A Formal Model of Trajectories for the Aggregation of Semantic Attributes

A trajectory is a set of time-stamped locations of a moving object usually recorded by GPS sensors. Today, an abundance of these data is available. These large quantities of data need to be analyzed to determine patterns and associations of interest to business analysts. In this paper, a formal model of trajectories is proposed, which focuses on the aggregation of semantic attributes. These attributes can be associated by the analyst to different structural elements of a trajectory (either to the points, to the edges, or to the entire trajectory). The model allows the analyst to specify not only these semantic attributes, but also to specify for each semantic attribute the set of aggregation operators (SUM, AVG, MAX, MIN, etc.) that the analyst considers appropriate to be applied to the attribute in question. The concept of PAV (package of aggregate values) is also introduced and formalized. PAVs can help identify patterns in traffic, tourism, migrations, among other fields. Experiments with real data about trajectories of people revealed interesting findings about the way people move and showed the expediency and usefulness of the proposal. The contributions in this work provide a foundation for future research in developing trajectory applications including analysis and visualization of trajectory aggregated data based on formal grounds.