## 3 HDELC Algorithm
### High-Dimensional Feature Space Reconstruction Process  
Reconstructing the high-dimensional feature space can maximize model diversity and local optimization performance. It divides the original high-dimensional data into relatively independent subsets of different feature spaces. Not only can the correlation between individual base classifiers be reduced, but also the operations are executed relatively faster due to the reduced size of the input feature space corresponding to each base classifier. The algorithmic flow of high- dimensional feature space reconstruction is given using the FSR algorithm (the abbreviation of feature subspace reconstruction strategy). ```
Input: The feature space selection matrix \(X\); Procedure
1: For \(i\) in \(1,\ldots,n\);
2: Calculate the information entropy \(Ent(x_{i})\);
3: Calculate the average value of information entropy \(Ave_{Ent}\);
4: if \(Ent(x_{i})\leq Ave_{Ent}\)
5: Place \(x_{i}\) in the set \(X^{S}\);
6: Or;
7: Place \(x_{i}\) in the set \(X^{W}\);
8: Set the filter factor \(\beta\);
9: Calculate the number of features \(\left|X^{W}_{\mathit{del}}\right|\) that are rejected in weak feature space;
10: Redivide and the weak feature space \(X^{W}\);
11: Refactor the feature space \(X^{\prime}\);
12: Use \(X^{\prime}\in\left(X^{\prime}_{1},X^{\prime}_{2},\ldots,X_{B}{}^{\prime}\right)\) to train the decision tree classifier \((\varphi_{1},\varphi_{2},\ldots,\varphi_{B})\);
13: Select the attribute screening factor corresponding to the maximum precision as the optimal attribute screening factor, and then determine the optimal feature selection set size \(\left|X^{best}\right|\);
14: Use PCA dimensionality reduction to reduce the original feature space \(X\) to \(\left|X^{best}\right|\) dimension. Output: The optimal feature selection set size \(\left|X^{best}\right|\) and feature-reconstructed dataset. ```  
**Algorithm 2** Feature subspace reconstruction strategy  
For the reconstruction process of the high-dimensional feature space, first, the entropy weight method [27] is used to obtain the information entropy of each feature and its weight. In this way, the importance of the features is evaluated. The mean value of information entropy of all features is calculated and used as the threshold value. The construction of the feature space reconstruction matrix will be based on this threshold value. Information entropy is directly related to the predictive uncertainty of the features, can provide an objective method to assess the contribution of the features, and can accurately quantify the uncertainty level of the features in the classification task. By measuring features with low information (i.e., high uncertainty) based on the information entropy mean, the complexity of the model can be effectively reduced, thereby reducing the risk of overfitting and improving the model's generalization ability. Using the mean value of information entropy as the delineation boundary of feature importance, the set of features with information entropy that is more significant than the threshold value is considered for a partial optimization operation. Second, the threshold value is used for feature importance classification. We optimize the set of features whose partial information entropy is more significant than the threshold value. In order to maximize the valuable information in the features and reduce the feature space size, the redundant features are discarded to load the model computation. We set the attribute screening factor \(\beta\) as the screening coefficient for the set of features more significant than the threshold, \(\beta\in[0.1,0.2,0.3,0.4,0.5]\), and perform a sensitivity analysis on it. The set of feature subspaces under each attribute rounding factor constraint is used to construct the feature space reconstruction matrix. When training on the samples, it is convenient to locate the target selected features quickly. A set of decision tree classifiers are trained using the set of feature subspaces under each attribute discard factor constraint.