## 3 Methodology
### Feature Selection Method  
Step 1. Preliminary selection of indicators  
By summarizing the literature, we systematically categorize and establish four core evaluation dimensions--transportation capacity, infrastructure investment, economic development level, and international openness--thereby constructing a multidimensional assessment framework. Considering regional developmental disparities, we implement a stratified indicator pool strategy for flexible metric adaptation. Specifically, the transportation capacity dimension focuses on freight volume and turnover rates across highway, waterway, and railway networks. Infrastructure investment incorporates fixed-asset indicators from key projects of road, rail, and port construction. Economic development metrics integrate GDP aggregates and industrial structure parameters. International openness evaluation encompasses total import-export volume. Based on this framework, we then collect indicator data. Step 2. Data processing  
For the collected data, we use a more robust multiple imputation (MI) to complete the data. The Imputation Phase (IP) is the process of constructing a probability model and generating \(m\) complete datasets based on observed data. Assuming the interpolation depends on the fully observed covariate \(X\) and partially observed \(Y\), the specific formula is as follows:  
\[Y_{\text{miss}}^{(k)}\sim P(Y_{\text{miss}}\big{|}Y_{\text{obs}},X),\ k=1,2, \ldots,m \tag{2}\]  
where \(Y_{\text{obs}}\) is the observed data, \(Y_{\text{miss}}\) is the missing data, \(m\) is the number of interpolated datasets, and \(P(\cdot)\) is the model-based predicted distribution. After applying multiple imputation techniques, complete monthly data for multiple indicators are derived. This is subsequently followed by outlier detection via the interquartile range (IQR), calculated as follows:  
\[\text{IQR}= Q_{3}-Q_{1} \tag{3}\]  
where \(Q_{1}\) is the first quartile, which is the 25 th percentile; and \(Q_{3}\) is the third or fourth percentile, which is the 75 th percentile. From this, it can be concluded that the boundary of outliers is  
\[[Q_{1}-1.5\times\text{IQR},Q_{3}+1.5\times\text{IQR}] \tag{4}\]  
Step 3. Correlation analysis  
To validate the correlation between the collected data and container throughput, we employ Pearson's correlation coefficient for the primary correlation analysis and Spearman correlation coefficient for supplementary verification. The formula is as follows:  
\[\gamma=\frac{\sum_{i=1}^{n}\big{(}X_{i}-\overline{X}\big{)}\big{(}Y_{i}- \overline{Y}\big{)}}{\sqrt{\sum_{i=1}^{n}\big{(}X_{i}-\overline{X}\big{)}^{2 }}\sqrt{\sum_{i=1}^{n}\big{(}Y_{i}-\overline{Y}\big{)}^{2}}}=\frac{\text{Cov} (X,Y)}{\sigma_{X}\sigma_{X}} \tag{5}\]  
where \(n\) represents the sample size; \(X_{i},Y_{i}\) are the observed values of the variables; and \(\overline{X},\overline{Y}\) are the means of the variables. In the second expression, \(\text{Cov}(X,Y)\) represents the covariance between \(X\) and \(Y\), and \(\sigma_{X}\) and \(\sigma_{Y}\) represent the standard deviation of \(X\), \(Y\)[PERSON]'s rank correlation coefficient is the process of converting raw data into ranks and calculating the Pearson correlation coefficient of ranks. The specific formula is as follows:  
\[\rho=\frac{\text{Cov}(\text{rank}(X),\text{rank}(Y))}{\sigma_{\text{rank}(X)} \sigma_{\text{rank}(Y)}} \tag{6}\]  
where \(\text{rank}(X)\) and \(\text{rank}(Y)\) are the sorted position numbers. Step 4. K-means  
Next, in this section, in order to more rationally divide the data into multiple groups and give appropriate weights, we use k-means cluster analysis to deal with the correlation of these indicators. Firstly, the objective function of k-means is defined, and here the correlation distance is used with the following formula:  
\[J=\sum_{i=1}^{k}\sum_{x\in C_{i}}d(x,\mu_{i}) \tag{7}\]  
where \(J\) indicates the total distance within the cluster, which needs to be minimized. \(k\) denotes the number of clusters.