## 2 Materials and Methods
### Methods
#### 2.3.4 Accuracy Verification  
The Kappa coefficient and Figure Of Merit (FOM) were used to test and evaluate the accuracy of LUCC results simulated by the model. The Kappa coefficient based on the confusion matrix can accurately perform the consistency test. The Kappa value is between 0 and 1, and greater than 0.7 indicates that the simulation results are acceptable [33,34]. The calculation formula of Kappa is as follows:  
\[Kappa=\frac{p_{o}-p_{e}}{1-p_{e}} \tag{11}\]  
\[p_{o}=\frac{\sum\limits_{i=1}^{6}w_{i}}{n} \tag{12}\]  
\[p_{e}=\frac{\sum\limits_{i=1}^{6}a_{i}\times b_{i}}{n\times n} \tag{13}\]  
where \(i\) refers to LUCC type; \(w_{i}\) denotes the number of grids whose actual type is class \(i\) and predicted type is class \(i\); \(a_{i}\) represents the number of land use type \(i\) in the actual observation data; \(b_{i}\) represents the number of grids occupied by type \(i\) in the prediction results. At the same time, Accuracy and F1 were used to evaluate. Accuracy is the proportion of correct samples to the total number of samples, and it is the most simple and intuitive evaluation index in the classification problem. Precision embodies the distinguishing ability of the model to negative samples, the higher the Precision, the stronger the distinguishing ability of the model to negative samples; Recall reflects the ability of the model to identify positive samples, and the higher the Recall, the stronger the ability of the model to identify positive samples. F1 is the harmonic average of Accuracy and Recall. The higher F1 is, the more robust the model is. Accuracy and F1 involves four measures: TP (true positive), TN (true negative), FP (false positive), and FN (false negative), which are defined in Table 2.  
The formulas for \(Accuracy\) and \(F1\) are:  
\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{14}\]  
\[Precision=\frac{TP}{TP+FP} \tag{15}\]  
\[Recall=\frac{TP}{TP+FN} \tag{16}\]  
\[F1=\frac{2\times Precision\times Recall}{Precision+Recall}=\frac{2\times TP}{2 \times TP+FP+FN} \tag{17}\]  
Another effective multi-label evaluation method is Hamming_loss, which measures the proportion of samples with false prediction in all samples. Therefore, for Hamming loss, the smaller the value, the better the performance of the model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Observed Data** & **Prediction Result** & **Positive** & **Negative** \\ \hline Positive & TP & FN \\ Negative & FP & TN \\ \hline \hline \end{tabular} In the multi-classification problem, Positive refers to the type that needs to be measured, and Negative represents other types.  
\end{table} 
Table 2: The definitions of TP, TN, FP, and FN. \[Hamming\_loss=\frac{1}{mq}\sum_{i=1}^{m}\sum_{j=1}^{q}I(y_{j}^{(i)}\
eq\hat{y}_{j}^{ (i)}) \tag{18}\]  
where \(m\) is the total number of samples; \(q\) represents the number of types of samples; \(y_{j}^{(i)}\) represents the \(j\) label of the \(I\) th sample in the observed data; \(\hat{y}_{j}^{(i)}\) represents the \(j\) label of the \(I\) th sample in the predicted results. We use the'metrics' module under python3's'sklearn' package to calculate Accuracy, \(F1\) and _Hamming Loss_. In LUCC simulation, the accuracy of the model is often verified by comparing the simulation results with the real results. The above metrics only compares the simulation results with the land use/cover data of the simulated year (the last year) to evaluate the model. However, FOM evaluates the simulation results according to the difference between the actual results (including the base year and the end year) and the simulation results [35]. FOM inherently has the ability to better evaluate the ability of models to capture the conversion between land use/cover types. So compared with the above metrics, FOM more accurately reflects the consistency and accuracy of the simulation of complex geographic systems. The FOM value is between 0 and 1, and the higher the value, the higher the accuracy of the model prediction [35].