You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Community detection on social media has attracted considerable attention for many years. However, existing methods do not reveal the relations between communities. Communities can form alliances or engage in antagonisms due to various factors, e.g., shared or conflicting goals and values. Uncovering such relations can provide better insights to understand communities and the structure of social media. According to social science findings, the attitudes that members from different communities express towards each other are largely shaped by their community membership. Hence, we hypothesize that inter-community attitudes expressed among users in social media have the potential to reflect their inter-community relations. Therefore, we first validate this hypothesis in the context of social media. Then, inspired by the hypothesis, we develop a framework to detect communities and their relations by jointly modeling users' attitudes and social interactions. We present experimental results using three real-world social media datasets to demonstrate the efficacy of our framework.

Cited Abstract(s):
[1]: 

[2]: Social networks provide a wealth of data to study relationship dynamics among people. Most social networks such as Epinions and Facebook allow users to declare trusts or friendships with other users. Some of them also allow users to declare distrusts or negative relationships. When both positive and negative links co-exist in a network, some interesting community structures can be studied. In this work, we mine Direct Antagonistic Communities (DACs) within such signed networks. Each DAC consists of two sub-communities with positive relationships among members of each sub-community, and negative relationships among members of the other sub-community. Identifying direct antagonistic communities is an important step to understand the nature of the formation, dissolution, and evolution of such communities. Knowledge about antagonistic communities allows us to better understand and explain behaviors of users in the communities. Identifying DACs from a large signed network is however challenging as various combinations of user sets, which is very large in number, need to be checked. We propose an efficient data mining solution that leverages the properties of DACs, and combines the identification of strongest connected components and bi-clique mining. We have experimented our approach on synthetic, myGamma, and Epinions datasets to showcase the efficiency and utility of our proposed approach. We show that we can mine DACs in less than 15min from a signed network of myGamma, which is a mobile social networking site, consisting of 600,000 members and 8million links. An investigation on the behavior of users participating in DACs shows that antagonism significantly affects the way people behave and interact with one another.

[3]: Many networks can be modeled as signed graphs. These include social networks, and relationships interactions networks. Detecting sub-structures in such networks helps us understand user behavior, predict links, and recommend products. In this paper, we detect dense sub-structures from a signed graph, called quasi antagonistic communities (QACs). An antagonistic community consists of two groups of users expressing positive relationships within each group but negative relationships across groups. Instead of requiring complete set of negative links across its groups, a QAC allows a small number of inter-group negative links to be missing. We propose an algorithm, Mascot, to find all maximal quasi antagonistic communities (MQACs). Mascot consists of two stages: pruning and enumeration stages. Based on the properties of QAC, we propose four pruning rules to reduce the size of candidate graphs in the pruning stage. We use an enumeration tree to enumerate all strongly connected subgraphs in a top---down fashion in the second stage before they are used to construct MQACs. We have conducted extensive experiments using synthetic signed graphs and two real networks to demonstrate the efficiency and accuracy of the Mascot algorithm. We have also found that detecting MQACs helps us to predict the signs of links.

[4]: Given a signed network where edges are weighted in real number, and positive weights indicate cohesion between vertices and negative weights indicate opposition, we are interested in finding k-Oppositive Cohesive Groups (k-OCG). Each k-OCG is a group of k subgraphs such that (1) the edges within each subgraph are dense and cohesive; and (2) the edges crossing different subgraphs are dense and oppositive. Finding k-OCGs is challenging since the subgraphs are often small, there are multiple k-OCGs in a large signed network, and many existing dense subgraph extraction methods cannot handle edges of two signs. We model k-OCG finding task as a quadratic optimization problem. However, the classical Proximal Gradient method is very costly since it has to use the entire adjacency matrix, which is huge on large networks. Thus, we develop FOCG, an algorithm that is two orders of magnitudes faster than the Proximal Gradient method. The main idea is to only search in small subgraphs and thus avoids using a major portion of the adjacency matrix. Our experimental results on synthetic and real data sets as well as a case study clearly demonstrate the effectiveness and efficiency of our method.

[5]: There has been a recent increase of interest in analyzing trust and friendship networks to gain insights about relationship dynamics among users. Many sites such as Epinions, Facebook, and other social networking sites allow users to declare trusts or friendships between different members of the community. In this work, we are interested in extracting direct antagonistic communities (DACs) within a rich trust network involving trusts and distrusts. Each DAC is formed by two subcommunities with trust relationships among members of each sub-community but distrust relationships across the sub-communities. We develop an efficient algorithm that could analyze large trust networks leveraging the unique property of direct antagonistic community. We have experimented with synthetic and real data-sets (myGamma and Epinions) to demonstrate the scalability of our proposed solution.

[6]: During social interactions in a community, there are often sub-communities that behave in opposite manner. These antagonistic sub-communities could represent groups of people with opposite tastes, factions within a community distrusting one another, etc. Taking as input a set of interactions within a community, we develop a novel pattern mining approach that extracts for a set of antagonistic sub-communities. In particular, based on a set of user specified thresholds, we extract a set of pairs of sub-communities that behave in opposite ways with one another. To prevent a blow up in these set of pairs, we focus on extracting a compact lossless representation based on the concept of closed patterns. To test the scalability of our approach, we built a synthetic data generator and experimented on the scalability of the algorithm when the size of the dataset and mining parameters are varied. Case studies on an Amazon book rating dataset show the efficiency of our approach and the utility of our technique in extracting interesting information on antagonistic sub-communities.
Although there has been a great deal of efforts to detect communities, to the best of our knowledge, no previous work has been proposed to uncover the existence of antagonism and alliance between communities. However, some efforts have been made [4] [3] [2] [2]0 [1] [6] to detect only antagonistic communities. These methods can be roughly divided into two main categories. First category includes the methods [1] [6] utilizing frequent patterns in users' ratings to mine antagonistic communities. Second category includes the methods [4] [3] [2] [2]0 utilizing signed networks, having trust and distrust links, to detect antagonistic communities. A majority of these methods [3] [2] [2]0 detect a pair of subgraphs with most trust links preserved between the members of each subgraph and most distrust links remained between the members of different subgraphs. These methods are limited to detecting only a pair of antagonistic communities. To address this limitation, another method [4] has been proposed to detect multiple antagonistic communities by finding several dense subgraphs with the mentioned property. However, as experiments in [4] show such methods usually end up with large number of small subgraphs due to high sparsity of users' interactions in social media.