# Road Passenger Load Probability Prediction and Path Optimization Based on Taxi Trajectory Big Data
## 4 Methods and Models
### Mining and Evaluation Methods for Pick-Up and Drop-Off Points  
The DBSCAN clustering algorithm can discover non-spherical and irregular clusters, making it suitable for mining passenger hotspots with irregular distributions in trajectory data. However, the traditional DBSCAN clustering algorithm has issues such as poor clustering performance when an inappropriate radius is set and high time costs when processing large-scale data [31; 32]. Therefore, this paper uses a grid-optimized DBSCAN algorithm to mine trajectory data, optimizing the partitioning method to eliminate the need to query all trajectory points, thereby further reducing the algorithm's time complexity. The relevant parameter settings for the algorithm are as follows:  
Grid cell: first, set the division parameter \(\partial\); the entire data space is divided into a grid with side length \(\partial\), which is written as grid cell \(Cell\).  
\(Cell=\{c,c\}Cell=\{c_{1},c_{2},\cdots,c_{n}\},c_{1}=\{[l_{ij},h_{ij})\},1\leq i \leq n\), where \(h_{ij}-l_{ij}=\partial,i\) denotes the dimension, and \(j\) denotes the spatial ordinal.  
\(k\)-neighboring grid set: the grid cell \(Cell\) is set to the top, bottom, left, and right, respectively, extending \(k\) grid edge lengths after the rows into the rectangular region; the rectangular region contains a collection of grids is recorded as \(N_{cell}\), and rectangular region edge lengths are recorded as \(L\). The formula is as follows:  
\[L=\partial\times k \tag{3}\]  
where \(\partial\) is the division parameter, \(k\) is the number of neighboring grids in a single direction, and \(L\) is the side length of the rectangular region.  
\(E_{ps}\) rectangular domain: Considering the four vertices of the grid \(Cell\) as the center of the circle, a circle with radius \(E_{ps}\) is drawn with these four vertices as the center. The \(E_{ps}\) rectangular domain of grid cell \(Cell\) is defined as the area formed by the set of \(k\)-neighboring grids that can cover these four circles, as shown in Figure 4.  
In order to facilitate the calculation of the \(E_{ps}\) rectangular domain, the side length of the grid cell is selected as \(L_{pg}=E_{ps}/\gamma\), where \(L_{pg}\) is the side length of the grid cell, \(E_{ps}\) is the radius, and \(\gamma\) is a constant, which can be set according to the size of the data volume.  
After obtaining the passenger hotspots, the passenger hotspots are evaluated by considering the ratio of taxi supply and demand in the recommended area, the density of  
Figure 4: Schematic diagram of neighboring grids.  
the road network, and the number of passengers in the hottest spot. The TOPSIS algorithm is a method of sorting according to the degree of proximity of a finite number of evaluated objects to an idealized target, the core idea of which is to find out positive and negative ideal solutions by using corresponding algorithms to compare the index data of each index data with the positive and negative ideal solutions of each alternative solution and then compare the index data of each alternative program with the index data of the positive ideal solution and negative ideal solution, compare the proximity of each program to the positive ideal solution using the corresponding algorithm, and arrive at the ranking results of each program.