# An Analysis of ML-Based Outlier Detection from Mobile Phone Trajectories
## 3 Framework for Continuous PoI Detection in Smart Cities
### Interdisciplinary Pol Definition and Detection Aspects  
The definition of Pol [4] in the context of our work relates to MCS and integrates user social behaviour. Our PoI concept goes beyond the usual spatial data (e.g., GPS coordinates), and follows the line of work that considers PoIs to be a product of space, time, and some measure of influence/attraction [24]. For instance, [PERSON] et al. defined a framework for personalised tour recommendations based on user interests and network visit duration [25]. Their work assumes that there are already pre-established PoIs (municipality data), and the recommendation engine provides a recommendation based on such a PoI set only. However, the overlapping of different individual trajectories can also assist in detecting PoIs which are based on user preferences. From an individual (one user perspective) a PoI is related to the _social attractiveness_ of a user to a specific event or activity, which is defined by different attributes, geo-location being one such attribute. The social attractiveness level varies with time and space and increases with a larger visit to a specific location. For instance, a person can, in his/her daily routine, stop at a specific location due to having met an acquaintance, or even for curiosity and not necessarily due to an activity or event. This would be a transient SP and should not result in a PoI. From an aggregated perspective, a PoI can be detected by analysing the similarity of different trajectories in terms of social interaction and similarity patterns in social interaction. While PoI detection is a well-addressed issue in the context of geo-location systems where large and dense datasets are usually applied, we want to be able to detect PoIs  
Figure 1: Functional blocks of a framework for continuous detection of PoIs in a Smart City, assuming data obtained in close to real time from MCS applications. seamlessly, based on MCS and on individual anonymous trajectories collected by Smart City infrastructures and personal devices. Related literature concerning geo-location and localisation aspects describe several techniques for this purpose, e.g., collecting only geographic data users' paths for specific time windows (location), and collecting data from a triangulation of cellular transmitters (location). In the context of our work, it is relevant to consider seamless ways to correlate the trajectory data collected in close-to-real-time from different users. Such data may be then correlated with existing PoIs (geo-location) as well. The detection of new PoIs is, therefore, derived from cluster similarity obtained when considering multiple individual trajectories. For this purpose, our work currently considers two different definitions to detect PoIs. **Definition 1**. : _A PoI is defined by its edge betweenness, i.e., it is defined based on the number of individual trajectories crossing a specific point or within a specific radius. A PoI in this context can be detected via similarity analysis within a specific time and space range._  
**Definition 2**. : _A PoI is defined by the clustering derived from the spatial overlap of individual trajectories. A PoI in this context is detected when there are clusters that have high density._  
Both definitions are impacted by other parameters, for instance, speed, visit time, and time granularity. _Speed (v)_, defined in Equation (1), concerns the average speed that an individual user experiences during his/her periodic routine. In Equation (1), \(e\) corresponds to the distance travelled (in meters) and \(t\) corresponds to the time of travel. \[\delta v=\frac{\delta e}{\delta t} \tag{1}\]  
Another possibility to define speed is to consider speed as a result of the displacement between points in a trajectory, as provided in Equation (2).