## 3 Experimental Results and Discussion
### Results and Discussion of Machine Learning Models  
For four machine learning models, we experimented with five-fold cross-validation on the same estimates from the MLE for 2D FBM. Table 1 shows the classification rate of four machine learning models that learned from the first numerical data--the estimates of the Hurst exponent from the MLE for FBSs of 11 Hurst exponents; Table 2 shows the classification rate of four machine learning models that learned from the second numerical data--the estimates of the Hurst exponent from the MLE for FBIs of 11 Hurst exponents; Table 3 shows the classification rate of four machine learning models that learned from the third numerical data--the estimates of the Hurst exponent from the MLE for FBSs of 21 Hurst exponents; Table 4 shows the classification rate of four machine learning models that learned from the fourth numerical data--the estimates of the [PERSON] exponent from the MLE for FBIs of 21 [PERSON] exponents. Figure 5: Three images, each with 16 patches from different realizations of \(H=13/22\) (**a**) and \(H=15/22\) (**b**), and \(H=17/22\) (**c**). Figure 6: Two images, each with 16 patches from different realizations of \(H=19/22\) (**a**) and \(H=21/22\) (**b**). Among four machine learning models, we find from Tables 1-4 that the SVM has the best classification rate of 0.839. Therefore, we chose the SVM as our compared subject to deep learning models. In line with our intuition, the classification rates based on the FBSs are better than those based on the FBIs because FBIs are saved as images from FBSs with some finer details lost. Under the resolution of 1/11 of Hurst exponents, the classification rates are higher than 0.8 and acceptable; however, the classification rates are lower than 0.6 and generally unacceptable under the resolution of 1/21 of Hurst exponents. For most situations, images are usually captured or acquired, and hence, for comparison with deep learning models that often use images as inputs, we run the SVM on the estimates of the Hurst exponent from the MLE for FBIs and produced the confusion matrix (Table 5) and the classification report (Table 6). In the experiment, the SVM model used default parameters and was run under 80% data as the training set and 20% data as the test set. Tables 5 and 6 display a trend that lower Hurst exponents are easier to differentiate because they are much rougher to contain more details and much information; however, the worst case happens at Class 10 (\(H=20/22\)) instead of the last class, Class 11 (\(H=21/22\)) because the last class is not affected by its right neighboring Hurst exponent. Obviously, the best case is Class 1 (\(H=1/22\)); its recall rate is 1, and its precision is almost 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & **Mean** & **Std.** \\ \hline LR & 0.837 & 0.023 \\ SVMs & 0.839 & 0.023 \\ KNNs & 0.813 & 0.026 \\ DT & 0.826 & 0.025 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The classification rates of four machine learning models on the estimates of FBSs of 11 Hurst exponents. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & **Mean** & **Std.** \\ \hline LR & 0.554 & 0.032 \\ SVMs & 0.560 & 0.033 \\ KNNs & 0.497 & 0.017 \\ DT & 0.496 & 0.021 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The classification rates of four machine learning models on the estimates of FBIs of 21 Hurst exponents. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & **Mean** & **Std.** \\ \hline LR & 0.809 & 0.024 \\ SVMs & 0.814 & 0.023 \\ KNNs & 0.783 & 0.020 \\ DT & 0.800 & 0.023 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The classification rates of four machine learning models on the estimates of FBIs of 11 Hurst exponents. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** & **Mean** & **Std.** \\ \hline LR & 0.521 & 0.029 \\ SVMs & 0.532 & 0.031 \\ KNNs & 0.474 & 0.020 \\ DT & 0.475 & 0.020 \\ \hline \hline \end{tabular}
\end{table}