The study of social networks is a burgeoning research area. However, most existing work deals with networks that simply encode whether relationships exist or not. In contrast, relationships in signed networks can be positive ("like", "trust") or negative ("dislike", "distrust"). The theory of social balance shows that signed networks tend to conform to some local patterns that, in turn, induce certain global characteristics. In this paper, we exploit both local as well as global aspects of social balance theory for two fundamental problems in the analysis of signed networks: sign prediction and clustering. Motivated by local patterns of social balance, we first propose two families of sign prediction methods: measures of social imbalance (MOIs), and supervised learning using high order cycles (HOCs). These methods predict signs of edges based on triangles and \ell-cycles for relatively small values of \ell. Interestingly, by examining measures of social imbalance, we show that the classic Katz measure, which is used widely in unsigned link prediction, actually has a balance theoretic interpretation when applied to signed networks. Furthermore, motivated by the global structure of balanced networks, we propose an effective low rank modeling approach for both sign prediction and clustering. For the low rank modeling approach, we provide theoretical performance guarantees via convex relaxations, scale it up to large problem sizes using a matrix factorization based algorithm, and provide extensive experimental validation including comparisons with local approaches. Our experimental results indicate that, by adopting a more global viewpoint of balance structure, we get significant performance and computational gains in prediction and clustering tasks on signed networks. Our work therefore highlights the usefulness of the global aspect of balance theory for the analysis of signed networks.
Cooperative Medianet Innovation Center, Shanghai Jiao Tong University（上海交通大学协同媒体创新中心）
Node representation learning for signed directed networks has received considerable attention in many real-world applications such as link sign prediction, node classification and node recommendation. The challenge lies in how to adequately encode the complex topological information of the networks. Recent studies mainly focus on preserving the first-order network topology which indicates the closeness relationships of nodes. However, these methods generally fail to capture the high-order topology which indicates the local structures of nodes and serves as an essential characteristic of the ne…
In this paper, we present a novel method for constrained cluster size signed spectral clustering which allows us to subdivide large groups of people based on their relationships. In general, signed clustering only requires K hard clusters and does not constrain the cluster sizes. We extend signed clustering to include cluster size constraints. Using an example of seating assignment, we efficiently find groups of people with high social affinity while mitigating awkward social interaction between people who dislike each other.
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Nokia Research Center (NRC)（诺基亚研究中心）
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of the multi-layer graph for improved clustering of the vertices compared to using layers independently. We propose two novel methods, which are based on joint matrix factorization and graph regularization framework respectively, to efficiently combine the spectrum of the multiple graph layers, namely…
Recent technology and equipment advancements provide with us opportunities to better analyze Alzheimer's disease (AD), where we could collect and employ the data from different image and genetic modalities that may potentially enhance the predictive performance. To perform better clustering in AD analysis, in this paper we propose a novel model to leverage data from all different modalities/views, which can learn the weights of each view adaptively. Different from previous vanilla Non-negative Matrix Factorization which assumes data is linearly separable, we propose a simple yet efficient meth…
Seoul National University（首尔国立大学）；Korea Institute of Energy Technology（韩国能源技术研究院）
Graph contrastive learning has become a powerful technique for several graph mining tasks. It learns discriminative representation from different perspectives of augmented graphs. Ubiquitous in our daily life, singed-directed graphs are the most complex and tricky to analyze among various graph types. That is why singed-directed graph contrastive learning has not been studied much yet, while there are many contrastive studies for unsigned and undirected. Thus, this paper proposes a novel signed-directed graph contrastive learning, SDGCL. It makes two different structurally perturbed graph view…
Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective
School of Computer Science and Engineering（计算机科学与工程学院）；Division of Computer Science and Engineering（计算机科学与工程系）；Yam Pak Charitable Foundation School of Computing and Information Sciences（Yam Pak慈善基金会计算与信息科学学院）；Department of Computer Science（计算机科学系）
本文提出 LoRD 和 B-LoRD 两种低秩双随机聚类模型，仅松弛正交约束并引入块对角正则化，通过将非凸约束转化为线性凸约束，实现全局收敛的投影梯度下降优化，显著提升聚类性能。
University of Oxford（牛津大学）；The Alan Turing Institute（艾伦·图灵研究所）；Queen Mary University of London（伦敦玛丽女王大学）；Delft University of Technology（代尔夫特理工大学）
We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based diffuse interface model formulation utilizing the Ginzburg-Landau functional, based on an adaptation of the classic numerical Merriman-Bence-Osher (MBO) scheme for minimizing such graph-based functionals. The proposed objective function aims to minimize the total weight of inter-…
KTH Royal Institute of Technology（KTH皇家理工学院）；University of Science and Technology of China（中国科学技术大学）
Social networks are often modeled using signed graphs, where vertices correspond to users and edges have a sign that indicates whether an interaction between users was positive or negative. The arising signed graphs typically contain a clear community structure in the sense that the graph can be partitioned into a small number of polarized communities, each defining a sparse cut and indivisible into smaller polarized sub-communities. We provide a local clustering oracle for signed graphs with such a clear community structure, that can answer membership queries, i.e., "Given a vertex $v$, which…
Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clustering
State Key Laboratory for Novel Software Technology, Nanjing University（新型软件技术国家重点实验室，南京大学）；School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Ant Group（蚂蚁集团）；Westlake University（西湖大学）；College of Computer Science and Technology, National University of Defense Technology（国防科技大学计算机科学与技术学院）
We propose a signed network formation game, in which pairs of individuals strategically change the signs of the edges in a complete network. These individuals are members of a social network who strategically reduce cognitive dissonances by changing their interpersonal appraisals. We characterize the best-response dynamics for this game and prove that its implementation \pc{can} dynamically drive the network to a sociologically meaningful sign configuration called clustering balance. In this configuration, agents in the social network form one or more clusters that have positive relationships …
Node embeddings are a powerful tool in the analysis of networks; yet, their full potential for the important task of node clustering has not been fully exploited. In particular, most state-of-the-art methods generating node embeddings of signed networks focus on link sign prediction, and those that pertain to node clustering are usually not graph neural network (GNN) methods. Here, we introduce a novel probabilistic balanced normalized cut loss for training nodes in a GNN framework for semi-supervised signed network clustering, called SSSNET. The method is end-to-end in combining embedding gen…
North China Electric Power University（华北电力大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；Beihang University（北京航空航天大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Community detection is a common task in social network analysis (SNA) with applications in a variety of fields including medicine, criminology, and business. Despite the popularity of community detection, there is no clear consensus on the most effective methodology for signed networks. In this paper, we summarize the development of community detection in signed networks and evaluate current state-of-the-art techniques on several real-world data sets. First, we give a comprehensive background of community detection in signed graphs. Next, we compare various adaptations of the Laplacian matrix …
In order to study real-world systems, many applied works model them through signed graphs, i.e. graphs whose edges are labeled as either positive or negative. Such a graph is considered as structurally balanced when it can be partitioned into a number of modules, such that positive (resp. negative) edges are located inside (resp. in-between) the modules. When it is not the case, authors look for the closest partition to such balance, a problem called Correlation Clustering (CC). Due to the complexity of the CC problem, the standard approach is to find a single optimal partition and stick to it…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Signed networks are such social networks having both positive and negative links. A lot of theories and algorithms have been developed to model such networks (e.g., balance theory). However, previous work mainly focuses on the unipartite signed networks where the nodes have the same type. Signed bipartite networks are different from classical signed networks, which contain two different node sets and signed links between two node sets. Signed bipartite networks can be commonly found in many fields including business, politics, and academics, but have been less studied. In this work, we firstly…
University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）；University of Arkansas（阿肯色大学）
It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we derive theoretical approximations of spectral projections from such directed signed networks using matrix perturbation theory. We use the derived theoretical results to study the influences of negative intra cluster and inter cluster directed edges on node spectral projections. We then develop a spectral clustering based graph partition algorithm, SC-DSG, an…
In this paper, we perform the initial and comprehensive study on the problem of measuring node relevance on signed social networks. We design numerous relevance measurements for signed social networks from both local and global perspectives and investigate the connection between signed relevance measurements, balance theory and signed network properties. Experimental results are conducted to study the effects of signed relevance measurements with four real-world datasets on signed network analysis tasks.
Social networks and interactions in social media involve both positive and negative relationships. Signed graphs capture both types of relationships: positive edges correspond to pairs of "friends", and negative edges to pairs of "foes". The {\em edge sign prediction problem}, which aims to predict whether an interaction between a pair of nodes will be positive or negative, is an important graph mining task for which many heuristics have recently been proposed \cite{leskovec2010predicting,leskovec2010signed}. Motivated by social balance theory, we model the edge sign prediction problem as a no…
In this work, we study the behavior of Brazilian politicians and political parties with the help of clustering algorithms for signed social networks. For this purpose, we extract and analyze a collection of signed networks representing voting sessions of the lower house of Brazilian National Congress. We process all available voting data for the period between 2011 and 2016, by considering voting similarities between members of the Congress to define weighted signed links. The solutions obtained by solving Correlation Clustering (CC) problems are the basis for investigating deputies voting net…
SGA: A Graph Augmentation Method for Signed Graph Neural Networks
Huazhong Agricultural University（华中农业大学）；University of Electronic Science and Technology of China（电子科技大学）；The University of Auckland（奥克兰大学）；Southwest University（西南大学）
Community detection or clustering is a crucial task for understanding the structure of complex systems. In some networks, nodes are permitted to be linked by either "positive" or "negative" edges; such networks are called signed networks. Discovering communities in signed networks is more challenging than that in unsigned networks. In this study, we innovatively develop a non-backtracking matrix of signed networks, theoretically derive a detectability threshold for this matrix, and demonstrate the feasibility of using the matrix for community detection. We further improve the developed matrix …
We empirical study the signs' property in the directed signed social networks of Slashdot and Epinions by using an reshuffled approach. Through calculating the entropy $S_{out}$ and the giant component $G$, we find an interesting 90/10 phenomenon: each individual labels his/her neighbors as friends with $90\%$ or foes with $10\%$ uniformly random from the macroscopic perspective. We also find that the entropy $S_{out}$ is suppressed by the non-randomness of labeling sign. Our present work can prove how do the randomness and the non-randomness coexist in human behavior of labeling signs, qualit…
We introduce a reshuffled approach to empirical analyze signs' organization in real directed signed social networks of Epinions and Slashdots from the global viewpoint. In the reshuffled approach, each negative link has probability $p_{rs}$ to exchange its sign with another positive link chosen randomly. Through calculating the entropies of social status ($S_{in}$ and $S_{out}$) of and mimicking opinion formation of the majority-rule model on each reshuffled signed network, we find that $S_{in}$ and $S_{out}$ reach their own minimum values as well as the magnetization $|m^{*}|$ reaches its max…
We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Positive recommendations follow the standard consensus update while two types of negative recommendations, each modeling a different type of antagonistic or malicious interaction, are considered. Nodes may weigh positive an…
Much recent research on social networks has focused on the modeling and analysis of how opinions evolve as a function of interpersonal relationships. It is also of great interest to model and understand the implications of friendly and antagonistic relationships. In this paper, we propose a new, simple and intuitive model that incorporates the socio-psychological phenomenon of the boomerang effect in opinion dynamics. We establish that, under certain conditions on the structure of the signed network that corresponds to the so-called structural balance property, the opinions in the network pola…
We present an unsupervised model for inducing signed social networks from the content exchanged across network edges. Inference in this model solves three problems simultaneously: (1) identifying the sign of each edge; (2) characterizing the distribution over content for each edge type; (3) estimating weights for triadic features that map to theoretical models such as structural balance. We apply this model to the problem of inducing the social function of address terms, such as 'Madame', 'comrade', and 'dude'. On a dataset of movie scripts, our system obtains a coherent clustering of address …
We study asymptotic dynamical patterns that emerge among a set of nodes interacting in a dynamically evolving signed random network, where positive links carry out standard consensus and negative links induce relative-state flipping. A sequence of deterministic signed graphs define potential node interactions that take place independently. Each node receives a positive recommendation consistent with the standard consensus algorithm from its positive neighbors, and a negative recommendation defined by relative-state flipping from its negative neighbors. After receiving these recommendations, ea…
Mathematical Institute, University of Oxford（牛津大学数学研究所）；The Turing Institute（图灵研究所）；Nordita, Stockholm University and KTH Royal Institute of Technology（北欧理论物理研究所，斯德哥尔摩大学与皇家理工学院）
Link prediction is an open problem in the complex network, which attracts much research interest currently. However, little attention has been paid to the relation between network structure and the performance of prediction methods. In order to fill this vital gap, we try to understand how the network structure affects the performance of link prediction methods in the view of clustering. Our experiments on both synthetic and real-world networks show that as the clustering grows, the precision of these methods could be improved remarkably, while for the sparse and weakly clustered network, they…
In this paper, we consider the problem of assessing local clustering in complex networks. Various definitions for this measure have been proposed for the cases of networks having weighted edges, but less attention has been paid to both weighted and directed networks. We provide a new local clustering coefficient for this kind of networks, starting from those existing in the literature for the weighted and undirected case. Furthermore, we extract from our coefficient four specific components, in order to separately consider different link patterns of triangles. Empirical applications on several…
We take an image science perspective on the problem of determining brain network connectivity given functional activity. But adapting the concept of image resolution to this problem, we provide a new perspective on network partitioning for individual brain parcellation. The typical goal here is to determine densely-interconnected subnetworks within a larger network by choosing the best edges to cut. We instead define these subnetworks as resolution cells, where highly-correlated activity within the cells makes edge weights difficult to determine from the data. Subdividing the resolution estima…
We study the evolution of opinions (or beliefs) over a social network modeled as a signed graph. The sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends (positive links) or enemies (negative links). Pairs of nodes are randomly selected to interact over time, and when two nodes interact, each of them updates its opinion based on the opinion of the other node and the sign of the corresponding link. This model generalizes DeGroot model to account for negative links: when two enemies interact, their opinions go in opposite directions.…
A class of networks are those with both positive and negative links. In this manuscript, we studied the interplay between positive and negative ties on mesoscopic level of these networks, i.e., their community structure. A community is considered as a tightly interconnected group of actors; therefore, it does not borrow any assumption from balance theory and merely uses the well-known assumption in the community detection literature. We found that if one detects the communities based on only positive relations (by ignoring the negative ones), the majority of negative relations are already plac…
Attitudinal Network Graphs are signed graphs where edges capture an expressed opinion; two vertices connected by an edge can be agreeable (positive) or antagonistic (negative). A signed graph is called balanced if each of its cycles includes an even number of negative edges. Balance is often characterized by the frustration index or by finding a single convergent balanced state of network consensus. In this paper, we propose to expand the measures of consensus from a single balanced state associated with the frustration index to the set of nearest balanced states. We introduce the frustration …
We analyse signed networks from the perspective of balance theory which predicts structural balance as a global structure for signed social networks that represent groups of friends and enemies. The scarcity of balanced networks encouraged us to define the notion of partial balance in order to quantify the extent to which a network is balanced. We evaluate several numerical measures of partial balance and recommend using the frustration index, a measure that satisfies key axiomatic properties and allows us to analyse graphs based on their levels of partial balance. The exact algorithms used in…
