# QFC: A Parallel Software Tool for Feature Construction, Based on Grammatical Evolution
## 4 Experiments
### Experimental Results  
The parameters for the used methods are listed in Table 2. In all tables, an additional row was added at the end showing the average classification or regression error for all datasets, and it is denoted by the name AVERAGE. The columns of all tables have the following meaning:  
1. The column RBF stands for the results from an RBF network with \(H\) Gaussian units. 2. The column MLP stands for the results of a neural network with \(H\) sigmoidal nodes trained by a genetic algorithm. The parameters of this genetic algorithm are listed in Table 2.
3. The column FCRBF represents the results of the proposed method, when an RBF network with \(H\) Gaussian units was used as the evaluation model. 4. The column FCMLP represents the results of the proposed method, when a neural network trained by a genetic algorithm was used as the evaluation model. The parameters of this genetic algorithm are listed in Table 2.
5. The column FCNNC stands for the results of the proposed method, when the neural network construction model (nnc) was utilized as the evaluation model. 6. The column MRMR stands for the Minimum Redundancy Maximum Relevance Feature Selection method with two selected features. The features selected by MRMR are evaluated using an artificial neural network trained by a genetic algorithm using the parameters of Table 2.
7. The Principal Component Analysis (PCA) method, as implemented in Mlpack software [44], was used to construct two features. The features constructed by PCA are evaluated using an artificial neural network trained by a genetic algorithm using the parameters of Table 2.  
The experimental results for the classification datasets are listed in Table 3, and for regression datasets in Table 4. Furthermore, a comparison against MRMR and PCA is performed in Tables 5 and 6, respectively. Summarizing the conclusions of the experiments, one can say that the proposed method obviously outperforms the other techniques in most cases, especially in the case of regression datasets. In the case of data classification, there is a gain of the order of 30%, and in the case of regression data, the gain from the application of the proposed technique exceeds 50%. The gain in many cases from the application of the proposed technique can even reach 90%. In addition, the MRMR method seems to be superior in most cases to the PCA, possibly pointing the way for a future research on the combination of grammatical evolution and MRMR. Furthermore, among the three cases of models used to evaluate the constructed features (FCRBF, FCMLP, FCNNC), there does not seem to be any clear superiority of any of the three. However, we would say that the nnc method slightly outperforms the simple genetic algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**PARAMETER** & **MEANING** & **VALUE** \\ \hline \(H\) & Neural weights & \(10\) \\ \hline \(N_{C}\) & Chromosomes & 500 \\ \hline \(N_{F}\) & Features & 2 \\ \hline \(p_{S}\) & Selection rate & 0.10 \\ \hline \(p_{M}\) & Mutation rate & 0.05 \\ \hline \(N_{G}\) & Generations & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental parameters. In addition, one more experiment was done in order to establish the impact of the number of features on the accuracy of the proposed method. In this case, the RBF (FCRBF) network was used as the feature evaluator, and the number of generated features was in the interval [1...4]. The average classification error and the average regression error for all datasets are shown in Table 7. From the experimental results, the robustness of the proposed methodology is clearly visible, as one or two features seem to be enough to achieve high learning rates for the experimental data used. Furthermore, one more experiment was conducted to determine the effect of the maximum number of generations on the accuracy of the proposed method. Again, as an evaluator model, the RBF was used.