# RGCLN: Relational Graph Convolutional Ladder-Shaped Networks for Signed Network Clustering
## 2 Related Work  
In this section, we state the work related to graph representation learning. A large amount of research work related to graph embedding already exists in unsigned networks [20; 21]. The presence of negative chains in signed networks leads to the fact that methods in unsigned networks cannot be directly migrated and applied to signed networks. Therefore, all relevant algorithms for signed networks need to be redesigned and researched. Next, we mainly review various embedding algorithms related to signed networks. Ref. [22] used a signed Laplacian matrix and its normalized version for signed clustering. Ref. [23] proposed a multilevel signed network clustering framework based on a balanced normalized cut level (BNC), which solves the problem of the direct extension of a signed Laplacian from k > 2 to k-way and can obtain high-quality clustering results quickly. Ref. [24] derived a simple normalized signed (SNS) graph Laplacian matrix and a balanced normalized signed (BNS) graph Laplacian matrix, and the embeddingrepresentation obtained through the matrices have good node characterization capability. Ref. [13] proposed a regularized spectral clustering algorithm based on solving the generalized feature problem, which shows better robustness to noisy and sparse matrices compared to algorithms such as SNS and BNS.  
In addition to these Laplacian-based signed algorithms mentioned above, several studies have explored the possibilities of deep learning frameworks for embedding representations of signed network nodes. For example, ref. [25] used the sociological theory called balance theory to aggregate and transfer information between the nodes of a balanced path. In [26], a deep network embedding model is proposed to learn low-dimensional node vector representations with structural balance preservation. The model imposes a greater weight on the loss of negative chains, allowing the encoder to focus on capturing the more scarce negative connections. A new directed graph neural network model, SDGNN, was proposed in [27]. This model involves both balance theory and state theory and reconstructs all three types of features, link symbols, link directions, and directed triangles simultaneously, with a solid ability to learn node embeddings. The design of the three-part loss function of the SDGNN model has been explored in more depth by many subsequent studies. However, the embedding studies mentioned above have all focused on the link prediction task, and there is still much room for exploration in the community detection task.  
Most of the existing signed network representation learning methods [28; 29; 30; 31] were designed based on balance theory. [PERSON] [1] first learned signed network embeddings using objective functions guided by balance theory. [PERSON]. [6] proposed a node representation generation model based on adversarial learning using balance theory as the basis for determining pseudo-edge generation. [PERSON]. [32] used a masked self-attentive layer to estimate the importance of different types of links and then aggregated more critical information from neighboring nodes to generate node embeddings based on balance theory. A recent research advancement related to our work is [33]. In the SSSNET model proposed in [33], a new interpretation of the social balance theory of signed network embeddings takes a neutral stance on whether the enemy of an enemy is a friend. Although the SSSNET model is a first step towards abandoning balance theory, it is ultimately limited by the balanced path. The algorithm proposed in this paper does not involve sociological theory but instead designs a practical depth framework to capture potential information between neighbors.