# Leveraging Feature Extraction to Perform Time-Efficient Selection for Machine Learning Applications
## 4 Computational Study  
In the following section, the results extracted from the proposed solution are presented and compared to those of other wrapper-based feature selection methods. These results and their meaning are then further discussed. Taking into account the main problem referred to before, a test regarding the computation time necessary to create the interim features for all combinations of a dataset was carried out. To illustratively validate the concern regarding the exponential growth in the number of feature combinations, an experiment was conducted. The length of combinations (\(r\)) was fixed at five, a value chosen to strike a balance between computational feasibility and representativeness of the underlying trend. This test was carried out using the proposed method without applying any preliminary feature reduction steps, thereby isolating the impact of the combinatorial explosion. The results may be observed in the plot depicted in Figure 4.  
As expected, the exponential growth in potential combinations also significantly affects the temporal efficiency of the proposed algorithm, which only validates the importance  
Figure 4: Illustration of the theoretical exponential time growth associated with computing all feature combinations of fixed length \(r\) as the number of features \(n\) increases. of the first feature reduction steps proposed to counter it. Once that counter-measure was implemented, an experiment was designed to compare the performance of the proposed solution when compared to other feature selection methods. To evaluate the effectiveness of our proposed solution, we compare its performance against nine established wrapper-based feature selection methods. This set of algorithms was chosen to provide a diverse and challenging benchmark, as wrapper methods are known to produce high-performing feature subsets. The selection represents a wide array of state-of-the-art metaheuristic strategies commonly used for optimization and feature selection. Furthermore, all comparative algorithms were implemented using the Py_FS package, which provides a standardized and fair framework for evaluating performance and computational cost. The chosen methods were:  
1. Binary Bat Algorithm (BBA)
2. Cuckoo Search Algorithm (CSA)
3. Equilibrium Optimizer (EO)
4. Genetic Algorithm (GA)
5. Gravitational Search Algorithm (GSA)
6. Harmony Search (HS)
7. Mayfly Algorithm (MA)
8. Red Deer Algorithm (RDA)
9. While Optimization Algorithm (WOA)  
To conduct meaningful testing, a substantial number of data points are required. Consequently, thirty distinct datasets were utilized for both binary and multi-classification tasks, which may be reviewed in Table 1.  
The framework was designed as follows:  
1. All datasets are pre-processed in order to guarantee no missing rows and numerical features are standardized
2. A cycle iterates over each combination of existing datasets and methods. In each step, the following occurs (seen in Algorithm 2): 1. The dataset is read. 2. For datasets exceeding 10,000 rows, a stratified sample of 10,000 instances was used to reduce the computational load while preserving the original class distribution. This approach minimizes the loss of informative patterns and ensures that the sampled subset remains representative of the full dataset. 3. Its categorical features are encoded by using target encoding (these features are identified beforehand). 4. This dataset is used with the current method, which iterates over the proposed solution and the remaining methods (these use 30 agents, and a max of 50 iterations, as these are the chosen defaults of Py_FS) to find a solution set. 5. Given the solution set arrived at by the feature selection method, the best sets of features found for target lengths [2; 3; 4; 5] are retrieved. 6. For each of the target lengths, the best set found (if any) is used to train a default random forest classifier. 7. Performance metrics are then retrieved from the trained classifier. 3.