## 3 Loss Differentiation Feature Selection for LEO Satellite Network
### Packet Loss Differentiation Feature Selection Method  
The Relief algorithm represents a typical filtering approach. Its feature scoring and selection process is decoupled from classification algorithms, making it simple, convenient, and low in complexity. However, it is only suitable for calculating binary classification feature weights. The underlying principle is as follows: Firstly, positive samples and negative samples are segregated within the training dataset. For any given sample in the training dataset, one nearest-neighbor sample is selected from both same-class and different-class samples. If a particular feature attribute present in that sample exhibits greater similarity with its nearest neighbor from the same class compared to its nearest neighbor from a different class, it indicates a higher differentiation capability of that feature attribute. Consequently, larger feature scores or weights are assigned. Let the training set be \(D=\{(x_{i},y_{i})|x_{i}\in R^{m},m>0,y_{i}\in\{1,-1\},i=1,2,\cdots,n\}\), where \(n\) is the number of samples in the training set, and \(m\) is the number of feature attributes contained in each sample. The sample is \(\mathbf{x_{i}}=(x_{i}^{1},x_{i}^{2},\cdots,x_{i}^{k},\cdots,x_{i}^{m})\). Define the difference between samples \(\mathbf{x_{i}}\) and \(\mathbf{x_{j}}\) on the \(k\)th attribute as shown in Equations (1) and (2). If the feature is scalar:  
\[\mathrm{diff}(k,\mathbf{x_{i}},\mathbf{x_{j}})=\left\{ \begin{array}{ll}0,&x_{i}^{k}= x_{i}^{k}\\ 1,&x_{i}^{k}\
eq x_{j}^{k}\end{array} \right. \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Number** & **Symbol** & **Interpretation** \\ \hline F\({}_{9}\) & IAT & The interval of the last pair of adjacent packets \\ F\({}_{10}\) & IAT\({}_{\min}\) & The minimum interval between the last packet loss and \\  & & the present packet loss \\ F\({}_{11}\) & IAT\({}_{\max}\) & The average interval between the last packet loss and the \\  & & present packet loss \\ F\({}_{12}\) & IAT\({}_{\max}\) & The maximum interval between the last packet loss and \\  & & the present packet loss \\ F\({}_{13}\) & \(\frac{\mathrm{IAT}}{\mathrm{IAT}_{\min}}\) & The ratio of the IAT to the average IAT \\ F\({}_{14}\) & \(\frac{\mathrm{IAT}}{\mathrm{IAT}_{\max}}\) & The ratio of the IAT to the minimum IAT \\ F\({}_{15}\) & \(\frac{\mathrm{IAT}}{\mathrm{IAT}_{\max}}\) & The ratio of the IAT to the maximum IAT \\ F\({}_{16}\) & \(\frac{\mathrm{IAT}(t)}{\mathrm{IAT}(t-1)}\) & The ratio of the interval between the last pair of adjacent packets to the previous pair of adjacent packets \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The features regarding IAT. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Number** & **Symbol** & **Interpretation** \\ \hline F\({}_{17}\) & NUM\({}_{\mathrm{loss}}\) & Number of consecutive lost packets \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Packet loss number. If the feature is numeric:  
\[\text{diff}(k,\mathbf{x}_{i},\mathbf{x}_{j})=\left|\frac{x_{i}^{k}-x_{j}^{k}}{\underset{1 \leq l\leq n}{\max}\left\{x_{l}^{k}\right\}-\underset{1\leq l\leq n}{\min} \left\{x_{l}^{k}\right\}}\right| \tag{2}\]  
If \(\mathbf{x}_{i\text{,nh}}\) is the homogeneous nearest neighbor of \(\mathbf{x}_{i}\), and \(\mathbf{x}_{i\text{,nm}}\) is the heterogeneous nearest neighbor of \(\mathbf{x}_{i}\), then the iterative calculation formula for the weight of the \(k\)th feature is as follows:  
\[\theta_{k}(i)=\theta_{k}(i-1)-\frac{\text{diff}(k,\mathbf{x}_{i},\mathbf{x}_{\text{nh} })}{n}+\frac{\text{diff}(k,\mathbf{x}_{i},\mathbf{x}_{\text{nm}})}{n},i=1,2,\cdots,n \tag{3}\]  
After calculation, let \(\theta_{k}(n)=\theta_{k}\), and subsequently the larger \(\theta_{k}\) denotes a stronger classification ability associated with the \(k\)th feature attribute. Each individual weight of each specific feature is calculated using Equation (3) to form a vector \(\mathbf{\theta}=(\theta_{1},\theta_{2},\cdots,\theta_{m})^{T}\) representing all respective weights.