## 2 Materials and Methods
### Model Structural Details and Detection Process  
Our LVAE method consists of two parts: a variational autoencoder part and an integrated classifier part. Figure 2 illustrates the detection process. The variational autoencoder part has an input vector size of 79 and a latent space variable size of 2. Unlike other research works, our input is in the form of data. The encoder and decoder parts utilize fully connected neural networks.  
The encoder has an input dimension of 79 and a hidden layer with 79 nodes and a ReLU activation function. The second hidden layer also has 79 nodes and a sigmoid activation function. The output latent vector dimension has a mean and variance of 2. The Gaussian distribution vector is then combined with the output, resulting in the latent space vector, \(Z\).  
Input: data set \(\overline{X}\).  
Output: Classification results \(R_{i}\).  
1: Data preprocessing: removing redundant information, filling in missing values and normalization.  
2: Iteration  
3: for c = 1 in rang (1, 9)  
4: Input data \(\overline{x}_{i}\) into the classifier to get the predicted value \(h_{\theta}(\overline{x})_{i}\)  
5: Backpropagation calculates Equation (6) losses and gradients.  
6: Gradient descent.  
7: end for  
8: Until Equation (6) converges.  
9: Output the classification result for each classifier \(R_{i}\) (\(i=1,2,3,4,5,6,7,8\)).  
10: for c = 1 in rang(1, 9)  
11: if (\(R_{i}>R_{i}\) (\(i=1,2,3,4,5,6,7,8\)))  
12: Output classification result \(R_{i}\).  
13: end if  
14: end for  
15: Output the classification results \(R_{i}\). ```  
**Algorithm 2** Training Integrated Classifiers  
The decoder takes the input latent space variable, \(Z\). The first hidden layer is a neural network with 79 nodes and a ReLU activation function. The second hidden layer is also a neural network with 79 nodes and a sigmoid activation function. The output layer is a fully connected neural network with a tanh activation function.  
After gradient descent using our designed log-cosh loss function, the reconstructed data are obtained. The reconstructed data and the original data are then preprocessed together, and the preprocessed original data are input into the integrated classifier for training. The reconstructed data are input into the trained model for classification. Now, let us discuss the structure of the integrated classifier.  
Multi-Layer Perceptron (MLP): The input dimension is 78, and the hidden layer is a neural network with 80 nodes and a ReLU activation function. The output layer has a dimension of 1 and uses a softmax activation function.  
Naive Bayes (NB): A model defined by scikit-learn library.  
Decision Tree (DT): A model defined by scikit-learn library.  
Random Forest (RF): A model defined by scikit-learn library.  
Support Vector Machine (SVM): A model defined by the scikit-learn library.  
Logistic Regression (LR): A model defined by scikit-learn library.  
Gradient Boosting (GB): A model defined by scikit-learn library.  
Gated Recurrent Unit (GRU): A total of 80 nodes are used for the hidden layer and a sigmoid activation function is used; the dropout is set to 0.2. The output layer is set to 1, and softmax is used for the activation function.