## 3 Results and Discussion
### Comparisons of Different ML Models for Estimating Leaf Area of \(D\). mobile Leaves

Table 8: Comparative statistical performance analysis of MLR, SVR, GBR, and ANN with different inputs, i.e., LW, LW\({}^{2}\), LW\({}^{3}\), L\({}^{2}\)W, L\({}^{2}\)W\({}^{2}\), L\({}^{2}\)W\({}^{3}\), L\({}^{3}\)W, L\({}^{3}\)W\({}^{2}\), L\({}^{3}\)W\({}^{3}\) studied for LA estimation of _D. mobile._Previous studies on leaf area modeling by [34, 47, 54, 60, 100, 101] depicted that ANN outperformed MLR. On the contrary, in our study ANN could not perform better in other input combinations than MLR as well as GBR except in L\({}^{2}\)W\({}^{2}\) input combinations of testing results where, ANN18 with (2-5-10) architecture secured a rank of eleventh based on AR ranking (Table 9) (R\({}^{2}\) = 0.97, MAE = 0.77 and RMSE = 1.03), which may be due to its inherent disadvantages such as overfitting. The reason behind this abrupt performance is due to the observed training results of ANN18, which shows R\({}^{2}\) = 0.95, MAE = 0.93, and RMSE = 1.36 denoting an overfit. The problems of local minima as well as selection of suitable hyper-parameters suitable for our study may be the other causes of such results of ANN18 [102]. From Table 9 it can be seen that SVR occupied ranks between twenty-first to thirty-first among the 36 models. So, it can be inferred that SVR was unable to perform better than three other ML models tested in our dataset. For evaluating the prediction quality, a scatter plot of predicted LA and measured LA values along with the reference line (y = x) of \(D\). _nobile_ for the four ML models viz., MLR, SVR, GBR, and ANN in the testing period was used (Figure 6). A deviation of the regression line of predicted LA and measured LA values from the reference line is suggestive of a bias. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{3}{c}{**Ranks Based on Training Results**} & \multicolumn{3}{c}{**Ranks Based on Testing Results**} & \multirow{2}{*}{**Average**} & \multirow{2}{*}{**Final Rank**} \\ \cline{2-2} \cline{6-9}  & **R\({}^{2}\)** & & & & & & & & \\ \hline
**GBR7** & 7 & 4 & 8 & 11 & 2 & 2 & 5.67 & **1** \\ MLR5 & 1 & 1 & 3 & 7 & 13 & 12 & 6.17 & 2 \\
**GBR6** & 8 & 5 & 9 & 12 & 3 & 3 & 6.67 & **3** \\
**GBR5** & 9 & 6 & 10 & 13 & 4 & 4 & 7.67 & **4** \\
**GBR4** & 11 & 8 & 11 & 14 & 5 & 5 & 9.00 & **5** \\
**GBR9** & 3 & 2 & 6 & 9 & 28 & 6 & 9.00 & **6** \\ MLR4 & 10 & 7 & 1 & 5 & 19 & 13 & 9.17 & 7 \\
**GBR8** & 5 & 3 & 7 & 10 & 29 & 7 & 10.17 & **8** \\
**GBR3** & 12 & 9 & 12 & 15 & 6 & 8 & 10.33 & **9** \\
**GBR2** & 14 & 10 & 13 & 16 & 7 & 9 & 11.50 & **10** \\ ANN18 & 22 & 27 & 20 & 2 & 1 & 1 & 12.17 & 11 \\ MLR2 & 2 & 12 & 2 & 6 & 30 & 22 & 12.33 & 12 \\ MLR8 & 4 & 15 & 4 & 8 & 25 & 18 & 12.33 & 13 \\
**GBR1** & 17 & 11 & 14 & 17 & 8 & 10 & 12.83 & 14 \\ ANN10 & 13 & 22 & 18 & 1 & 24 & 16 & 15.67 & 15 \\ ANN6 & 15 & 23 & 16 & 19 & 11 & 15 & 16.50 & 16 \\ ANN2 & 18 & 13 & 17 & 20 & 20 & 14 & 17.00 & 17 \\ MLR7 & 6 & 18 & 5 & 30 & 26 & 21 & 17.67 & 18 \\ ANN15 & 23 & 29 & 23 & 4  
The main limitations of performance metrics viz., R\({}^{2}\), MAE, and RMSE matrices as seen in our study is that if algorithm A outperforms B based on only r\({}^{2}\), then again it takes down A and brings up B on the basis of either MAE or RMSE. This is in accordance with the  
Figure 6: Comparison of predicted and measured values of leaf area of \(D\). _nobile_ using MLR, SVR, GBR, and ANN models in different input combinations. The \(x\)-axis represents measured values of leaf area by ImageJ software and \(y\)-axis denotes the predicted values by the two models above. The red line represents the reference line (\(y=x\)). Blue triangles represent the regression line of the predicted and measured leaf area. R\({}^{2}\) refers to the coefficient of determination, MAE refers to mean absolute errors and RMSE refers to root mean square errors (cm\({}^{2}\)). theorem of No Free Lunch (NFL) and the solution depends on the domain of the problem and knowledge of algorithms by the analysts [103; 104].