## 4 Machine Learning Algorithms
### Data Preprocessing  
#### 4.1.1 Parameter Selection for Model Training  
The dataset for this study comprises well-log measurements from 243 core samples, including natural Gamma Ray (GR; API), Gamma Ray without uranium (KTH; API), acoustic travel time (AC; us/ft), compensated neutron log (CNL; %), bulk density (DEN; g/cm\({}^{3}\)), and spectral Gamma-Ray components (potassium [K; %], thorium [Th; ppm], and uranium [U; ppm]). TOC content was measured for all samples using standard geochemical methods. Bivariate correlation analyses (Figure 5) revealed a strong positive relationship between TOC and GR ([PERSON]'s r = 0.82, \(p<\) 0.01; [PERSON]'s \(p\) = 0.79, \(p<\) 0.01), aligning with uranium-organic matter coupling theory [23]. In contrast, radioelement concentrations (K, Th, U) showed negligible correlations with TOC (\(\,\left|\,\mathrm{r}\,\right|<\) 0.3, \(p>\) 0.05). Variance inflation factor (VIF) analysis identified moderate collinearity between AC and DEN (VIF = 4.7), necessitating dimensionality reduction via PCA with a cumulative contribution threshold of 85%.  
Figure 4: Schematic workflow of the RFR algorithm.  
A three-tiered parameter selection strategy was implemented to optimize feature space. Initial screening retained eight logging curves exhibiting statistically significant correlations with TOC ( \(\left|\,\mathrm{r}\,\right|>0.3\), \(p<0.05\)). To address multicollinearity, PCA was applied to variables with VIF \(>4\), retaining principal components with eigenvalues exceeding unity under the Kaiser-Guttman criterion, which collectively explained 89.3% of the total variance; see Table 1. Depth calibration prioritization selected GR as the reference curve due to its superior vertical resolution (\(\pm 0.1\) m) compared to AC (\(\pm 0.3\) m) and DEN (\(\pm 0.2\) m), coupled with high uranium anomaly sensitivity (response coefficient = 0.89, \(p<0.01\)) and minimal borehole collapse correction errors (<8%); uranium anomaly sensitivity is quantified through standardized response coefficients (\(\beta\)) calculated via  
\[\beta_{GR}=\frac{COV(GR,U_{core})}{\sigma_{GR}\sigma_{U}}=0.89(p<0.01) \tag{1}\]  
where \(U_{core}\) represents core-measured uranium content from XRF analysis, with covariance calculation limited to intervals where CALI \(\leq 15\%\) (borehole integrity threshold).  
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Pearson’s r** & **Spearman’s \(\rho\)** & **VIF** \\ \hline GR & 0.82 & 0.79 & 1.2 \\ DEN & \(-0.76\) & \(-0.73\) & 4.7 \\ AC & 0.58 & 0.52 & 4.7 \\ CNL & 0.31 & 0.28 & 2.1 \\ K & 0.18 & 0.15 & 1.1 \\ Th & 0.22 & 0.19 & 1.3 \\ U & 0.27 & 0.24 & 1.4 \\ \hline \end{tabular}
\end{table}
Table 1: Rank-correlation analysis between logging parameters and TOC content.  
Figure 5: Rank-correlation matrix analysis between TOC and well-logging parameters.  
The final input parameters (GR, KTH, AC, CNL, DEN, K, Th, U) were integrated into an optimized feature space using SHAP value-weighted aggregation. Feature weights (\(w_{i}\)) were calculated as  
\[w_{i}=\frac{SHAP_{I}}{\sum_{j=1}^{m}SHAP_{j}} \tag{2}\]  
where \(w_{i}\) represents the normalized weight of the \(i\)-th feature in the optimized feature space, and m denotes the total number of features included in the model. The SHAP values were derived from 10,000 Monte Carlo permutations of the training set, with kernel weighting coefficients calibrated against core-based TOC measurements [6].