## 2 Materials and Methods
### DBSCAN Technique  
Clustering methods are AI techniques aimed to identify groups of similar instances in a multivariate dataset: the so-called clusters. Among the different approaches existing in the literature, the density-based clustering methods perform the cluster identification by exploiting the idea that a cluster is a contiguous region of high point density in a data space, whereas low density regions represent noise.  
One of the most powerful density-based clustering methods is surely the abovementioned Density-based Spatial Clustering of Applications with Noise (DBSCAN) introduced by [PERSON] et al. [37] in 1996. In short, the DBSCAN algorithm works by considering three types of points: _core points_, _density-reachable points_ and _outliers_. In detail, a point in some space to be clustered can be identified as _core point_ if it is characterized by at least a minimum number of points (_minPoints_) within a selected distance (_eps_). As for _density-reachable points_, they are points reachable from a _core point_ through a path, such as \(p_{1}\), \(p_{2}\), \(\ldots\), \(p_{n}\)where \(p_{1}\) is a _core point_ and \(p_{n}\) is the _density-reachable point_. A point that is not reachable from any other point is classified as _outlier_, i.e., it represents noise.  
The workflow of the DBSCAN is presented below. DBSCAN starts with randomly selecting a point \(B\). Then, it collects all the points within a space with center \(B\) and radius _eps_. This space is referred as to the neighborhood of the point \(B\). If the neighborhood of the point \(B\) does not contain a number of points equal to _minPoints_, the point \(B\) is marked as an _outlier_. Otherwise, the algorithm creates a first cluster containing \(B\) and all points density-reachable from it. In turn, the new points are marked as _core points_ if their _eps_-neighborhood contains at least a _minPoints_ number of points, and the points density-reachable from them are added to the cluster. In brief, the cluster is built, incrementally, by adding all the points density-reachable from a _core point_ already present in the cluster. The cluster is complete when there are no other points that can be added. This occurs when the new added points are not _core points_. Once a cluster is completed, the DBSCAN algorithm selects a new random point out of the already completed clusters and repeats the process. It is worth noting that a point recognized as _outlier_ can be found in the neighborhood of a different point and can be introduced in the cluster of this point. Therefore, only at the end of the algorithm process, it is possible to definitely mark a point as _outlier_. By analyzing how DBSCAN works, there is a clear need to opportunely set two hyper-parameters: the radius of the neighborhood, _eps_, and the minimum number of points required inside of a cluster, _minPoints_. Figure 1 reports an example to clarify the functioning of the DBSCAN algorithm [38].  
DBSCAN algorithm is one of the most cited density-based clustering methods in the literature. It has been successfully used in several domains, such as urban planning, traffic congestion management and anomaly detection [39]. In the context of spatially extended data, DBSCAN has been already used for dealing with LiDAR data [40; 41] and Terrestrial Laser Scanning Data [42]. The main advantage of this clustering algorithm is the ability to discover clusters of arbitrary shapes in spaces of any dimension and effectively identify noise points. Starting from this analysis, DBSCAN seems a suitable approach for achieving one of the goals of this paper, that is, the identification of buildings by exploiting data acquired by means of the SBAS-DInSAR technique, without knowing a priori the number of buildings in the area, their shape, and the dimension of the initial dataset.