# Multi-View Cluster Structure Guided One-Class BLS-Autoencoder for Intrusion Detection
## 3 Proposed Method
### Multi-View Co-Association Matrix Optimization
```
0:
1:for each view \(v=1\) to \(V\)do
2: Apply K-means to produce \(B\) base partitions and compute the corresponding binary partition matrices \(\{P_{1}^{v},\ldots,P_{B}^{v}\}\) according to Equation (1);
3: Compute the view-specific co-association matrix \(G^{v}\) according to Equations (2) and (3);
4:endfor
5: Compute \(Q=\frac{1}{V}\sum_{v=1}^{V}G^{v}\);
6:repeat
7: Update \(G\) according to Equation (8);
8: Update \(G=G^{+}\);
9: Update \(Q=G\);
10:until\(G\) converges Output The multi-view co-association matrix \(G\);
```  
**Algorithm 1** Multi-view co-association matrix optimization  
In the scenario of multi-view one-class intrusion detection, network traffic data originate from diverse terminal devices, and the training set consists of only normal samples, making conventional binary classification algorithms difficult to adapt directly. To this end, this paper aims to fully leverage multi-view normal samples to train an intrusion detection model, which identifies anomalous samples independently and efficiently across different data sources while maintaining ensemble decision-making capabilities. Instead of learning the direct mapping relationship between samples and class labels, this paper proposes a multi-view cluster structure guided one-class BLS-autoencoder (MOCBLSAE), which learns discriminative patterns of normal traffic data based on the cross-view global cluster structure and the reconstruction of intra-view local features, thereby enabling the identification of unknown anomalous samples. Finally, an intrusion detection framework is constructed based on multiple MOCBLSAE models. The framework of MOCBLSAE is shown in Figure 1. Specifically, in the \(v\)-th view, MOCBLSAE first applies orthogonal stochastic weights and biases during the generation of feature nodes and enhancement nodes, then constructs the hidden layer \(A^{v}\) by concatenating multiple feature nodes and enhancement nodes to enhance the model's generalization capability [31] as follows:  
\[A^{v}=[F_{1}^{v}\;F_{2}^{v}\;\ldots\;F_{p}^{v}\;E_{1}^{v}\;E_{2}^{v}\;\ldots \;E_{q}^{v}], \tag{10}\]  
\[F_{i}^{v}=\phi_{f}(X^{v}W_{i}^{v}+C_{i}^{v}), \tag{11}\]  
\[s.t.\;W_{i}^{v}(W_{i}^{v})^{T}=I,\;(C_{i}^{v})_{u}(C_{i}^{v})_{u}^{T}=1,\;(C_{ i}^{v})_{u}=(C_{i}^{v})_{v},\]  
\[E_{j}^{v}=\phi_{e}(X^{v}W_{j}^{v}+C_{j}^{v}), \tag{12}\]  
\[s.t.\;W_{j}^{v}(W_{j}^{v})^{T}=I,\;(C_{j}^{v})_{u}(C_{j}^{v})_{u}^{T}=1,\;(C_{ j}^{v})_{u}=(C_{j}^{v})_{v},\]  
where \(W_{i}^{v}\) and \(W_{j}^{v}\) are orthogonal stochastic weight matrices, \(C_{i}^{v}\) and \(C_{j}^{v}\) are orthogonal stochastic bias matrices, \((C_{i}^{v})_{u}\) and \((C_{j}^{v})_{u}\) are the \(u\)-th row vectors of \(C_{i}^{v}\) and \(C_{j}^{v}\), and \(\phi_{f}\) and \(\phi_{e}\) are activation functions. After obtaining the hidden layer \(A^{v}\in\mathbb{R}^{n\times l}\), MOCBLSAE incorporates global cluster structure information to capture the discriminative patterns of diverse normal samples, thereby achieving effective data reconstruction. In addition, MOCBLSAE lacks reconstruction capability for anomalous data, allowing for rapid identification through reconstruction errors. Based on this idea, the objective function of MOCBLSAE is designed as follows:  
\[\min_{G}||G-Q||_{F}^{2},\ s.t.G\geq 0. \tag{7}\]0  
where \(A^{v}\) is the hidden layer, \(W^{v}\) is the connecting matrix between the hidden layer and the output layer, \(g_{ij}\) is the \(ij\)-th entry of the global co-association matrix \(G\), \(((W^{v})^{T}(A^{v})^{T})_{i}\) represents the column vector of \((W^{v})^{T}(A^{v})^{T}\), and \(\lambda\) and \(\alpha\) are trade-off parameters. The first term of problem (13) minimizes the reconstruction error of normal samples, the second term prevents overfitting by imposing the Frobenius norm, and the third term preserves the global cluster relationships among samples. In order to optimize the objective function, it can be reformulated into a matrix form as follows:  
\[\min_{G}||G-Q||_{F}^{2},\ s.t.G\geq 0. \tag{7}\]1  
where \(L_{G}\) is the Laplacian matrix of \(G\).