## 6 Methodology
### Cauterization Analysis and Discussion  
This section presents the acquired experimental findings. To gain deeper insights into the data, we employed two algorithms: density-based spatial clustering of applications with noise (DBSCAN) and ordering points to identify the clustering structure (OPTICS) to extract clusters of varying data densities. Both algorithms can significantly enhance the efficiency and accuracy of data analysis in space missions, leading to new insights. The dependence in time of the normalized status vector is shown in Figure 21, the figure shows the dependence in time of the state space of Juno (Juno's position and motion over time) for three operation phases (OPs): OP1 (top), OP2 (middle), and OP3 (bottom). The y-axis represents the \"Status Structures\", which likely refers to the normalized values of the acceleration, jerk, and snap (a.j.s). The x-axis shows the time in hours. The graph shows how the normalized acceleration, jerk and snap (a.j.s) of Juno change over time for the three different operation phases. The x-axis shows the time in hours; we have 900 rows (5x vectors/minute x 60 min). Clustering is a fundamental methodology that has witnessed meteoric expansion in recent years within the realm of machine learning algorithms. DBSCAN is a popular clustering algorithm used in predictive analytics that identifies dense regions in a dataset by grouping data points that are in proximity to one another according to a specified distance metric [40]. DBSCAN and OPTICS are both density-based clustering algorithms used in unsupervised machine learning. DBSCAN starts by selecting a random point and identifying all the elements within a certain radius (eps) from that point. These elements are then classified as either \"core\", \"border\" or \"noise\" points based on their distance from other elements. Core points are those that have a minimum number of neighboring elements (minPts) within an _eps_ radius, while border points are those that are within eps radius of core points but do not have the required number of neighbouring points. The algorithm then groups the core points and their border points into clusters, and any remaining elements are classified as noise. Figure 21: Dependence in time of the state space of Juno (\(\hat{r}\), \(\hat{v}\), \(\hat{a}\), \(\hat{j}\), \(\hat{s}\)): OP1: (**left**); OP2 (**middle**); and OP3 (**right**). DBSCAN does have the capability to locate clusters of varying sizes and forms, and it can also identify noise in the data [41]. The DBSCAN algorithm should be employed to reveal links and patterns in data that are challenging to identify manually yet may be significant and beneficial for discerning patterns and forecasting trends. These linkages and structures may be pertinent and beneficial since they can aid in predicting trends [42]. It creates a single cluster out of data points that have been \"densely packed\". It does this by analyzing the localized density of the data elements in the vast datasets to find any clusters that may exist. The fact that DBSCAN clustering can withstand the presence of outliers is the most fascinating aspect of this method. In contrast to K-means, which requires us to define the number of centroids in advance, this method does not demand that we provide any information on the number of clusters in advance. Epsilon and minPoints are the only two parameters that DBSCAN requests from its users. Epsilon represents the radius of the region that must be created around each data point to evaluate its density, while minPoints specifies the minimum number of data points that must fall within this region for the point to be identified as a core point. OPTICS is an extension of DBSCAN that aims to overcome some of its limitations. OPTICS also identifies core points, border points, and noise points, but it does not require the _eps_ parameter to be set in advance. Instead, it uses a reachability distance measure to determine the density of points in the dataset.