## 3 Methodology
### Ensemble Model
In the second part, we share similar operations with Rot-Pro ([PERSON] et al., 2018). The projection matrix for each dimension of an entity is defined as follows:  
\[Pro\_Matrix(i)=\left[ \begin{array}{cc}cos\theta_{i}&-sin\theta_{i}\\ sin\theta_{i}&cos\theta_{i}\end{array} \right]^{-1}\left[ \begin{array}{cc}x_ {i}&0\\ 0&y_{i}\end{array} \right]\left[ \begin{array}{cc}cos\theta_{i}&-sin\theta_{i} \\ sin\theta_{i}&cos\theta_{i}\end{array} \right], \tag{5}\]  
where \(1\leq i\leq k\), \(x_{i}\in\{0,1\}\) and \(y_{i}\in\{0,1\}\), while \(\theta_{i}\) is the rotation phase in each dimension. We use a complex number to represent an entity; thus, the projection is described as follows:  
\[\left[ \begin{array}{c}Re(h_{c\_proj}[i])\\ Im(h_{c\_proj}[i])\end{array} \right]=Pro\_Matrix(i)\left[ \begin{array}{c}Re(h_ {2}[i])\\ Im(h_{2}[i])\end{array} \right], \tag{6}\]  
where \(1\leq i\leq k\), \(h_{2}\) is a head entity embedding in the second part, \(h_{2}\in\mathbb{C}^{k}\); \(Re(h_{2}[i])\) represents the real number of its \(i\)th dimension, and \(Im(h_{2}[i])\) represents the imaginary number of its \(i\)th dimension. Tail entity embedding \(t_{2}\) in the second part performs similar projection operations, i.e., \(t_{2}\in\mathbb{C}^{k}\). After carrying out these projections, we obtain the projected head entity \(h_{c\_proj}\) and projected tail entity \(t_{c\_proj}\). Then, we rotate the projected head entity \(h_{c\_proj}\). The rotation for each dimension of \(h_{c\_proj}\) is as follows:  
\[\left[ \begin{array}{c}Re(h_{c\_proj}[i])\\ Im(h_{c\_proj}[i])\end{array} \right]=\left[ \begin{array}{cc}cos\phi_{i}&- sin\phi_{i}\\ sin\phi_{i}&cos\phi_{i}\end{array} \right]\left[ \begin{array}{c}Re(h_{c\_proj}[i]) \\ Im(h_{c\_proj}[i])\end{array} \right], \tag{7}\]  
where \(1\leq i\leq k\) and \(\phi_{i}\) is relational rotation phase in each dimension. The rotated result \(h_{c\_rot}\) is expected to be close to the projected tail embedding \(t_{c\_proj}\), and the distance function in the second part is defined as follows:  
\[dist_{2}=\|h_{c\_rot}-t_{c\_proj}\|_{2}. \tag{8}\]Semantic hierarchies usually exist in the field of cybersecurity. For example, for entities at different levels of the hierarchy, CWE-345 (efficient verification of data authentication) is the parent of CWE-352 (cross-site request forgery). For entities at the same level of the hierarchy, CWE-345 (dfficient verification of data authentication) is the peer of CWE-20 (improve input validation). While rotations can distinguish entities at different levels of the hierarchy, there are nonetheless inadequacies in distinguishing entities at a hierarchy of the same level. HAKE demonstrates that angular information is well able to capture differences between entities at the same level of the hierarchy. For entities at the same level of the hierarchy, their measurement scores at different levels of the hierarchy can be considered very similar. Due to different points on the same circle possessing different phases, the difference in phases is used to distinguish them. The phase mapping of the head entity \(h_{3}\), relationship \(r_{3}\), and tail entity \(t_{3}\) satisfies the following relationship:  
\[(h_{3}+r_{3})mod\ 2\pi=t_{3}, \tag{9}\]  
where \(h_{3},r_{3},t_{3}\in[0,2\pi)^{k}\). Because the phase difference in the same plane changes periodically, we use periodic function \(sin(x/2)\) to calculate the difference between the head entity and tail entity at the same level of the hierarchy. The formula is as follows:  
\[dist_{3}=\|sin(\frac{h_{3}+r_{3}-t_{3}}{2})\|_{1}. \tag{10}\]  
The dynamic adjustment of the weights of various rotation and projection methods during training can improve the effectiveness of ensemble learning. The process of dynamically adjusting weights is shown in Algorithm 1.