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People hold both sorts of emotions-positive and negative against each other. Online social media serves as a platform to show these relationships, whether friendly or unfriendly, like or dislike, agreement or dissension, trust or distrust. These types of interactions lead to the emergence of Signed Social Networks (SSNs) where positive sign represents friend, like, trust, agreement and negative sign represents foe, dislike, distrust and disagreement. Although an immense body of work has been dedicated to the field of social networks; the field of SSNs remains not much explored. This survey first frames the concept of signed networks and offers a brief discourse on the two most prevalent theories of social psychology applied to study them. Then, we address the various state-of-the-art issues which relates the real world scenarios with signed networks. Grounded along the network attributes, this survey talks about the different metrics used to analyze these networks and the real world datasets used for observational purposes. This paper, makes an attempt to follow the contours of research in the area to provide readers with a comprehensive understanding of SSNs elaborating the open research areas.
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Signed Social Networks: A Survey
Nancy Girdhar and K. K. Bharadwaj
School of Computer and Systems Sciences,
Jawaharlal Nehru University, New Delhi-110067, India
{nancy.gr1991, kbharadwaj}
Abstract. People hold both sorts of emotions-positive and negative against each
other. Online social media serves as a platform to show these relationships,
whether friendly or unfriendly, like or dislike, agreement or dissension, trust or
distrust. These types of interactions lead to the emergence of Signed Social
Networks (SSNs) where positive sign represents friend, like, trust, agreement
and negative sign represents foe, dislike, distrust and disagreement. Although
an immense body of work has been dedicated to the field of social networks;
the field of SSNs remains not much explored. This survey first frames the con-
cept of signed networks and offers a brief discourse on the two most prevalent
theories of social psychology applied to study them. Then, we address the vari-
ous state-of-the-art issues which relates the real world scenarios with signed
networks. Grounded along the network attributes, this survey talks about the
different metrics used to analyze these networks and the real world datasets
used for observational purposes. This paper, makes an attempt to follow the
contours of research in the area to provide readers with a comprehensive under-
standing of SSNs elaborating the open research areas.
Keywords: Signed Social Networks, Structural Balance Theory, Status Theory,
Modularity, Frustration
1 Introduction
One of the intrinsic potential benefits of social media is that one can take a deep in-
sight in one’s life as people are using it as a platform to open up with their opinions,
emotions, thoughts and their beliefs on various topics on the web. They can express
their views in various forms by liking or disliking as different people have different
opinions on a particular topic. So, in addition to the concept of trust, support and
friendship, these social interactions can also reflect disagreements and conflicts
among the people on the social media sites. Thus, it is significant to take into consid-
eration the hostile relations (negative links) along with the friendly associations (posi-
tive links) between the users. The social networks having information about the type
of links (positive or negative) among the users besides the links itself are termed as
Signed Social Networks (SSNs).
Although, a plethora of approaches is dedicated for the analysis of social networks
(SNs); however most of them consider these networks as having only friendly (posi-
tive) relationships while ignoring the hostile (negative) ones entirely. The increase in
the number of users on social networking sites as well as information about the posi-
tive and negative relationships among them has driven the researchers towards inves-
tigating the accountabilities of these relationships in the mining of social network
data. Many research works [20], [18] have encountered a significant change in the
nature and complexity of social graph, once the negative links are introduced in the
networks. This lays the foundation for utilizing the negative links in various applica-
tions such as link prediction [19], [21], [28], [30], [33], recommender systems [16],
[29] and community detection [1, 2], [18], [32]. Therefore, these SSNs are recently
grabbing inexorable attention from the research community. This article reviews the
various state-of-the-art issues of SSNs.
The rest of the article is organized as follows: Section 2 gives a brief on the back-
ground details of SSNs. Section 3 describes the state-of-the art and Section 4 discuss-
es the datasets and evaluation metrics used for analyzing signed networks. Finally, the
Section 5 presents some future research directions along with the conclusion.
2 Background
According to Moshirpour [23], Signed Networks are defined as the extension of
networks that include the additional information about positive and negative links.
Signed Social Network: Mathematically, [19] a directed signed social network
represented as signed graph can be defined as  where, is the vertex set
representing nodes of the network, is the edge set that represents the links
of the network and  is a function which assigns  value if
there is a positive link (friend/trust) from node to node ,  is assigned if there is
a negative (foe/distrust) link from node to node and if there is no link between
the two nodes [6].
For example: Let a signed network having users U1U2, U3, U4, U5 is
represented by a directed graph and is the corresponding adjacency matrix as
shown in Fig. 1. Here, a friend (positive) relation is shown with a green color edge
and a foe (negative) relation is represented with a red color edge.
U1 U2 U3 U4 U5
U1   
U2    
U3    
U4  
U5   
Fig. 1. Graphical representation of a Directed SSN
Ignoring the direction of the signed links, the network can be converted into undi-
rected network assuming the links between the nodes as bidirectional and thus, the
adjacency matrix representation of the undirected network will be symmetric in na-
2.1 Theories of Signed Networks
To analyze these online SSNs there are two different theories [20]. A brief descrip-
tion of each of these theories is given as follows
Structural Balance Theory is the fundamental theory formulated by Heider in
1946 [14]. Based on the concept of Friend-of-a-Friend (FOAF), this theory is a no-
tion to understand the structure, cause of tensions and conflicts between the two sen-
timents (positive and negative) in a network of actors (users). Further, Cartwright and
Harrary in 1956 [5] modeled it in terms of signed graphs. This theory rests on the
assumption that certain configurations of positive and negative edges are socially
more probable than others. Ignoring the identities of the actors, four configurations
are possible: “my friend’s friend is my friend”, “my friend’s enemy is my enemy”,
“my enemy’s friend is my enemy”, “my enemy’s enemy is my friend”.
According to the structural balance theory, a balanced triad is one with either one
or three positive links (i.e., odd number of positive links) among three people. In Fig.
2, the first two triads are balanced as they have an odd number of positive links while
later two are unbalanced as they have even number of positive links. This theory is
pertinent on undirected networks only.
Fig. 2. Various Configurations of Social Triads
Social Status Theory suggested by Guha et al., [12] and further developed by Lesko-
vec et al., [20] proposes to use status of a person as the factor to decide whether a
person will make a link (positive or negative) with another person in the network.
Status can be in terms of social status (popularity, fame) or it can be economical sta-
tus (money, power). Pagerank is one of the most popular ways to calculate status
score in social networks.
According to this theory, if individual (creator) makes a positive link to individ-
ual (recipient), then believes that has higher status than him, whereas a nega-
tive link originated from individual to indicates that considers status of  low-
er than him. It is evident that the status theory is more suitable for directed networks.
To check whether triads of a network satisfy status theory, take each negative link in a
triad, inverse its direction and the flip the sign of the link (positive sign) then the re-
sultant triad should be acyclic in nature.
Computation of Status of a node: The status of a node in a directed network
can be computed [19] as follows:
 (1)
where, 
and 
 denotes the number of positive and negative links re-
ceived by the node from other nodes in the network respectively. Similarly, 
and 
 is the number of positive and negative links generated by the node in
the network, respectively.
Balance Theory vs Status Theory: In order to sense the difference between bal-
ance theory and status theory, assume the case that node connects negatively to
node , further node connects negatively to node . Now what will be the sign of
the link connecting node to node ? Considering balance theory’s configuration
“My enemy’s enemy is my friend”, predicts the sign of the link between and as
positive, whereas, the status theory predicts the sign of the link from to as nega-
tive. In other words, the result of balance theory differs from the results of status theo-
ry in this case.
3 State-of the-art
Link Prediction in SSNs: Traditional link prediction approaches used for social
networks are massively based on the concept of “friendship”. Thus, neglecting the
other side of relationships viz., antagonism. Users in these networks find it difficult to
decide among the people they trust from those they don’t. Thus, they find it vague and
obscure to distinguish between a friend and an acquaintance [4], [33]. Therefore,
these approaches are not well suitable for analyzing and predicting links in SSNs.
Recently, researchers have begun to investigate on how to turn an unsigned ac-
quaintances network into signed trust/distrust network [19], [30], [33]. A variety of
available networks like Epinions, Slashdot, Wikipedia etc. have also started labeling
links explicitly either as friend/foe [17] or trust/distrust [11], [26]. A number of theo-
ries in sociology [3], [20] provide deeper insight into the fundamental principles
which explain how the patterns of negative and positive links resulted into different
kinds of relationships. According to structural balance theory [5], [14], people in
signed networks [12], [20] tend to follow the notion of FOAF whereas, status theory
is based on the concept of social status which people possess in a society.
Thus, the sign inference problem, which aims to infer the unknown relationship be-
tween two entities, can be achieved by learning from balance or status information of
signed networks.
Community Detection (CD) in a social network is identification of set of nodes
that are more densely connected to each other than to the rest of the network [2], [24].
Different approaches in the literature are proposed to tackle the problem of com-
munity detection in social networks. Some traditional clustering algorithms assume
communities as disjoint structure, where as some approaches assume communities as
overlapping structures in the real-world networks [18]. Graph partitioning algorithms
[8], hierarchical clustering algorithms [18] have also been used for CD in social net-
works etc. As CD in signed social networks is a bit different from the CD in social
networks, its definition should take into account the extra information about the type
of links among the users besides the links itself which is stated as follows:
Community Detection in SSNs attempts to partition the network in such a way
that each partition should have dense positive intra-connections and sparse negative
intra-connections. One way to do such optimization is by using the concept of modu-
larity introduced by Newman [24].
Trust, Distrust and Reputation in Community Detection: In recent few years a
lot of work is done on trust and reputation. Trust and distrust are personal characteris-
tics while reputation is a public characteristic of a person/organization. Trust and
reputation are very necessary components in real world social networks and these are
incorporated in most of the domains like recommender systems [16], [26], e-learning,
e-commerce, semantic web and so on.
Recently, researchers have begun to scrutinize on how to transform an unsigned
social network into signed trust/distrust network [12], [19], [30], [33]. A variety of
existing networks have also started tagging links explicitly either as friend/foe [17] or
trust/distrust [12] (like Epinions, Slashdot, Wikipedia). To bring any online model or
network more near to the physical world, it is inevitable to incorporate trust and repu-
tation in it.
Social Recommender Systems: The principle intent of Social Recommender Sys-
tems (SRSs) is to ease information overload over social media users by delivering the
most attractive and relevant content/items they are looking for. SRSs that suggest
content, people and communities often used personalization techniques [7] to adapt
the needs and interests of an individual user or a group of users. There is a lot of work
done both in industry and academia for developing new approaches in recommender
systems over the last decade.
In SSNs, not only the information about the relationships, but also the type of rela-
tionships are given which can be used to make better recommender systems than ex-
isting as it will be easy to recommend things to a group of people having similar lik-
4 Datasets and Evaluation Metrics used for Signed Networks
In this section we have provided a list of publicly available real world signed da-
tasets and benchmark datasets used for observational purposes:
4.1 Datasets
website which is a “who-trust-whom” online social network of a general
consumer review site on which users can post reviews about the various products
and services. The rating of reviews is done on the scale of 1 to 5 by different review-
ers who label them by like/dislike based on their trust/distrust on the review.
is a tech-based news website which enables users to tag other users as
friends” or foes”. On this site, users can also tag other users negatively. Here, a
friend tag is considered as a positive link and a foe tag is considered as a negative
network is an adminship election dataset in which users cast their votes
to promote individuals for admin post. A positive vote is considered as a positive
link and a negative vote is viewed as a negative link.
Slovene Parliamentary Party Network [10] represents the relations among 10 po-
litical parties of Slovene Parliamentary. The weights on the links assessed are based
on the scale of -3 to +3, where the positive and negative weight shows similarity and
dissimilarity between the pair of parties respectively.
Gahuku-Gama Subtribes Network [27] describes the positive and negative alli-
ances among 16 Gahuku-Gama Subtribes. Since, it is an unsigned network, which
can be converted by assuming links between same community as positive and be-
tween different communities as negative.
Table 1. shows the different datasets that are used for analysis of SSNs.
Table 1. Description of the datasets.
Slovene Parlia-
mentary Party
Ground Truth Available
Used in articles
[19], [20]
[19], [20]
[19], [20]
[1], [32]
4.2 Evaluation metrics for SSNs
Let a signed network  be partitioned into communities
 and is the adjacency matrix corresponding toie., 
Given a node , and  are the positive and the negative degrees of
node respectively.
Modularity [24] measures how good the partition of the network is, by taking into
account the degree distribution. In signed networks, a division of the network should
be done such that it takes into account the contribution of binary links (positive or
negative links) available among the nodes in the network. Thus, modified definition
of modularity [1, 2], [18] is given by the equation (2).
  (2)
when both the nodes and belong to the same community
else and denotes the community to which the node belongs.
For signed overlapping communities, is the number of communities which in-
clude vertex , modularity  [22] is computed as given in the equation (3).
  (3)
Frustration [8] measures the unstability in the network. Frustration is the sum of
number of inter-positive links between the communities and the number of intra-
negative links within the [1, 2] communities which is given in the equation (4).
 (4)
Frustration implies mutually antagonistic or hostile groups with few imbalances.
Therefore, to detect communities frustration minimization can serve as an objective
function [1, 2].
Social Balance Factor: To determine whether a network is structurally balanced or
not, social balance factor () [25] can be used. A network with number of balanced
triads and total number of triads given by  and  respectively, the social
balance factor of the network is computed as follows:
 (5)
Error Rate: It is based on the concept of frustration, which is used to measure the
partitioning quality of a signed network. The error rate of a partition can be defined
[1], [32] as follows:
 (6)
where,  is defined in equation (4). It is obvious that the smaller the value of
the better will be the partition quality.
5 Conclusion and Future Challenges
In this paper, we presented a survey of Signed Social Networks (SSNs) and dis-
cussed trends and perspectives of further research. We have discussed signed network
theories and different metrics used to analyze and evaluate these networks. Signed
networks mimic the real world scenarios, grabbing the attention of many researchers
and thus emerging as a popular research field. There are many research challenges
which are yet to be addressed in this area. Some of them are briefly listed as follows:
It would be interesting to integrate users’ tastes and their trusted friends’ into col-
laborative filtering techniques for more accurate recommendations [7], [15].
The role of positive and negative links in online settings can be exploited in the
field of community detection to discover overlapping communities, hierarchical
structures and analysis of time evolving communities which are not yet much ex-
plored in the context of SSNs [6], [15], [19], [22].
Fusion of trust-distrust and trust-reputation mechanisms into formulation of tech-
niques can enhance the strength and effectiveness of the schemes for SSNs [9],
[11, 12], [31].
Although, a lot of work is done in the field of link prediction, but monolithically
considering links as positive [21], which is far from the case of real world net-
works as they consist of negative links too. So, development of new procedures to
identify relevant parameters for link prediction using the information obtained
from the SSNs could be a future research direction [19], [25], [28], [33].
Other promising research direction would be incorporation of trust in recommender
systems and utilization of trust inference mechanism in sparse SSNs to handle the
sparsity problem [26], [28].
Discovering new schemes for similarity computation between various profile fea-
tures in SSNs and incorporation of social trust and reputation for quality social
recommendations [26], [28].
Information entropy describes the uncertainty associated with a given probability
distribution. The applications of entropy concept in complex networks are widely
and deeply applied. Nevertheless, the application of entropy in signed networks is
currently limited and challenged [13].
Percolation is one of the best studied processes in statistical physics and serves as a
conceptual framework to treat more factual problems such as collective behavior,
robustness of networks. This concept is still very less dealt in the view of signed
networks [13].
Along with the positive and content-centric interactions, the user generated content
is pervasively available in social media that can be used to investigate, whether us-
er generated content is useful and can be helpful in negative link prediction prob-
lem [30].
Both the theories, social balance and status are applicable only when a link partici-
pates in some triads, which is not always true in the case of real world networks
which are sparse and links may or may not participate in the triads [15]. Hence, the
prediction accuracy will be compromised in these cases. Thus, new psychology so-
cial theories like Emotional Information, Diffusion of Innovations and Individual
Personality could be very helpful for studying the problem of signed link formation
Another interesting research direction is to study link analysis in dynamic signed
networks by deploying the social theories [3].
Due to the dearth of publicly available datasets with ground truth information it is
difficult to analyze and comprehend the performance of various algorithms on
SSNs for different tasks [15]. Furthermore, the signed directed dataset having inte-
gration of users attributes with links is also not available. Thus, the focus of re-
search community can also be concentrated on development such datasets.
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... According to this, a triad is said to be balanced if it has odd number of positive links (either one or three positive links). Thus, social balance factor (SBF) is the ratio of number of balanced triads to the number of total triads in the network (Adamic and Adar 2003;Girdhar and Bharadwaj 2016;Patidar et al. 2012). ...
... Being the fundamental research field of social networks, link prediction continues to enthrall the research community. Numerous such efforts focus on the problem of missing links and to tackle the problem of sparsity in signed social networks (Girdhar and Bharadwaj 2016;Leskovec et al. 2010b;Patidar et al. 2012;Tang et al. 2015;Yang et al. 2012). Several methodologies and mathematical models (Backstrom and Leskovec 2011;Fire et al. 2013;Gong et al. 2011;Kleinberg 2002;Quercia and Capra 2009) have been developed to show how people interact with one another and establish link in social networks. ...
... This section illustrates the details of datasets used for experimental setup and metrics used to evaluate the performance of the proposed models. Further, it describes various experiments conducted on benchmarked synthetic dataset of friends and foes network (FFN) (Patidar et al. 2012) as well as real-world datasets of Epinions (Girdhar and Bharadwaj 2016) and Slashdot (Girdhar and Bharadwaj 2016) to study the performance of our proposed scheme. We have study the effectiveness of our proposed models with respect to the following baseline technique. ...
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Signed social networks are those in which users of the networks are connected with some interdependencies such as agreement/disagreement, liking/disliking, friends/foes, loving/despising, and companions/enemies. Most individuals in signed social networks have many relations in terms of friends, foes, following and followers. All these relations are usually asymmetric and subjective, thus difficult to predict. To resolve the fundamental problem of sparsity in the networks, substantial amount of research work has been dedicated to link prediction; however, very little work deals with the antagonistic behavior of the users while considering the asymmetric and domain-dependent nature of links. This paper is based on the concept that All Relations Are Not Equal and some relations are stronger than other relations. For instance some friends may be acquaintances of an individual, whereas another may be friends who care about him/her. In this paper, a fuzzy computational model is proposed based on trust and distrust, as a decision support tool that dissects relevant and reliable information of the users to distinguish the stronger relations from the weaker ones. Further, we have proposed two different link prediction models based on local information and local–global information to overcome the problem of sparsity in signed social networks. An extensive experimental study is performed on benchmarked synthetic dataset of friends and foes network and publicly available real-world datasets of Epinions and Slashdot. The results obtained are promising and establish the efficacy of our proposed models.
... In signed networks besides the information about the link density, we have information about the type of links also. CD in SSNs can be defined as the partition of the network into communities such that it has dense positive intracommunity connections and negative inter-community connections (Girdhar & Bharadwaj, 2016). ...
... Frustration can be defined as the sum of the number of positive links between different communities and negative links within the community. Based on the structural balance theory, the links constituting the unbalanced triads contributes to frustration, resulting in instability of whole network (Girdhar & Bharadwaj, 2016;Leskovec, Huttenlocher, & Kleinberg 2010). ...
... Social Balance Factor According to structural balance theory, a triad is structurally balanced if the number of positive edges in the triad is odd (1-configuration and 3-configuration) as shown in Figure 1. For a network to be balanced, it should be divided into two clusters such that all the positive links lies within a cluster and the negative links lies between the clusters (Girdhar & Bharadwaj, 2016). Thus, to find whether a network is structurally balanced, we have to compute the social balance factor. ...
Clustering of like‐minded users is basically the goal of community detection (CD) in social networks and many researchers have proposed different algorithms for the same. In signed social networks (SSNs) where type of link is also considered besides the links itself, CD aims to partition the network in such a way to have less positive inter‐connections and less negative intra‐connections among communities. So, approaches used for CD in unsigned networks do not perform well when directly applied on signed networks. Most of the CD algorithms are based on single objective optimization criteria of optimizing modularity which focuses only on link density without considering the type of links existing in the network. In this work, a multiobjective approach for CD in SSNs is proposed considering both the link density as well as the sign of links. Precisely we are developing a method using modularity, frustration and social balance factor as multiple objectives to be optimized (M‐F‐SBF model). NSGA‐II algorithm is used to maintain elitism and diversity in the solutions. Experiments are performed on both existing benchmarked and real‐world datasets show that our approach has led to better solutions, clearly indicating the effectiveness of our proposed M‐F‐SBF model.
... Social media sites owe their phenomenal success and popularity largely to the billions of users of these sites that grabbed the attention of many researchers to examine social media phenomenon and its role in contemporary society. Sharing information (photos, videos, texts) on social networks has become a trend now, making these social networks common venue of crowdsourcing, folksonomy and user-generated content [9]. Despite the users' friendly kinship, the fingerprints of users' antagonistic behavior cannot be denied in social networks, thereby social networks are not untouched with hostile relations shown by users towards other users in the form of dislike, poor ratings and negative comments etc. ...
... Despite the users' friendly kinship, the fingerprints of users' antagonistic behavior cannot be denied in social networks, thereby social networks are not untouched with hostile relations shown by users towards other users in the form of dislike, poor ratings and negative comments etc. These positive and negative interactions among users of these networks directed to the advent of Signed Social Networks (SSNs) comprised of both types of relationships: friendly and hostile [9,15]. Friendly (positive) and hostile (negative) relations are symbolized with +1 and −1 respectively, annotated on the links between users in the network. ...
... Step 3: Fitness Function is used to quantify the quality of solutions produced by genetic algorithm and to direct its focus to produce optimal solutions. For computation Objective Function1: Status of a node in the network can be defined as the sum of degrees of positive incoming links deg þ in and negative outgoing links deg À out of the node minus the sum of degrees of positive outgoing links deg þ out and negative incoming links deg À in of the node [9], given by Eq. (1). ...
... The sentiments such as friends or foes, agreements or disagreements, likes or dislikes, trust or distrust, group joining or departing, and so on can be bi-categorized into positive connections such as friends, agreements, or likes and negative connections such as foes, disagreements, or dislikes. Such interactions yield to the development of Signed Social Networks (SSNs) [11], [12]. Certainly, SM signed networks are noisy and sparse usually with a massive number of users and multitudes of relationships. ...
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Deep learning (DL) has attracted increasing attention on account of its significant processing power in tasks, such as speech, image, or text processing. In order to the exponential development and widespread availability of digital social media (SM), analyzing these data using traditional tools and technologies is tough or even intractable. DL is found as an appropriate solution to this problem. In this paper, we keenly discuss the practiced DL architectures by presenting a taxonomy-oriented summary, following the major efforts made toward the SM analytics (SMA). Nevertheless, instead of the technical description, this paper emphasis on describing the SMA-oriented problems with the DL-based solutions. To this end, we also highlight the DL research challenges (such as scalability, heterogeneity, and multimodality) and future trends. INDEX TERMS Social media data, dynamic network, deep learning, feature learning.
... These kinds of relationships give rise to the appearance of signed social networks (SSNs) in which positive sign means like a friend, trust, and negative sign presents dislike, rival, and distrust. 29 That is, social networks contain information regarding the positive links or negative links that highly influence the establishment of the future structure of the network. However, most of the social webs considered as possessing only friendly (positive) relationships, whereas neglecting the hostile (negative) ones entirely. ...
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Social network analysis (SNA) has attracted a lot of attention in several domains in the past decades. It can be of 2‐folds: one is content‐based, and another one is structured‐based analysis. Link prediction is one of the emerging research problems, which comes under structured‐based analysis that deals with predicting the missing link, which is likely to appear in the future. In this article, the supervised machine learning techniques have been implemented to predict the possibilities of establishing the links in future. The major contribution in this article lies in feature construction from the topological structure of the network. Several structured‐based similarity measures have been considered for preparing the feature vector for each nonexisting links in the network. The performance of the proposed algorithm has been extensively validated by comparing with other link prediction algorithms using both real‐world and synthetic data sets.
An important aspect of social networks is to enable people to express their bias. Modelling this behaviour in the form of sentiment links results in a network topology commonly referred to as a signed network. Contemporary work in the signed network domain suggests that negative links can play a key role in signed link analysis. However, signed networks suffer with the data sparseness problem as there is little proportion of signed links in the complete network. The complexity of the problem increases as negative links are much more infrequent than positive ones, indicating that majority of users are more prone towards positive temperament instead of negative one. In this research, we focus on the challenges associated with signed link analysis and address the negative link prediction problem. We introduce a set of ensembles which exploits the hidden interactions of communities and scales up the negative link prediction task in a signed network. Using a scalable embedding framework, network representation is learned, which is given to a set of ensembles for the prediction of negative links. Robustness and efficiency of the approach are tested through experiments conducted on real-life signed network datasets.
With the ever-increasing popularity of social software, we can easily establish a signed social network (SSN) by capturing users’ attitudes (i.e., trust/distrust, friend/enemies, consent/opposition) toward other people. However, the social relationships among users are often very sparse in an SSN, which impede the effective extension of the users’ social circle significantly. To tackle this issue, researchers often use link prediction methods to search for missing links and predict new links in the network. However, existing link prediction methods cannot protect user’s private information well. Considering this shortcoming, we propose a Simhash-based link prediction method with privacy-preservation. Concretely, we first apply Simhash to build less-sensitive user indices and then determine the ”probably similar” friends (i.e., candidates) of a target user based on his or her indices. Through theoretical analysis, it can be known that the method proposed in this paper can effectively protect users’ proprietary information. Second, for each candidate, we calculate his/her trust and distrust values with the target user. Third, we use Social Balance Theory to evaluate the possibility of building a link between the candidate and the target user based on the trust and distrust values. Finally, we conducted a set of experiments on the real-world Epinions dataset. Experimental results prove the advantages of our proposal in terms of overcoming the sparsity problem, compared to other competitive approaches.
The formation of public opinion on the network is a hot issue in the field of complex network research, and some classical dynamic models are used to solve this problem. The signed network is a particular form of the complex network, which can adequately describe the amicable and hostile relationships in complex real-world systems. However, the methods for studying the dynamic process of public opinion propagation on signed networks still require to be further discussed. In this paper, the authors pay attention to the influence of negative edges in order to design a two-state public opinion propagation mechanism suitable for signed networks. The authors first set the interaction rules between nodes and the transition rules of node states and then apply the model to synthetic and real-world signed networks. The simulation results show that there is a critical value of the negative edge ratio. When the negative edge ratio exceeds this critical value, the evolutionary result of public opinion will change from a consistent state to a split state. This conclusion is also consistent with the distribution result of opinions within communities in the signed network. Besides, the research on the network structural balance shows that the model makes the network evolve in a more balanced direction.
A wide range of data science problems can be modeled in terms of a graph (or network), e.g., social, sensor, communication, infrastructure, and biological networks. The nodes in a graph/network represent the entities of interest, and the edges reflect relations between these entities, such as geographic proximity (e.g., wireless networks), social relations (e.g., Facebook), biological mechanisms (e.g., brain networks), similarity (e.g., texts by identical authors), and statistical dependencies (e.g., gene expression data). Graph signal processing (GSP) advocates the use of graphs as combined data and computation models and has become a groundbreaking and powerful paradigm for solving diverse learning and inference tasks in the area of data science. GSP uses tools from linear algebra, (spectral) graph theory, computational harmonic analysis, and optimization theory to extend conventional signal processing concepts to data located on irregular domains that are characterized by graphs (networks). For entry-level expositions of GSP fundamentals and the relevant state of the art, we refer to [1]-[4] and the May 2018 Proceedings of the IEEE.
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In the problem of edge sign classification, we are given a directed graph (representing an online social network), and our task is to predict the binary labels of the edges (i.e., the positive or negative nature of the social relationships). Many successful heuristics for this problem are based on the troll-trust features, estimating on each node the fraction of outgoing and incoming positive edges. We show that these heuristics can be understood, and rigorously analyzed, as approximators to the Bayes optimal classifier for a simple probabilistic model of the edge labels. We then show that the maximum likelihood estimator of this model approximately corresponds to the predictions of a label propagation algorithm run on a transformed version of the original social graph. Extensive experiments on a number of real-world datasets show that this algorithm is competitive against state-of-the-art classifiers in terms of both prediction performance and scalability. Finally, we show that troll-trust features can also be used to derive online learning algorithms which have theoretical guarantees even when edges are adversarially labeled.
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Numerous real-world relations can be represented by signed networks with positive links (e.g., trust) and negative links (e.g., distrust). Link analysis plays a crucial role in understanding the link formation and can advance various tasks in social network analysis such as link prediction. The majority of existing works on link analysis have focused on unsigned social networks. The existence of negative links determines that properties and principles of signed networks are substantially distinct from those of unsigned networks, thus we need dedicated efforts on link analysis in signed social networks. In this paper, following social theories in link analysis in unsigned networks, we adopt three social science theories, namely Emotional Information, Diffusion of Innovations and Individual Personality, to guide the task of link analysis in signed networks.
We propose Shapley Value based centrality measures for signed social networks. We also demonstrate that they lead to improved precision for the troll detection task.
Conference Paper
Recommender systems play a crucial role in mitigating the information overload problem in social media by suggesting relevant information to users. The popularity of pervasively available social activities for social media users has encouraged a large body of literature on exploiting social networks for recommendation. The vast majority of these systems focus on unsigned social networks (or social networks with only positive links), while little work exists for signed social networks (or social networks with positive and negative links). The availability of negative links in signed social networks presents both challenges and opportunities in the recommendation process. We provide a principled and mathematical approach to exploit signed social networks for recommendation, and propose a model, RecSSN, to leverage positive and negative links in signed social networks. Empirical results on real-world datasets demonstrate the effectiveness of the proposed framework. We also perform further experiments to explicitly understand the effect of signed networks in RecSSN.
Recommendation on signed social rating networks is studied through an innovative approach. Bayesian probabilistic modeling is used to postulate a realistic generative process, wherein user and item interactions are explained by latent factors, whose relevance varies within the underlying network organization into user communities and item groups. Approximate posterior inference captures distrust propagation and drives Gibbs sampling to allow rating and (dis)trust prediction for recommendation along with the unsupervised exploratory analysis of network organization. Comparative experiments reveal the superiority of our approach in rating and link prediction on Epinionsand Ciao, besides community quality and recommendation sensitivity to network organization.
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 maximum value at $p_{rs}=0$. Namely, individuals share the homogeneous properties of social status and dynamic status in real directed signed social networks. Our present work provides some interesting tools and perspective to understand the signs' organization in signed social networks.
Conference Paper
Signed social networks have become increasingly important in recent years because of the ability to model trust-based relationships in review sites like Slashdot, Epinions, and Wikipedia. As a result, many traditional network mining problems have been re-visited in the context of networks in which signs are associated with the links. Examples of such problems include community detection, link prediction, and low rank approximation. In this paper, we will examine the problem of ranking nodes in signed networks. In particular, we will design a ranking model, which has a clear physical interpretation in terms of the sign of the edges in the network. Specifically, we propose the Troll-Trust model that models the probability of trustworthiness of individual data sources as an interpretation for the underlying ranking values. We will show the advantages of this approach over a variety of baselines.