## 4 Results and Discussion  
### Spatial Autocorrelation of Elements  
#### 4.1.1 Univariate Spatial Autocorrelation of Individual Elements  
We calculated the spatial autocorrelation and cross-correlation indicators of each element using open-source software packages Geoda ([[http://geodacenter.github.io](http://geodacenter.github.io)]([http://geodacenter.github.io](http://geodacenter.github.io)), accessed on 28 May 2021) and spdep ([[https://github.com/r-spatial/spdep](https://github.com/r-spatial/spdep)]([https://github.com/r-spatial/spdep](https://github.com/r-spatial/spdep)), accessed on 4 April 2021). Then, we applied the Z-score to test the significance of spatial autocorrelation and cross-correlation statistics. Because the global Moran's I can be tested by normal or permutation tests [8], the Z-score was calculated by Monte Carlo simulation by randomly  
Figure 5: Algorithm for generating frequent itemsets. Figure 6: Algorithm for extracting strong association rules based on frequent itemsets. sampling 999 permutations. The global Moran's I, global Geary's C, and global Getis-Ord's G for 15 elements passed the statistical significance test and were consistent with each other (Table 3). The global Moran's I and Geary's C are both suitable for characterizing the overall spatial pattern of an element; however, the global Getis-Ord's G only indicates whether an element's concentration exhibits a positive correlation (LL-clustered or HH-clustered) or is randomly distributed. It cannot be used to ascertain a negative correlation or compare the correlation between elements. The global Getis-Ord's G shows that all 15 elements have a positive correlation in the study area. The global Moran's I and Geary's C show that Au is randomly distributed, and the other 14 elements are positively correlated. The elements, ordered from high to low correlation, are Sb, Zn, Pb, Cu, Cd, As, Sn, Bi, Ag, Mo, Co, W, La, and Nb (Table 3). Except for Au, the global Moran's I and Geary's C are consistent with Getis-Ord's G. According to the geological survey report, an Au deposit was found in the study area [59]. However, because of the low concentrations of Au in most sampling points of the study area, it would be easy to overlook the local clustering in the global spatial autocorrelation analysis. We calculated the local Moran's I of major elements in the study area and visualized the results via a Voronoi diagram (Figure 7). [PERSON] (1995) proposed a local indicator of spatial association (LISA) statistic that satisfies the following two requirements: (a) the LISA for each observation gives an indication of the extent of significant spatial clustering of similar values around that observation; and (b) the sum of LISAs for all observations is proportional to a global indicator of spatial association [11]. By calculating the local Moran's I, \(I(i)\), in each quadrant, this divides the concentrations of elements into five categories: insignificant, high-high (HH), low-low (LL), low-high (LH), or high-low (HL) clustering [11]. A local Moran's I clustering map (LMIC) represents different types of association between the value at a given location and its spatial lag, i.e., the weighted average of the values in the surrounding locations. The LISA significance map is shown in Figure 8, in which we set \(p\) = 0.05. The local Moran's I clustering map is shown in Figure 9. These results are consistent with the Moran's I clustering results, which show that the HH and LL clustering in LMIC can reflect the spatial pattern of elements' concentrations with a certain statistical significance. In addition, maps of local Moran's I have natural transitions from strong to weak, which capture the local details and are consistent with the distributions of elements in nature. Moreover, we also calculated indicators of the local Geary's C and the local Getis-Ord's G of all the elements in the study area. The HH- and LL-clustered values of the local