## 4 Results and Discussion
### Association Rules among Multiple Elements
#### 4.2.2 Comparison with Bivariate Spatial Cross Correlation  
The affinity of elements is the ability of elements to preferentially coexist with each other. The most abundant anions in the crustal system are oxygen (O) and sulfur (S). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \(t_{k}\) & \(i_{1}\) & \(i_{2}\) & \(i_{3}\) & \(i_{4}\) & \(i_{5}\) & \(i_{6}\) & \(i_{7}\) & \(i_{8}\) & \(i_{9}\) & \(i_{10}\) & \(i_{11}\) & \(i_{12}\) & \(i_{13}\) & \(i_{14}\) & \(i_{15}\) \\ (**Point)** & **(Au)** & **(Sn)** & **(Ag)** & **(As)** & **(Sb)** & **(Bi)** & **(Co)** & **(Cu)** & **(La)** & **(Pb)** & **(Zn)** & **(W)** & **(Mo)** & **(Nb)** & **(Cd)** \\ \hline
1 & HL & & & HH & HH & & & HH & HH & HH & HH & HH & HH \\
2 & & & LL & & HH & & HH & & & HL & & & HH & & \\
3 & & HH & & & LH & HH & LH & & & & HH & & & & HH \\
4 & HH & HH & & & HH & & HH & & & LH & & & & & HH \\
5 & & LL & LL & LL & LL & LL & LL & LL & LH & HL & LL & & & & LL \\
6 & & LL & LL & LL & LL & LL & LL & LL & LL & LL & LL & LL & LL & & LL \\... &... &... &... &... &... &... &... &... &... &... &... &... &... &... &... \\
4959 & & HH & HH & HH & HH & HH & HH & HH & LH & HH & HH & HH & HH & HH \\ \hline \end{tabular}
\end{table} 
Table 7: Original example dataset for association rule mining. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Element** & **Insignificant** & **High–High** & **Low–Low** & **Low–High** & **High-Low** \\ \hline Au & 4023 & 113 & 466 & 163 & 194 \\ Sn & 2584 & 300 & 1786 & 190 & 99 \\ Ag & 1706 & 560 & 2286 & 336 & 71 \\ As & 1931 & 521 & 2137 & 259 & 111 \\ Sb & 1192 & 867 & 2509 & 305 & 86 \\ Bi & 2352 & 351 & 1973 & 194 & 89 \\ Co & 1810 & 981 & 1613 & 327 & 228 \\ Cu & 2036 & 570 & 2044 & 169 & 140 \\ La & 2025 & 659 & 1529 & 417 & 329 \\ Pb & 3740 & 65 & 796 & 315 & 43 \\ Zn & 1662 & 793 & 2049 & 200 & 255 \\ W & 2442 & 332 & 1874 & 193 & 118 \\ Mo & 2289 & 414 & 1952 & 128 & 176 \\ Nb & 2749 & 478 & 1132 & 329 & 271 \\ Cd & 2054 & 556 & 1927 & 303 & 119 \\ \hline \end{tabular}
\end{table} 
Table 8: Counts of items in local Moran’s I clustering (LMIC) of elements. \begin{table}
\begin{tabular}{c c c} \hline \hline
**ID** & **Association Rules** & **Support Degree** & **Confidence** \\ \hline a & [As (H=H)] \(\Rightarrow\) [Sb (HH)] & 0.076 & 0.73 \\ b & [Cd (HH)] \(\Rightarrow\) [Zn (HH)] & 0.090 & 0.81 \\ c & [W (HH)] \(\Rightarrow\) [Cu (HH)] & 0.051 & 0.76 \\ d & [Cu (HH)] \(\Rightarrow\) [Co (HH)] & 0.089 & 0.77 \\ e & [Bi (HH)] \(\Rightarrow\) [Cu (HH)] & 0.059 & 0.83 \\ f & [Mo (HH)] \(\Rightarrow\) [Sb (LL)] & 0.065 & 0.77 \\ g & [Zn (HH), Ag (HH)] \(\Rightarrow\) [Cd (HH)] & 0.058 & 0.81 \\ h & [Cd (HH), Ag (HH)] \(\Rightarrow\) [Zn (HH)] & 0.058 & 0.92 \\ i & [Cd (HH), Ag (HH)] \(\Rightarrow\) [Zn (HH)] & 0.053 & 0.93 \\ j & [As (HH), Zn (HH)] \(\Rightarrow\) [Cd (HH)] & 0.053 & 0.82 \\ k & [Zn (HH), Sb (HH)] \(\Rightarrow\) [Cd (HH)] & 0.055 & 0.71 \\ l & [Cd (HH), Sb (HH)] \(\Rightarrow\) [Zn (HH)] & 0.055 & 0.93 \\ m & [Zn (HH), As (HH)] \(\Rightarrow\) [Sb (HH)] & 0.052 & 0.82 \\ n & [Cu (HH), La (LL)] \(\Rightarrow\) [Co (HH)] & 0.052 & 0.76 \\ o & [Co (HH), Sb (LL)] \(\Rightarrow\) [La (LL)] & 0.056 & 0.73 \\ \hline \end{tabular}
\end{table} 
Table 9: Mined association rules among elements. Therefore, according to the geochemical affinities, the 15 elements are divided into the following three categories: (1) native elements, i.e., Au; (2) sulfides, i.e., Sn, Ag, As, Sb, Bi, Cu, Co, Pb, Zn, and Cd; and (3) oxides and lithophiles, i.e., Mo, Nb, W, and La.