# Adaptive Hierarchical Density-Based Spatial Clustering Algorithm for Streaming Applications
## 3 Methodology
### Data Preparation  
The dataset was created to replicate individuals moving about in a public environment. Individual movement can be separated into global and local motions, which can be simulated using a prospective method and a spatial network-based route. Individual global and local movements, as well as global and local movements of groups of people, are all included in the dataset for this study. As a result, it is critical to consider a few factors. First is the distribution of the points and the standard deviation of the distribution. The points are generated using a Gaussian distribution from the ground up. We assume the Gaussian form whenever we need to express real-valued random variables whose distribution is unknown. The probability density function f(x) can be expressed as equation [18] below:  
\[f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-p}{\sigma})^{2}} \tag{2}\]  
where \(\sigma\) is the standard deviation and \(\mu\) is the mean of the distribution. The Central Limit Theorem (CLT), which studies the sum of many random variables, is primarily responsible for this tendency. According to CLT, as the number of terms in the summation rises, the normalized sum of a number of random variables, regardless of the distribution they came from, converges to a Gaussian distribution. The movements of individual points are also modeled after the Gaussian distribution [18]. The movement of the synthetic clusters, however, are made to move in a specific direction. Each cluster will have a different density and direction of movement. For this study, the points start out at the corners of the pathway and move across to the other side of the frame. The geolocation of the points are then extracted frame-by-frame and used by the HDBSCAN algorithm for clustering.  
It becomes more difficult to produce original and different material for situations with high numbers of entities as the number of people participating grows. The nondeterministic characteristics of the system and the environment must be included in realistic modeling and simulation of complex systems. With the emphasis on assessing the system's safety in abnormal or failure settings, nondeterminism is deeply ingrained. It will quickly become too time consuming to develop or alter features for each individual one by one. If we apply a set of traits to a large number of people at once, however, we risk creating undesirable artifacts on a wider scale, such as an \"army-like\" look with excessively uniform or periodic distributions of people or characteristics. Since simulated data are quite perfect, we built in randomization to account for some disorder in real world datasets. For the simulation in this research, the number of points are predetermined per cluster, and at every time-slice, the points are simulated to move in a random direction with a set seed within the confounds of a distance. This will ensure that the dataset mimics the actual movements of the crowd. The overall clusters will move as instructed to move as a whole. Five total clusters are simulated with different densities, numbers of points, as well as shapes of clusters.