## 5 Performance Analysis
### Model Analysis Results  
In this section, the best models of test accuracy with ABCP-descriptor for each dataset will be analyzed. Table 4 shows the general information about the parse trees of the best model with has highest test classification with 97.3% in DS_Broadtz. The complexity in Table 4 was calculated according to Equation (3). As shown in the table, the sub-trees connected to the _code_ node depend on different depth and number of nodes. A tree representation of the model test success for the DS-Broadtz dataset is shown in Table 5. The equations of the sub-trees of the best model in Figure 15 is shown in Table 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Node** & **Depth** & **Complexity** \\ \hline Tree 1 & 7 & 3 & 17 \\ Tree 2 & 5 & 3 & 11 \\ Tree 3 & 7 & 3 & 17 \\ Tree 4 & 19 & 5 & 69 \\ Tree 5 & 21 & 6 & 83 \\ Tree 6 & 3 & 2 & 5 \\ Tree 7 & 19 & 6 & 87 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Information about Subtrees of Best Model of ABCP-Descriptor for DS-Broadtz. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Descriptor** & **Dataset** & **Criteria** & **Best Test Fitness** & **Test Classification Success (\%)** \\ \hline \multirow{6}{*}{ABCP-descriptor} & \multirow{6}{*}{Broadtz} & Mean & 0.03 & 94.55 \\  & & Maximum & 0.03 & 97.3 \\  & & Minimum & 0.01 & 93.3 \\  & & Standard deviation & 0.01 & 1.17 \\ \cline{2-4}  & \multirow{6}{*}{Kylberg} & Mean & 0.05 & 89.71 \\  & & Maximum & 0.14 & 95.19 \\  & & Minimum & 0.02 & 71.63 \\  & & Standard deviation & 0.03 & 6.38 \\ \hline \multirow{6}{*}{LBPs,1} & \multirow{6}{*}{Broadtz} & Mean & 90.63 \\  & & Maximum & 93.8 \\ \cline{1-1}  & & Minimum & 87.3 \\ \cline{1-1}  & & Standard deviation & 1.92 \\ \cline{1-1} \cline{2-4}  & \multirow{6}{*}{Kylberg} & Mean & 90 \\ \cline{1-1}  & & Maximum & 93.13 \\ \cline{1-1}  & & Minimum & 87.13 \\ \cline{1-1}  & & Standard deviation & 1.9 \\ \hline \multirow{6}{*}{GP-descriptor} & \multirow{6}{*}{Broadtz} & Mean & 94.40 \\ \cline{1-1}  & & Standard deviation & 0.81 \\ \cline{1-1} \cline{2-4}  & & Mean & 93.21 \\ \cline{1-1} \cline{2-4}  & & Standard deviation & 1.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results of descriptor. Figure 15: Best Model of ABCP-Descriptor for DS-Broadtz. A tree representation of the model test success for the DS-Kylberg dataset is shown in Figure 16. The equations of the sub-trees of the best model in Figure 16 are shown in Table 7. When the tables of the highest classification test accuracy for the DS-Kylberg dataset (Table 6, Table 7) are evaluated, it can be seen that the sub-trees of the model are more complex than the best model sub-trees of DS-Broadtz. Many inputs in the lower trees (such as \(x_{14}\), \(x_{15}\), \(x_{20}\)) are common in the model. The _code_ node of the best models for both datasets have 7 subtrees and the trees have depth of 2-6. As the number of nodes and depth of the tree increase, the tree complexity increases. \begin{table}
\begin{tabular}{c c c c} \hline  & **Node** & **Depth** & **Complexity** \\ \hline Tree 1 & 5 & 3 & 11 \\ Tree 2 & 7 & 3 & 17 \\ Tree 3 & 3 & 2 & 5 \\ Tree 4 & 13 & 6 & 51 \\ Tree 5 & 9 & 4 & 27 \\ Tree 6 & 33 & 6 & 145 \\ Tree 7 & 11 & 4 & 33 \\ \hline \end{tabular}
\end{table} 
Table 6: Information about Subtrees of Best Model of ABCP-Descriptor for DS-Kylberg. \begin{table}
\begin{tabular}{c c} \hline  & **Equation** \\ \hline Tree 1 & \(x_{22}/(x_{9}*x_{20})\) \\ Tree 2 & \((x_{2}*x_{22})*(x_{19}+x_{14})\) \\ Tree 3 & \((x_{3}-x_{5})\) \\ Tree 4 & \(\left(x_{15}+(x_{7}-x_{15})*\left(\frac{x_{23}-x_{20}}{x_{12}}\right)\right)-x_ {18}\) \\ Tree 5 & \(x_{4}-((x_{24}-x_{11})*(\frac{x_{17}^{2}}{x_{13}^{2}}))\) \\ Tree 6 & \(\left((x_{11}+x_{14})-(x_{12}-x_{14})\right)*\left(\frac{x_{15}*(x_{9}-x_{16})} {\frac{x_{22}}{x_{7}^{2}}}\right)\right)-((x_{5}*((x_{15}+x_{5})-(x_{9}+x_{15} ))-\left(x_{24}-(\frac{x_{19}}{x_{15}})\right))\) \\ Tree 7 & \((x_{15}-(x_{1}/x_{20}))/((x_{9}+x_{14})*x_{5})\) \\ \hline \end{tabular}
\end{table}