Role-based network embedding aims to map network into low-dimensional node representations while preserving structural similarities. Adjacency matrix contain both the local and global information of a network, but it cannot directly represent the role of nodes. So it is essential to extract higher-order structural features from adjacency matrix for role-based network embedding (structural equivalence). While being sensitive to noise in real networks in general, the features extracted by some identical methods cannot truly represent the role of nodes. Therefore, we propose a deep learning framework RESD. In detail, we first propose extracting higher-order structural features for each node in the network. Then, we utilize the Variational Auto-Encoder (VAE) to model the nonlinear relationship of the features, reduce noise and improve the robustness of embedding. Furthermore, in the embedding space, we apply a degree-regularized constraint to guide the representation learning for preserving key structural information of nodes (e.g., degrees), which may be lost due to the principle of VAE framework. Finally, we construct a unified objective function to learn the node embedding for role discovery by preserving the structural features and node degree. We compare our model with several state-of-the-art methods on real-world networks. The results of extensive experiments demonstrate the effectiveness of our model and prove that our model scales well with dimension and network size.

基于角色的网络嵌入旨在将网络映射为低维节点表示形式，同时保留结构相似性。邻接矩阵既包含网络的本地信息又包含网络的全局信息，但不能直接表示节点的角色。因此，从邻接矩阵中提取高阶结构特征对于基于角色的网络嵌入（结构等效性）至关重要。虽然通常对真实网络中的噪声敏感，但是通过某些相同方法提取的特征并不能真正代表节点的角色。因此，我们提出了一个深度学习框架RESD。详细地说，我们首先建议为网络中的每个节点提取更高阶的结构特征。然后，我们利用变分自动编码器（VAE）对特征的非线性关系进行建模，降低噪声并提高嵌入的鲁棒性。此外，在嵌入空间中，我们应用度数正则约束来指导表示学习，以保留节点的关键结构信息（例如度数），这可能由于VAE框架的原理而丢失。最后，我们构造了一个统一的目标函数，以通过保留结构特征和节点度来学习用于角色发现的节点嵌入。我们将我们的模型与现实网络中的几种最新方法进行了比较。