multi-site-multi-branch companies, with different levels of profitability, employment and operating conditions, making it impossible to develop and apply the same business strategy for all sites. Therefore, it seems purposeful to search for methods to group mines into typologically similar sets for comparison purposes, and to develop analogous business models for typologically similar groups. Comparisons made within the groups also become a source of information on the need for changes in certain areas of management, or to replicate good practices that work in other similar facilities. The method of stochastic taxonomy, which has a long tradition in the issue under consideration, can be used to group mining companies into statistically similar sets. The first time the term 'taxonomy' was used to refer to the classification of objects can be found in [PERSON] [2]. Over the years that followed, the method was developed and applied to the classification of various research objects [2; 3; 4; 5; 6; 7; 8]. The method groups objects (e.g., mining companies) into sets characterised by a high degree of similarity and heterogeneity with respect to other sets. Based on taxonomic measures, the studied objects are classified into so-called typologically similar groups. By dividing objects into typologically similar groups, sets of objects are obtained that are homogeneous with respect to the set criteria. The designated statistically homogeneous sets concentrate objects characterised by similar qualitative features, and provide a basis for comparative analysis for any objects outside the sets as well as within the sets. Typological division of objects into statistically homogeneous sets is made on the basis of parameters, features that are relevant to the purpose of the study. In recent years. other approaches have also been developed, including those using artificial intelligence methods such as cluster analysis methods, e.g., clustering with the EM algorithm or the k-means method, as well as neural networks [9; 10; 11; 12; 13; 14; 15]. The cluster analysis algorithm using the EM (expectation value maximization) method can be used to solve diverse research problems. It is useful wherever one seeks to group objects on the basis of similarity of variance [16]. The term \"cluster analysis\" was introduced almost a century ago by [PERSON] [17], and later developed by [PERSON] [18]. The use of cluster methods has increased significantly over the past 30 years [16]. Cluster analysis has been applied in various fields, including economics and sociology [19]. The k-means algorithm is an iterative algorithm that divides a dataset into K predefined distinct clusters, with each data point belonging to only one cluster. As a result of the calculation, the data points inside the clusters are as similar as possible, with maximum cluster diversity. Data points to a cluster are assigned in such a way that the sum of the squares of the distances between the data points and the cluster centroid (the arithmetic mean of all data points belonging to that cluster) is minimised. The lower the variability within clusters, the more homogeneous (similar) the data points in the same cluster. The k-means algorithm is very popular and used in various applications such as market segmentation, document clustering, image segmentation and compression, etc. [20]. The use of neural networks for clustering datasets generally means using Kohonen networks. These are self-organising learning networks of the competitive-with-competition type.