# RGCLN: Relational Graph Convolutional Ladder-Shaped Networks for Signed Network Clustering
###### Abstract  
Node embeddings are increasingly used in various analysis tasks of networks due to their excellent dimensional compression and feature representation capabilities. However, most researchers' priorities have always been link prediction, which leads to signed network clustering being under-explored. Therefore, we propose an asymmetric ladder-shaped architecture called RGCLN based on multi-relational graph convolution that can fuse deep node features to generate node representations with great representational power. RGCLN adopts a deep framework to capture and convey information instead of using the common method in signed networks--balance theory. In addition, RGCLN adds a size constraint to the loss function to prevent image-like overfitting during the unsupervised learning process. Based on the node features learned by this end-to-end trained model, RGCLN performs community detection in a large number of real-world networks and generative networks, and the results indicate that our model has an advantage over state-of-the-art network embedding algorithms. signed graphs; network embedding sign graph convolution; community detection +
Footnote †: journal:  
The core idea of the algorithms currently developed for clustering problems in signed networks can be summarized by the well-known sociological theory, \"balance theory\" [15]. Balance theory can be summarized simply by saying that the friend of a friend and the enemy of an enemy are both friends. This makes most algorithms involving this theory minimal, excluding nodes that do not satisfy the theory. To address the above problem, our framework discards this very limiting theory and uses only deep networks to capture node information. The node embedding algorithm proposed in this paper is based on a multi-relational graph convolutional structure and draws on the design concepts of fused spectral graph convolutional networks and U-Net [16] in GCLN [17]. Due to the particularity of graph convolution, there will be an over-smoothing problem during depth stacking, so most models only obtain first-order and second-order neighbor information [18; 19]. However, experiments confirm that our framework can effectively avoid this problem during the deepening process. To better distinguish the different information represented by positive and negative links in signed networks, we use relational graph convolution in the ladder-shaped depth framework, which means that our framework is not strictly symmetric. Thanks to our abandonment of balance theory, there is no need to precisely follow balanced paths in the process of information aggregation and transfer, which significantly simplifies our framework. To show better results in unsupervised tasks and to further avoid extreme divisions, we add size constraints. The soft constraint prevents individual loss-guided models from falling into local optima during training. We evaluate the effectiveness of RGCLN in several real-world networks and generative networks for semi-supervised and unsupervised tasks, and both end up with good experimental results. The main contributions of our paper are as follows:  
* A novel end-to-end optimized asymmetric ladder-shape framework is designed for signed networks, which can capture the deep hidden features and domain information of nodes and well solve the problem that graph convolution cannot be deeply superimposed. * The framework behaves as an asymmetric structure, which effectively avoids the overfitting problem. * The design concept of end-to-end optimization makes the framework more friendly to the signed clustering problem. * The size constraint is defined and incorporated to avoid extreme divisions in unsupervised learning, which dramatically improves the performance of the model. The rest of this paper is organized as follows. In Section 2, we discuss current work related to this paper and briefly introduce related research and recent advances in node embedding on signed networks. Section 3 introduces the model proposed in this paper, the RGCLN.