# Learning Embedding for Signed Network in Social Media with Hierarchical Graph Pooling
## 1 Introduction  
Many social relationships could be represented by assigned networks with positive or negative sign edges. Positive edges in a signed network represent positive ties, such as friends, trust, and support, whereas negative edges represent negative relationships, such as enemies, mistrust, and resistance [1]. In addition, complicated systems exist where positive and negative interactions are implicit. For example, a hyperlink on a website may convey acceptance or disapproval of the target page, depending on the semantics of both pages. It has been proven that such invisible negative links are predictable, and they can convey significantly different feature information than positive links [2]. It is increasingly recognized that mining adversarial relationships in social systems has a wide range of applications in social network analysis, such as social sentiment analysis [3; 4; 5] and relationship recommendation [6]. Network embedding refers to learning a fixed-length, low-dimensional vector for each node. It is essential for a variety of social network analysis tasks, such as link prediction, node classification, etc., and it has gained interest in data mining and social computing [7; 8; 9; 10; 11; 12]. Recently, network embedding has been greatly improved by graph neural networks (GNNs) because of their tremendous end-to-end modeling capabilities. By combining graph theory and the convolution theorem, [PERSON] [13] developed the first graph convolutional neural (GCN) network. However, this is hampered by a high level of temporal complexity. In order to address this issue, ChebNet [14] and GCN suggest parametrizing the convolution kernel in spectral approaches to minimize temporal complexity. Despite being spectral approaches, these two have started spatially defining node weight matrices. Inspired by these major approaches, spatial methods began to represent node weights using the attention mechanism, sample mechanism, and aggregate mechanism. However, traditional GCNs cannot be used on signed networks [15; 16] since there exist specific principles led by social theory, such as \"the enemy of my enemy is myfriend\", which demonstrates that negative links can have a big impact on the quality of node embeddings. For the purpose of accurately locating the role of the negative links, many tremendous efforts have been devoted to designing network embedding methods, especially for signed networks. For example, SiNE [17] (Signed Network Embedding) learned a low-dimensional vector embedding by using structure balance theory in signed networks. SGCN [18] expanded GCN to signed networks and designed both positive and negative aggregators for the purpose of generating node embeddings based on balance theory. SiGAT [19] integrated attention mechanisms to signed directed networks and built a motifs-based graph neural network model. However, few known approaches take the hierarchical graph pooling of the networks into consideration, which is critical for improving the representation power of a graph, in light of the fact that hierarchical graph pooling can enhance representation learning with high-order structural information. Motivated by these analyses, a novel signed graph representation framework SHGP to learn Signed network embedding with hierarchical graph pooling is proposed. Instead of only applying aggregators when aggregating information from neighboring nodes, SHGP employs a pooling operator to learn the hierarchical graph pooling of real signed graphs and use the learned hierarchical graph pooling also as part of the node representation. Our main contributions are threefold:  
* A graph pooling layer is introduced to learn effective signed network embedding, which utilizes a pooling mechanism to perform standard global pooling. Further, the essence of this pooling mechanism is to pick a subset of critical nodes to enable the encoding of high-level features and the hierarchical graph pooling of signed networks.