# Multi-View Network Representation Learning Algorithm Research
## 4 Experiments and Evaluations
### Baseline Algorithms  
To evaluate the performance of MVNR, we introduce the following algorithms of network representation as baseline algorithms. The representation length of all the baseline methods is set to 200. **DeepWalk:** DeepWalk is the most classical algorithm which adopts only network structural features to learn the network representations. we use the Skip-Gram model and Hierarchical Softmax for DeepWalk. **Line**: Line is a recently proposed algorithm to solve the representation learning of big-scale networks. Line is a method capturing local features based on the probability loss function, which provides 1 st Line and 2 nd Line models. Similar as our MVNR, it uses 1-step and 2-step neighboring vertices to learn the network representations. **node2 vec**: node2 vec also adopts the BFS and DFS strategy to capture the higher order neighboring vertices. Meanwhile, node2 vec define a second-order random walk to balance the DFS and BFS. **NEU**: This algorithm is from the paper \"Fast Network Embedding Enhancement via High Order Proximity Approximation,\" which is a higher order network representation learning algorithm. In this paper, the NEU algorithm convert the lower-order representations trained by DeepWalk into the higher-order representation. **GraRep**: It is a new network representation learning algorithm, which can capture higher order network features by matrix factorization and representation concatenation. **Weight-based Matrix Factorization (WMF)**: For the \(k\)-step network, we define the matrix \(W^{(k)}\) as the link weight matrix of the \(k\)-th network view. We then use the SVD algorithm to factorize the matrix \(W^{(k)}\), here \(W^{(k)}\approx U^{(k)}S^{(k)}{(V^{(k)})}^{T}\). We regard \(U^{(k)}{(S^{(k)})}^{0.5}\) as the network representation vectors. **MVNR:** It is our proposed algorithm. In this experiment, we adopt the different \(k\) values to capture the \(k\)-step vertex relational information and learn the network representation. \(\lambda\) as 0.5 for Citeseer and Cora and 0.1 for Wiki. **Unweighted MVNR**: This algorithm is a simplified MVNR algorithm with the equal weights for different \(k\)-step networks, we call this algorithm as Un_MVNR. Other optimizations are the same as MVNR. The MVNR algorithm proposed is a higher order network representation learning algorithm. Therefore, we choose three classical network representation learning algorithms of lower order, such as DeepWalk, Line and node2 vec. node2 vec improves the random walk of DeepWalk, Line and DeepWalk aim to factorize the structure feature matrix of network; the proposed MVNR is also an NRL algorithm based on matrix factorization form of DeepWalk. So, we take DeepWalk, Line and node2 vec as the baseline algorithms. In addition, we also choose two classical network representation learning algorithms of higher order for comparison and analysis, such as GraRep and NEU. DeepWalk is the most classical network representation learning algorithm. Line and node2 vec are classical network representation learning algorithms based on DeepWalk. GraRep and NEU are higher order network representation learning algorithms accepted by top-level conference and they are also classical \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Node** & **Edge** & \
\begin{tabular}{c} **The Number** \\ **of Classes** \\ \end{tabular} & **Average Degree** &
\begin{tabular}{c} **Average** \\ **Path Length** \\ \end{tabular} \\ \hline Citeseer & 3312 & 4732 & 6 & 2.857 & 9.036 \\ Cora & 2708 & 5429 & 7 & 4.01 & 6.31 \\ Wiki & 2405 & 17981 & 19 & 14.953 & 3.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Network datasets descriptions. representative algorithms of higher order representation learning algorithms. WMF and Un_MVNR are the simplified versions of MVNR algorithm, which are used to measure the performance influence of weight matrix on MVNR algorithm. The parameter setting of these algorithms is introduced in algorithm description part of Section 4.2.