## 2 Density-Based Spatial Clustering of Applications with Noise (DBSCAN) Description  
In density-based clustering, an assumption is made: clusters are dense regions in space, separated by regions of lower density [16]. A dense cluster is a region which is \"density connected\", i.e., the density of points in that region is greater than a minimum [17]. DBSCAN is an example that searches for dense areas and expands these recursively to find arbitrarily dense-shaped clusters. The two main parameters of DBSCAN are the \(\varepsilon\) (\"Epsilon\") and the \"minimum points\". The \(\varepsilon\) defines the radius of the \"neighbourhood region\" while the \"minimum points\" define the minimum number of constellation points (i.e., symbols) that should be contained within that neighbourhood. DBSCAN arbitrarily picks up a point until all of them have been visited. If the predefined number of \"minimum points\" is within the radius \(\varepsilon\), then all these points are considered to be part of the same cluster. The clusters are then expanded by recursively repeating the neighbourhood calculation for each neighbouring point. However, for the unallocated points, if the number of points within the \(\varepsilon\)-neighbourhood is less than a predefined threshold, they are designated to be \"noisy\" and are not assigned to a particular cluster. Noisy data are not further processed in conventional DBSCAN. Here, a 2 nd loop clustering is proposed to be applied only for these noisy data using (1) K-means [11] or (2) the minimum distance between an unlabelled point and the clustered points. A schematic diagram for conventional DBSCAN is depicted in Figure 1 when the minimum points are 4. In Figure 1, the following assumptions are assumed [18]:  
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The steps related to the conventional and modified DBSCAN are listed below, where the algorithm converges until all constellation points have been allocated to a cluster or labelled as \"noisy\" only if conventional DBSCAN is considered (step 5 below--1 st loop) [17; 18]:  
1. Randomly select a point \(p\) (referred in Figure 1) in the constellation map.
2. Retrieve all constellation points directly density reachable from \(p\) that satisfy the condition of the radius \(\varepsilon\) limits.
3. If the constellation point \(p\) is a core point, a cluster is formed. Search recursively and find all of its density-connected points and assign them to the same cluster as \(p\).
4. If \(p\) is not a core point, the DBSCAN algorithm \"scans\" for the rest of the unvisited constellation points.
5. DBSCAN 1 st loop: Points that are un-clustered are labelled as zero points (\"noisy points\") where linear equalisation is performed only on these points, and then the conventional DBSCAN algorithm stops.
6. DBSCAN 2 nd loop (extra novel step):  
1. _Method-1:_ K-means clustering is activated for the \"noisy points\" using the Lloyd's algorithm [11; 12]:
2. Assignment: Allocate each observation to the cluster whose mean has the least squared Euclidean distance (\"nearest\" mean) [11; 12].
3. Update: Calculate the new means to be the centroids of the observations in the new clusters [8; 9]. K-means converges when assignments do not change.
4. _Method-2:_ Calculation of minimum distance between the unlabelled \"noisy points\" and the clustered points.