## 2 Methodology  
### Database Generation and Pre-Processing  
Very high-quality dataset of intrinsic compressibility index and basic soil's index parameters compiled from rigorous literature search are utilised for this study. Standardised methods of oedometer testing were adopted by the authors for data collection from the reconstituted soils [11; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. Given the diverse nature and sets of data of intrinsic compressibility index (herein considered as the independent feature), it was necessary to transform and normalise these data into usable continuous variables to enable an improvement of the significance of findings, greater size effects, lesser threats to any causal inferences (i.e., the validity of statistical conclusion), and more reliable results. A two-step approach of data transformation was followed [34]. Step one involved a transformation of the intrinsic compressibility variables into a percentile rank resulting in uniformly distributed probabilities. Step two then applied the inverse-normal transformation to the results of step one into a variable comprising normally distributed z-scores. Figure 2 indicates the normally distributed dataset of the method with very low values of skewness (0.123457) and kurtosis (\(-\)0.09139) (Table 1) meaning therefore that the dataset is very reliable for use in the ML modelling. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Mean** & \
\begin{tabular}{c} **Standard** \\ **Error** \\ \end{tabular} &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & **Kurtosis** & **Skewness** & **Min.** & **Max.** & **Range** \\ \hline
0.789244 & 0.124782 & 1.36121 & \(-\)0.0914 & 0.123457 & 0.08 & 8.5 & 8.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of intrinsic compressibility index (\(C_{c}^{*}\)). Figure 2: Distribution of intrinsic compressibility index. On the other hand, a total of six explanatory features are used in this research namely, reconstituted soil intrinsic constants (e\({}_{\rm L}\), e\({}_{\rm P}\) and e\({}_{100}\)), Afterberg limits (Liquid limit (LL) and plasticity index (PI)) and a soil texture parameter, specific gravity (G). Table 2 depicts important statistical components of these features. It is observed that the range of values for the liquid limits (minimum and maximum of 22% and 560% respectively) and plasticity indices (minimum value of 5% and 508% respectively) suggest wide coverage of the soils of different plasticity properties. Frequency distribution of the independent features of the dataset as depicted in Figure 3 generally indicates non-uniform distribution for all the variables except for the specific gravity of the soils. The pattern of distribution which is noticed to be mostly right skewed indicates a very strong relationship among the features. Three classes of soils defined according to the USCS were captured in this study. This will be very useful for the multinomial classification prediction considered subsequently in this research to determine the ability of the models to learn between the different categories of soils used. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Statistic** & **G** & **LL** & **PL** & **PI** & \(\mathbf{e_{L}}\) & \(\mathbf{e_{P}}\) & \(\mathbf{\epsilon^{*}_{100}}\) \\ \hline Mean & 2.71 & 87.62 & 31.11 & 56.50 & 2.37 & 0.84 & 1.51 \\ Standard Error & 0.01 & 8.375 & 1.196 & 7.82 & 0.22 & 0.03 & 0.10 \\ Standard Deviation & 0.10 & 91.36 & 13.05 & 85.25 & 2.43 & 0.36 & 1.08 \\ Kurtosis & 0.86 & 13.93 & 9.15 & 16.11 & 12.94 & 11.59 & 9.53 \\ Skewness & \(-0.5\) & 3.60 & 2.05 & 3.94 & 3.49 & 2.36 & 2.78 \\ Range & 0.56 & 538 & 96 & 503 & 13.68 & 2.75 & 6.65 \\ Min. & 2.37 & 22 & 12 & 5 & 0.59 & 0.31 & 0.45 \\ Max. & 2.93 & 560 & 108 & 508 & 14.27 & 3.06 & 7.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistics of explanatory features. Figure 3: Distribution of ML features.