# Compression Index Regression of Fine-Grained Soils with Machine Learning Algorithms
## 2 Dataset and Methods  
### Dataset  
In this study, a new dataset was created by carefully selecting the data used in various studies from the literature [43; 44; 45; 46; 47]. The features of the new dataset were standardized by removing the mean and scaling the unit variance. The input parameters of the dataset included the liquid limit (LL), plastic limit (PL), water content (\(w\)), plasticity index (PI), specific gravity (\(G_{s}\)), and initial void ratio (\(e_{0}\)), and the output parameter was the compression index (\(C_{c}\)). A classical technique called train-test split, used as an alternative to the cross-validation method, was employed to determine the most appropriate train and test split ratio by experimenting with several different splits. Based on the optimal train-test split ratio, the training and testing sets contained 732 and 183 samples, respectively. As a result of this technique, all the data in the testing set were entirely unseen during the training phase. Table 2 contains statistical numerical data obtained from estimating the minimum value, arithmetic mean, maximum value, and standard deviation of the dataset variables. In addition, Figure 1 displays the value distributions of the dataset variables. A statistical tool known as [PERSON]'s correlation coefficient was used to measure the direction and degree of the relationship between two variables. The coefficient value for these variable spans from \(-1\) to \(1\), with \(1\) representing a fully positive monotonic connection, \(-1\) representing a fully negative monotonic relationship, and \(0\) indicating the absence of a monotonic relationship between the variables. Figure 2 shows a [PERSON]'s correlation coefficient matrix of all the parameters in the dataset in this study. The \(p\)-value was used to assess whether the correlation between two variables was statistically significant. Generally, if the \(p\)-value is 0.05 or lower, the relationship is considered non-random and statistically significant. Figure 3 demonstrates the [PERSON]'s correlation coefficient \(p\)-value matrix of all the parameters in the dataset in this study. Table 3 lists [PERSON]'s correlation coefficient and its \(p\)-value for the input parameters LL, \(w\), PL, PI, \(G_{s}\), and \(e_{0}\) and the output parameter, \(C_{c}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & \begin{tabular}{c} **Minimum** \\ **Value** \\ \end{tabular} & \begin{tabular}{c} **Mean** \\ **Value** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline Water content, \(w\) & 10.20 & 34.10 & 99.00 & 13.64 \\ Plastic index, PI & 0.00 & 24.16 & 96.60 & 12.60 \\ Plastic limit, PL & 0.00 & 48.07 & 103.00 & 17.16 \\ Liquid limit, LL & 0.00 & 25.13 & 87.20 & 7.85 \\ Initial void ratio, \(e_{0}\) & 0.36 & 0.96 & 3.50 & 0.38 \\ Specific gravity, \(G_{s}\) & 2.43 & 2.67 & 2.83 & 0.07 \\ Compression index, \(C_{c}\) & 0.05 & 0.29 & 1.00 & 0.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistic results of the dataset variables. Figure 1: Histogram of the variables in the dataset. Figure 3: Spearman’s correlation coefficient \(p\)-value matrix.