## 2 Materials and Methods
### Feature Engineering  
Generally, we generate a high-quality and representative subdataset through data preprocessing. Then, we can remove some redundant features from the dataset using feature engineering works, which make the model training more accurate and efficient. The model in this paper first proposes to remove irrelevant features after the preprocessing work using an integrated feature engineering method consisting of Information Gain (IG) [23] and Fast Correlation-Based Filter (FCBF) [24] to retain the important features.  
(1) Information Gain (IG): The IG algorithm is a commonly used feature selection method to select important features. IG indicates the amount of information obtained or entropy change, which can be used to measure how much information a feature can bring to the target variable. Moreover, the time complexity of the IG algorithm is O(n), and it can quickly obtain the importance score of each feature, so we believe that the IG algorithm is well suited to our preconceived ideas in the feature engineering phase. We can calculate the importance score for each feature. This will help us to select some features that are most relevant to the detection task. Assuming that T is the target variable, for each feature represented by the random variable \(X\), the IG value of the feature \(X\) is represented by (1):  
\[IG(T\mid X)=H(T)-H(T\mid X) \tag{1}\]  
where \(H(T)\) is the entropy of the target variable \(T\), and \(H(T\mid X)\) is the conditional entropy of \(T\mid X\).  
(2) Fast Correlation-Based Filter (FCBF): Although the IG-based feature selection method can remove some unimportant features while guaranteeing a low time complexity, we can still find many redundant features that are not removed. Feature redundancy may increase the time complexity and space complexity and also increase the probability that the model will be misled by the redundant data. In that case, the performance of our model may be degraded and may also increase the risk of overfitting. Therefore, we will introduce the FCBF algorithm to solve the above problem. We remove the redundant features by calculating the correlation of the input features, which can help to improve the performance and efficiency of the model. In FCBF, the symmetric uncertainty (SU) is calculated to measure the correlation between features by normalizing the IG value, as shown in Formula (2):  
\[SU(X,Y)=2\frac{IG(X\mid Y)}{H(X)+H(Y)} \tag{2}\]  
\(SU(X,Y)\) is in the range [0,1]; a value of 1 means that the two features of \(X\) and \(Y\) are completely correlated, and a value of 0 means that the two features are completely independent. The FCBF algorithm searches for features in the feature space according to the SU value of the feature space until the entire feature space is searched. We will consider highly correlated features as redundant and keep only one of them. In the proposed FCBF algorithm, the \(SU\) value of each pair of features is calculated as their correlation. The correlation threshold \(\alpha\) is optimized by BO-GP [25]. The BO-GP is a Gaussian Process-based Bayesian Optimization algorithm for solving the global optimal solution of a black-box function. The principle of BO-GP algorithm is to approach the global optimal solution step by step by continuously evaluating the objective function and adjusting the position of the next evaluation according to the evaluation result. When the correlation value between two features is greater than \(\alpha\), the feature with higher feature importance is retained, and the feature with lower feature importance is discarded. Repeat the correlation calculation and feature rejection process until every pair of features in the feature list is not highly correlated (SU <= \(\alpha\)). In this paper, the model combining the IG algorithm and the FCBF algorithm is called IG-FCBF.