# SubvectorS_Geo: A Neural-Network-Based IPv6 Geolocation Algorithm
## 3 The SubvectorS_Geo Algorithm
### Encoder
#### 3.3.3 Path Encoding  
Landmark path encoding and entity encoding to be measured in \(E_{ld}\). The feature encoding is performed for M*N landmark paths. \[C_{l}=(R_{cl},T_{l}) \tag{10}\]  
\[C_{l}=(AS,P_{i},L,P_{mn(/a)},H_{s},T_{l}) \tag{11}\]  
\[C_{t}=(R_{ct},T_{t}) \tag{12}\]  
\[C_{t}=(AS,P_{i},L,P_{mx(/a)},H_{s},T_{t}) \tag{13}\]  
\(C_{l}\) and \(C_{t}\) are the path coding vectors of landmarks and targets. \(R_{cl}\) and \(R_{ct}\) are the route feature coding vectors of landmarks and targets. The dimensions of the \(R_{cl}\) and \(R_{ct}\) vectors and the encoded features are the same: \(AS\) is the AS domain information code of the terminal IP. \(P_{i}\) is the encoded value that identifies the IP. \(L\) is the value of the code that evaluates the presence of the closest common router. \(P_{mn(/a)}\) is the common address prefix ofthe landmark and the closest common router. \(P_{mx(/a)}\) is the common address prefix of the target and the closest common router. \(H_{s}\) is the encoded value to evaluate the presence of similar routes for hostnames. \(T_{l}\) and \(T_{t}\) are the remaining path delay vector encoding of the network for the landmark and the target in the trusted region approximated by the routing feature, respectively. Routing vector encoding: Coding tasks for geographically correlated routing features in the traceroute measurement data. \(R_{cl}\) and \(R_{ct}\) are encoded representations of the routing features for landmark paths and destination paths. The coding features and coding methods are the same. The detailed process for routing code (\(R_{cl}\)) for landmark paths is as follows. \[P_{i}= \begin{cases}P_{m,n,i}&\text{if }\ P_{m,n,i}\ \text{ in }R_{i}\\ \gamma&\text{if }\ P_{m,n,i}\ \text{not in }R_{i}\end{cases} \ (1<i<k) \tag{14}\]  
\[L= \begin{cases}1&\text{if }\ P_{m,n,i}\ \text{ in }E_{lrp}\\ 0&\text{if }\ P_{m,n,j}\ \text{ not in }E_{lrp}\end{cases}  \tag{15}\]  
\(P_{m,n,k}\) is the \(k\)th IPv6 routing address on the probing path of the \(m\)th probe in the \(E_{ld}\) dataset for the \(n\)th landmark route or the terminal routing address. In the screening evaluation of identification IPs, to pursue the geographically strong correlation of identification IPs for terminal routing, the inverse path order for screening is adopted. That is, the order starting from the terminal IP(\(P_{m,n,k}\)) to the end of the starting IP(\(P_{m,n,1}\)). When \(P_{m,n,i}(1<i<k)\) exists in the identity IP set \(R_{i}\), \(P_{i}\) takes the value of the identity IP route \(P_{m,n,i}\). Otherwise, \(P_{i}\) takes the value of \(\gamma\). In the screening task of the closest common router: \(P_{m,n,j}\) is the any route IP in a path after the identification IP. The path segment starting from the identification IP(\(P_{m,n,i}(1<i<k)\)) to the terminal route IP(\(P_{m,n,k}\)) screens the closest common router near the terminal in the reverse path order. When any IPv6 route (\(P_{m,n,j}(i<j<k)\)) on the path exists in the closest common router set \(E_{lrp}\), \(L\) is assigned a value of 1. Else, \(L\) is assigned a value of 0. \[P_{mn(/\alpha)}= \begin{cases}P_{nm(/\alpha)}&\text{if }\ P_{m,n,j(/\beta)}=P_{m,n,k (/\beta)}\ \text{ and }\ \beta>\alpha\\ \lambda&\text{else}\end{cases}  \tag{16}\]  
\(P_{nm(/\alpha)}\) approximates the trusted region based on the closest common router. It likewise supports the credibility of the region delineated by the closest common router. \(P_{mn(/\alpha)}\) analyzes the geographic association of the closest public router and terminal IPs by filtering their common prefixes, taking the value of \(P_{nm(/\alpha)}\) when the number of common prefix bits of the closest common router and terminal IP satisfies \(\beta>\alpha\). Otherwise, \(P_{nm(/\alpha)}\) takes the value of \(\lambda\). The \(\alpha\) assignment takes into account the address prefix segment provided in the Whois information as a way to limit the common prefix. \[H_{s}= \begin{cases}1&\text{if }\ h_{m,n,c}\ \text{ similar }h_{nc}\ (h_{nc}\ \text{ in }H_{lrp})\\ 0&\text{else}\end{cases}