## 6 Methodology
### Cauterization Analysis and Discussion
A large normalized radius signifies a larger Eps value, which means more data points are considered neighbors of a given point. DBSCAN merges points and clusters that are within the Eps distance, reducing the overall number of clusters and potentially reducing the number of core points (fewer central points in larger clusters). Figure 23: Properties of the hourly status vectors in OP3, downsampled by 20: mean no. of DBSCAN core points vs. normalized radius. A small normalized radius signifies a smaller Eps value. Only very close neighbors are considered. This can lead to the separation of data points into more numerous, smaller clusters, potentially increasing the number of core points (more data points might be central to smaller clusters). The work point in the image likely refers to a specific operating condition or state of interest. The location of the work point on the curve indicates the average number of core points obtained for that specific condition using a chosen normalized radius. The information about the hourly status vectors in OP3, downsampled by 20: the DBSCAN cluster elements are provided in Figure 24. The image depicts a graph showing the results of applying the DBSCAN clustering algorithm to the hourly status vectors in OP3, after downsampling the data by a factor of 20. This axis represents the value of the normalized radius used in the DBSCAN algorithm. As discussed earlier, the normalized radius is obtained by dividing the Eps parameter (neighborhood radius) by a characteristic distance scale of the data. It allows for comparing the clustering results across datasets with different units or scales. The y-axis shows the number of clusters identified by DBSCAN for different values of the normalized radius. The graph typically shows a curve that starts high on the left and decreases as the normalized radius increases on the x-axis. This is because, with a larger normalized radius (larger Eps), more data points are considered neighbors, leading to the merging of smaller clusters into larger ones, resulting in fewer overall clusters. Conversely, a smaller normalized radius (smaller Eps) creates stricter neighborhood criteria, causing data points to be separated into more numerous, smaller clusters. The hourly status vectors in OP3 likely represent a set of numerical values that capture the state of the system at each hour. By applying DBSCAN and analyzing how the number of clusters varies with the normalized radius, we can gain insights into the inherent groupings or patterns within the status vectors. The imagery in Figure 25 depicts a graph that shows the distribution of the number of clusters (cardinality) identified by the DBSCAN algorithm across 100 runs. The graph visualizes the variability in the number of clusters obtained by DBSCAN across multiple runs. This can be due to several factors. Sensitivity to initialization order: DBSCAN can be sensitive to the order in which data points are processed, especially for data on the borders of clusters. Running the algorithm multiple times with different starting points can sometimes lead to slightly different clusterings. Figure 24: Properties of the hourly status vectors in OP3, downsampled by 20: DBSCAN cluster elements. Parameter sensitivity: The choice of the normalized radius (Eps) can significantly impact the number of clusters. The graph might show a spread of cluster cardinalities if the chosen radius falls in a sensitive region of the curve (where small changes in the radius lead to large changes in the cluster count). Stochasticity: If the DBSCAN implementation uses any random elements (e.g., random tie-breaking rules), it can introduce some level of randomness into the clustering process, potentially leading to variations across runs. The ideal scenario would be a tight cluster around a specific cardinality value, indicating consistent clustering across all the runs. The interpretation of the variability depends on the specific application and the desired level of consistency in the clustering results.