## 4 Experimental Evaluation
### Representation of Features with Different Numbers of Neurons
The blue, red, and orange bars indicate the training times obtained by FISTA, G-FISTA, and LC-FISTA, respectively. From the results illustrated in Figure 2, we infer that the proposed G-FISTA and LC-FISTA algorithms are faster than FISTA for training the ELM-AE. In the following, we demonstrate the efficiency of the proposed method using four evaluation criteria: the MAE, \(R^{2}\) score, IA, and TIC. A summary of the MAE and \(R^{2}\) values is given in Table 5. The closer the value of MAE to zero, and the closer the value of \(R^{2}\) to one, the better the performance of the autoencoder. From the values of the metrics given in Table 5, we can see that the order of magnitude is similar, and there is no significant difference between the shrinkage-thresholding methods, meaning that the proposed method maintains the same level of accuracy as the FISTA algorithm. Taking the UMist database as an example, we see that when \(L=1500\), the average MAE values obtained by FISTA, G-FISTA, and LC-FISTA are 0.0172, 0.0181, and 0.0178, while their \(R^{2}\) scores are 0.9861, 0.9846, and 0.9851, respectively. The IA and TIA metrics are also important for evaluating the capability of the proposed learning system. These fit metrics are described in Table 6. As the average values of the IA and TIA approach one and zero, respectively, the feature representation improves. Table 7 shows the MIN and MAX statistical indices for the proposed model on all the selected databases. This table indicates the minimum and maximum absolute errors for the ELM-AE in the testing stage. From the results of this experimental analysis, we can conclude that the FISTA algorithm has a similar generalization capability as G-FISTA and LC-FISTA. Figure 2: Bar graph representing the average training times required by FISTA, G-FISTA, and LC-FISTA for the ELM-AE. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(L\)} & \multirow{2}{*}{**Algorithm**} & \multicolumn{6}{c}{**IA**} & \multicolumn{6}{c}{**TIC**} \\ \cline{3-14}  & & **CIFAR10** & **UMist** & **MNIST** & **N NORB** & **SCars** & **Caltech256** & **CIFAR10** & **UMist** & **MNIST** & **N NORB** & **SCars** & **Caltech256** \\ \hline \multirow{2}{*}{100} & FISTA & 0.9734 & 0.9790 & 0.9799 & 0.9879 & 0.9386 & 0.9559 & 0.0700 & 0.0712 & 0.1288 & 0.0247 & 0.1207 & 0.0981 \\  & G-FISTA & 0.9732 & 0.9793 & 0.9799 & 0.9867 & 0.9386 & 0.9559 & 0.0701 & 0.0708 & 0.1288 & 0.0247 & 0.1208 & 0.0981 \\  & LC-FISTA & 0.9733 & 0.9793 & 0.9800 & 0.9879 & 0.9386 & 0.9559 & 0.0701 & 0.0708 & 0.1288 & 0.0247 & 0.1208 & 0.0981 \\
500 & FISTA & 0.9973 & 0.9917 & 0.9998 & 0.9791 & 0.9729 & 0.9800 & 0.0228 & 0.0449 & 0.0211 & 0.0123 & 0.0829 & 0.0678 \\  & G-FISTA & 0.9973 & 0.9918 & 0.9998 & 0.9971 & 0.9729 & 0.9800 & 0.0228 & 0.0454 & 0.0211 & 0.0123 & 0.0829 & 0.0678 \\
1000 & FISTA & 1.0000 & 0.9581 & — & 0.9999 & 0.9827 & 0.9869 & 0.0018 & 0.0350 & — & 0.0028 & 0.0668 & 0.0551 \\  & G-FISTA & 1.0000 & 0.9948 & — & 0.9999 & 0.9827 & 0.9870 & 0.0018 & 0.0363 & — & 0.0028 & 0.0669 & 0.0551 \\  & LC-FISTA & 1.0000 & 0.9949 & — & 0.9999 & 0.9827 & 0.9869 & 0.0018 & 0.0358 & — & 0.0028 & 0.0669 & 0.0551 \\  & LC-FISTA & 1.0000 & 0.9949 & — & 0.9999 & 0.9827 & 0.9869 & 0.0018 & 0.0358 & — & 0.0028 & 0.0669 & 0.0551 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: IA and TA values achieved by FISTA, G-FISTA and LC-FISTA for training of the ELM-AE. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(L\)} & \multirow{2}{*}{**Algorithm**} & \multicolumn{6}{c}{**MAE**} & \multicolumn{6}{c}{**\(R^{2}\) Score**} \\ \cline{3-14}  & & **CIFAR10** & **UMist** & **MNIST** & **N NORB** & **SCars** & **Caltech256** & **CIFAR10** & **UMist** & **MNIST** & **N NORB** & **SCars** & **Caltech256** \\ \hline \multirow{2}{*}{100} & FISTA & 0.0546 & 0.0415 & 0.0489 & 0.0184 & 0.0921 & 0.0837 & 0.9009 & 0.9209 & 0.9241 & 0.9533 & 0.7896 & 0.8426 \\  & G-FISTA & 0.0547 & 0.0413 & 0.0488 & 0.0185