## 4 Experimental Evaluation
### Representation of Features with Different Numbers of Neurons  
The computational complexity and execution time of the proposed method are explored in this section. For this purpose, several cases are considered with varying numbers of neurons in the hidden layer of the ELM-AE. In this phase of the experiments, we selected the measures of training time, RMSE, MAE, \(R^{2}\), IA, TIC, MIN, and MAX for comparison on the test set. These evaluation indicators were obtained as a result of training the ELM-AE with the shrinkage-thresholding class of algorithms introduced in Section 2.2. Table 4 presents the training times and values of RMSE for the ELM-AE on each of the six datasets, for increasing numbers of neurons in the hidden layer. These experimental results show that the training speeds achieved by G-FISTA and LC-FISTA were lower than that obtained by FISTA. For example, for the CIFAR10 set, with 100 neurons in the hidden layer, the computation time for rthe ELM trained by FISTA was 21.92 s, while the G-FISTA and LC-FISTA algorithms achieved average values of 12.31 s and 12.91 s. Likewise, when we increased the number of hidden neurons \((L)\), the training time obtained by G-FISTA and LC-FISTA was approximately half that required by FISTA. At the test stage, the RMSE metric achieved by the G-FISTA and LC-FISTA algorithms proposed in this paper indicated a similar level of error as the current FISTA algorithm. This evaluation metric became smaller as the parameter \(L\) was increased. For MNIST and CIFAR10, we obtained evaluation metrics of up to \(L=500\) and \(L=1000\), respectively. Figure 1: G-FISTA Algorithm: plot of RMSE for training, validation, and testing sets versus the number of neurons. \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}{**RMSE**} & \multicolumn{6}{c}{**Training Time (Sep)**} \\ \cline{3-13}  & & **CIFAR10** & **UMIst** & **MNIST** & **NORB** & **SCAs** & **Caltech256** & **CIFAR10** & **UMIst** & **MNIST** & **NORB** & **SCAs** & **Caltech256** \\ \hline
100 & FISTA & 0.0751 & 0.0583 & 0.0856 & 0.0385 & 0.1284 & 0.1205 & 21.92 & 2.92 & 25.47 & 22.33 & 38.22 & 63.61 \\  & G-FISTA & 0.0753 & 0.0580 & 0.0856 & 0.0385 & 0.1285 & 0.1205 & 12.31 & 2.40 & 16.73 & 12.09 & 18.73 & 35.73 \\
500 & L-CFSTA & 0.0751 & 0.0579 & 0.0855 & 0.0385 & 0.1285 & 0.1205 & 12.91 & 2.34 & 18.97 & 11.17 & 20.61 & 33.03 \\
500 & FISTA & 0.0422 & 0.0368 & 0.0096 & 0.0193 & 0.088 & 0.0836 & 48.46 & 11.42 & 51.24 & 48.40 & 83.23 & 122.15 \\  & G-FISTA & 0.0242 & 0.0373 & 0.0096 & 0.0193 & 0.088 & 0.0836 & 26.97 & 10.27 & 32.06 & 26.49 & 42.16 & 75.94 \\  & L-CFSTA & 0.0242 & 0.0370 & 0.0096 & 0.0193 & 0.088 & 0.0837 & 27.61 & 9.49 & 35.92 & 24.26 & 42.52 & 69.93 \\
1000 & FISTA & 0.0019 & 0.0288 & — & 0.0044 & 0.0178 & 0.0681 & 78.80 & 29.78 & — & 80.18 & 153.88 & 211.51 \\  & G-FISTA & 0.0019 & 0.0288 & — & 0.0044 & 0.0718 & 0.0681 & 43.14 & 26.82 & — & 46.54 & 80.08 & 125.85 \\  & L-CFSTA & 0.0019 & 0.0294 & — & 0.0044 & 0.0718 & 0.0681 & 44.83 & 25.07 & — & 42.34 & 78.10 & 182.85 \\
1500 & FISTA & — & 0.0244 & — & 0.0015 & 0.0617 & 0.0589 & — & 57.79 & — & 116.54 & 221.72 & 285.91 \\  & G-FISTA & — & 0.0257 & — & 0.0015 & 0.0617 & 0.0589 & — & 48.39 & — & 69.18 & 117.10 & 176.85 \\  & L-CFSTA & — & 0.0253 & — & 0.0015 & 0.0617 & 0.0589 & — & 46.48 & — & 63.09 & 116.60 & 162.03 \\
2000 & FISTA & — & 0.0214 & — & 0.0003 & 0.0543 & 0.0522 & — & 60.69 & — & 161.86 & 297.65 & 379.08 \\  & G-FISTA & — & 0.0229 & — & 0.0003 & 0.0543 & 0.0522 & — & 78.74 & — & 95.27 & 158.85 & 239.25 \\  & L-CFSTA & — & 0.0225 & — & 0.0003 & 0.0543 & 0.0522 & — & 75.55 & — & 86.17 & 162.87 & 222.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Training times and RMSE values achieved by FISTA, G-FISTA, and LC-HSTA for training of the ELM-AE. For each dataset, we show the execution time of the proposed method in Figure 2. A bar chart represents this evaluation measure as a function of the number of neurons.