# A Novel Traffic Analysis Zone Division Methodology Based on Individual Travel Data
## 2 Data Preprocessing
### Space-Time Mapping and Discretization  
As a common kind of individual travel data, bus smart-card data include the card number, station number, boarding/alightment time, bus line, station, etc. The geographic information of the bus network is used as spatial data, including the names and numbers of bus lines and stations, and line routing information. The two types of data are matched through the line of passengers getting on and off the bus and the station coding rules, and the travel data are matched with the space line network to obtain the travel information \(J_{n}\) of passengers getting on and off the bus at the station \(s_{n}\) (see Equation (1)). Here, \(P_{i}\) represents the travel information of passenger \(i\), including information on boarding time \(T_{i1}\), boarding station \(S_{i1}\), alighting time \(T_{i2}\), and alighting station \(S_{i2}\) (see Equation (2)). \[J_{n}=[P_{1},P_{2},\dots,P_{n}] \tag{1}\]  
\[P_{i}=[T_{i1},S_{i1},T_{i2},S_{i2}] \tag{2}\]  
In the spatial dimension, according to the passenger travel information \(J_{n}\) at station \(s_{n}\), the total number of trips \(E_{n}\) at the corresponding station and the number of trips \(OD_{n}\) between different stations are obtained. Then, based on the distribution of bus stations, the Delaunay triangulation method is used to divide the space into Tyson polygon areas centered on a bus station. Then, the total number of trips \(E_{n}\) of station \(s_{n}\) is mapped to the corresponding Tyson polygon area \(V_{n}\), where a Delaunay triangular mesh is applied; this is a triangular meshing method based on the construction of a given set of points, and for any triangle, its outer circle contains no other points.Assuming that there are 20 randomly distributed bus stations, the Delaunay triangular mesh method is divided as shown in Figure 1, where the different bus stations and their corresponding trip volumes are indicated. The abscissa \((x)\) and ordinate \((y)\) in Figure 1 represent the normalized position of the bus station on the two-dimensional plane, reflecting the relative geometric relationship between the stations. The location of the station is represented by a normalized dimensionless unit, which is evenly distributed in the \([0,1)\) area. The Tyson polygon is dual to the Delaunay triangulation, and by using the perpendicular bisector of the line joining the centers of the outer circles of the Delaunay triangle as a boundary, the Tyson polygon corresponding to that point is obtained. The Tyson polygon consists of all points that are closer to the seed point of that polygon than any other seed point, and can be mathematically represented as  
\[V(h)=\{x|d(x,h)\leq d(x,q),\forall h\
eq q\} \tag{3}\]  
In Equation (3), \(V(h)\) denotes the Tyson polygon with \(h\) as the seed point, and \(d(x,y)\) denotes the distance between \(x\) and \(y\). The Tyson polygon obtained on the basis of Figure 1 is shown in Figure 2.  
Figure 1: Delineation diagram of Delaunay triangulation of bus stations. Figure 2: Tyson polygon division diagram of bus stations. Finally, a square grid is used to spatially discretize the area to be studied, and a discretized spatial cell is obtained. According to the spatial mapping relationship between the discretized cell and the Tyson polygon, the trips in the Tyson polygonal area are discretized into the spatial cell using the area-weighting method, and the total number of trips corresponding to each grid \(q_{k}\) is obtained, as shown in Figure 3, with the thermal value of the cell representing its trip volume. The purpose of the area-weighting method is to discretize the plane in Figure 2 into a uniform grid unit of \(20\times 20\), calculate the intersection area of each polygon and the grid unit, and allocate the total travel volume of the bus station to the intersecting grid unit according to the area ratio.