## 6 Results and Discussion  
To determine the best approach between ELM and PCA-ELM, initially, the dataset of 232 variables and 96 samples is standardized. Then, principal component analysis is performed, and the spread of the obtained components can be observed in Figure 4. The first 16 components have a greater percentage of the variance than the rest of the components, meaning all the characteristics of the original dataset are present in those 16 principal components. Figure 4: Scree plot explaining the spread of principal components. Figure 3: Principal component 1 vs. principal component 2. From Table 1 the percentage variance of the obtained 16 principal components is as follows: 32.4, 23.3, 14.8, 8.4, 5.02, 2.5, 2.01, 1.3, 1.04, 0.94, 0.73, 0.701, 0.668, 0.59, 0.54, 0.455, and the cumulative contribution rate is 95.639%. It signifies that the 16 principal components represent 95.639% of the original dataset characteristics. A conventional ELM model using a sigmoid activation function with 50 hidden nodes is developed, and the original data of 232 variables is given as training and testing samples. In the next part of the simulation, the dimensionality of the huge input data is reduced using PCA and then integrated into ELM, continuing with the same ELM design of a sigmoid activation function and 50 hidden nodes. A comparison of the predictions using both the approaches--ELM and PCA-ELM, during training and testing--consists of 2 general parts: relative errors and training time. Results shown in Table 2 highlight that the conventional ELM model takes 13 ms, whereas PCA-ELM takes only 2 ms.  
More time for training and the relative errors are high compared to the PCA-ELM integrated model, and the cause of high-dimensional data can be observed on a network model. So, the PCA-ELM integrated model has the best prediction capability and is more accurate towards training time. In addition, the ELM and PCA-ELM models using a sigmoid activation function with 100 hidden nodes are developed. From Table 3, the relative errors and training time for both the models can be observed. Now, an accurate prediction model is established, but the choice of the number of hidden nodes and activation functions is a failing factor. To begin, PCA-ELM models using a sigmoid activation function with different ranges of hidden neurons of 3, 30, 50, 80, and 100 were created, with mean square errors of 160, 23, 14, 33, and 22 respectively. From Table 4, the results show that the prediction model using the sigmoid function should be implemented with a high range of hidden nodes (mostly 30 or more hidden nodes). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters/Approach** & **ELM** & **PCA–ELM** \\ \hline training sum of squares error & 0.02 & 0.015 \\ training time (in milliseconds) & 13 & 2 \\ training relative error & 0.009 & 0.01 \\ the testing sum of squares error & 0.05 & 0.023 \\ testing relative error & 0.065 & 0.017 \\ MSE & 39.932 & 14.711 \\ MAE & 3.902 & 2.969 \\ MAPE & 0.696 & 0.526 \\ RMSE & 6.319 & 3.835 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ELM model and PCA–ELM integration model using a sigmoid activation function with 50 hidden neurons. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters/Approach** & **ELM** & **PCA–ELM** \\ \hline training sum of squares error & 0.002 & 0.015 \\ training time (in milliseconds) & 45 & 2 \\ training relative error & 0.001 & 0.01 \\ testing sum of squares error & 0.038 & 0.023 \\ testing relative error & 0.053 & 0.017 \\ MSE & 25.269 & 22.380 \\ MAE & 2.726 & 3.626 \\ MAPE & 0.481 & 0.639 \\ RMSE & 5.026 & 4.730 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: ELM model and PCA–ELM integration model using a sigmoid activation function with 100 hidden neurons. PCA-ELM models using a hyperbolic tangent activation function with different ranges of hidden neurons of 3, 30, 50, 80, and 100 are developed, and the mean square errors of the models are 107, 42, 61, 110, and 668, respectively.