## 4 Results
### Clustering Results  
This subsection provides information about the different clustering methods used during the study and the obtained results. A key point to evaluate clustering, in this case, is that data clustering was performed without prior knowledge of the actual data classes/clusters. It was impossible to use metrics such as accuracy, NMI, or other metrics requiring real clusters. Therefore, this paper used only the metrics that do not require real clusters and can be applied to solve real problems. Commonly used evaluation metrics for clustering without prior knowledge of labels include the silhouette coefficient, Davies-Bouldin index, and the Calinski-Harabasz index (CH Index). The silhouette coefficient measures the cohesion and separation of the clusters by comparing the average distance between data points within the same cluster to the average distance between data points in the nearest different cluster [74]. Higher silhouette coefficient values indicate better clustering quality, ranging from \(-1\) to \(1\). The Davies-Bouldin index evaluates the clustering quality by combining intra-cluster similarity and inter-cluster dissimilarity [75]. Lower Davies-Bouldin index values signify better clustering with compact and well-separated clusters. The Calinski-Harabasz index (CH Index) assesses clustering quality by comparing the ratio of the between-cluster dispersion to the within-cluster dispersion [76]. A higher CH index value indicates better clustering, as it signifies a greater separation between clusters relative to the dispersion within clusters. During data dimension reduction in this work, different data clustering methods were used, and their hyperparameters were changed, thus determining the most suitable data clustering method for the data. K-means variable parameter k is the number of clusters whose parameter set is {2, 3, 4, 5, 10, 20, 30}. DBSCAN changeable parameters: eps with set {0.1, 0.2, 0.3, 0.4, 0.5, 0.75}, and minimum samples {5, 10, 20, 30, 50, 100}. HDBSCAN changeable parameters: minimum cluster size set {10, 20, 30, 40, 50, 100}, minimum samples set {5, 10, 20, 50}, and epsilon set {0.1, 0.2, 0.3, 0.4, 0.5, 1}. BIRCH changeable parameters: number of clusters set {2, 3, 4, 5, 10, 20, 50}, and branching factor set {10, 20, 50, 100}. Affinity propagation damping factor set {0.5, 0.6, 0.7, 0.8, 0.9}. CBMIDE and RCBMIDE parameters: number of the cluster as earlier methods, number of projections directions T set {5, 10, 20, 50, 100}, smoothing parameter h {0.05, 0.1, 0.2, 0.3, 0.4, 0.5}, and probability of noise cluster set {0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5}. Below is a table of the best model results (see Table 2). More than 3000 models were created to evaluate the best available model for this task. As mentioned earlier, more than 3000 data clustering models were created based on the reduced dataset. The reduced dataset made it possible to perform calculations faster. The results presented in the previous subsection prove that it is possible to do this with almost no loss of information. Data clustering assessment was performed based on Davies-Bouldin and Calinski-Harabasz metrics. In this case, the main metric was time Davies-Bouldin. In the case of extremely similar values, the Calinski-Harabasz metric was considered. Based on the obtained results, it was found that the HDBSCAN method displayed the best results, with a Davies-Bouldin value of 0.4475. HDBSCAN has emerged as the best-performing method in this scenario due to its unique ability to manage clusters of varying densities and shapes, and its robustness in identifying noise points. Unlike other clustering algorithms that require a predefined number of clusters, HDBSCAN automatically detects the optimal cluster structure based on the data's underlying density distribution. This adaptability makes it particularly suitable for complex datasets with uneven densities and non-spherical clusters. Furthermore, it is important to note that good results were also obtained using the RCBMIDE clustering method.