## 2 Materials and Methods
### Methods
#### 2.2.2 RScan Algorithm Core Content Definition  
(1) **Definition 1--Region:**  
_Given a spatial dataset \(S_{d}=\{p_{1},p_{2},...,p_{n}\}\), where each \(p_{i}(1\leq i\leq n)\) represents a spatial data sampling point, the extent of the area containing this spatial data collection can be defined as shown in_ Table 2.  
(2) **Definition 2--Grid length and threshold:**  
_Grid length determines the size of the region \(D\) to be partitioned into grids, denoted as \(k\)._  
_A threshold is used to determine the neighborhood around a data point, denoted as \(\lambda\). A grid is only considered to be an active region if the number of data points in the grid exceeds this set threshold \(\lambda\)._  
**Definition 3--Grid cells:**  
_For region \(D\), whose longitude range is in \([\text{\rm lon}_{\min}\,,\,\text{\rm lon}_{\max}]\) and latitude range is in \([\text{\rm lat}_{\min}\,,\,\text{\rm lat}_{\max}]\), the region \(D\) is partitioned into two dimensions, longitude and latitude. Each attribute dimension is equidistributed into small intervals of length \(k\). The region \(D\) is then divided into a number of rectangular cells of size \(k\times k\), each consisting of small intervals, referred to as grid cells, denoted as \(U\)_  
**Definition 4--Grid density:**  
_For a grid cell \(U\), the spatial data points belonging to the grid cell are computed, the total number of which is the grid density of the grid cell \(U\), denoted by \(\text{\rm den}(U)\). When \(\text{\rm den}(U)=0\), it is called an empty grid cell; when \(\text{\rm den}(U)>0\), it is referred to as a non-empty grid cell._  
**Definition 5--Active grid cells:**  
_For a grid cell \(U\), if its grid density satisfies the condition \(\text{\rm den}(U)\geq\lambda\), then the grid cell \(U\) is said to be an active grid cell; otherwise, it is referred to as an ordinary grid cell._  
**Definition 6--Grid level classification:**  
_The geographic area is divided into different grid cells, and each grid cell is assigned a level based on different levels of the number of second-hand home transactions within each grid area to identify and categorize the activity in different areas._  
**Definition 7--Grid reachability:**  
_For two grid cells \(U\) and \(U^{\prime}\), if there exists a sequence of grids \(U_{1},U_{2},...,U_{a-1},U_{a}\), where \(U_{1}=U_{i}\) and \(U_{a}=U_{j}\), and if for \(1\leq t\leq a\), the grid density of each grid cell \(Ut\) is directly reachable to its next grid cell \(U_{t+1}\), then \(U_{i}\) is said to be grid-density reachable for \(U_{j}\). This also means that \(U_{i}\) is connected to \(U_{j}\) through the direct reachability of a series of grid cells, i.e., \(U_{i}\) grid is reachable to \(U_{j}\)._  
**Definition 8--Grid direct reachability:**  
_There exists a direct connection between two grid cells without passing through other grid cells, provided that the distance between them is within reasonable limits. In a given set of grids \(U\), there exist two grid cells \(U_{i}\) and \(U_{j}\) such that the distance between them does not exceed \(a\) times the size of the grid cell \(k\), i.e., the following condition is satisfied: \(\text{\rm dis}\left(U_{j},U_{j}\right)\leq\alpha\times k\)._  
_Where \(\text{\rm dis}\left(U_{i},U_{j}\right)\) denotes the distance between grid cells \(U_{i}\) and \(U_{j}\), \(k\) is the grid cell size, and \(\alpha\) is the distance coefficient. Typically, the distance coefficient \(\alpha\) takes a value between 1 and 2, often taking the value of 1.3._  
**Definition 9--Active region:**  
_An active region is a non-empty subset \(H\) of a given set \(U\) of grid cells that meets the following conditions as shown in Table 3:_