1. Introduction
The rapid growth of social media has led to an increased amount of user generated data and accordingly the impediment of finding reliable information (Beigi and Liu, 2018a; Alvari et al., 2018). Positive links (e.g., trust and friendship relations) play an important role in helping online users find relevant and credible information (Tang et al., 2013). They have also been demonstrated to benefit many social media applications including recommendation and information filtering (Xin et al., 2009; Beigi and Liu, 2018b). Similarly, negative links could help decision makers reduce uncertainty and vulnerability associated with decision consequences (Cho, 2006; Hardin, 2004; Larson and Hardin, 2004; McKnight and Chervany, 2001)
. Therefore, signed link prediction without negative links may result in a biased estimate of the effect of positive links
(Tang et al., 2014a). Thus it is sensible to investigate both positive and negative links together in signed link prediction.The problem of signed link prediction aims at inferring new positive/negative relations by leveraging existing ones. In recent years, the majority of the existing algorithms (Chiang et al., 2011; Leskovec et al., 2010) use the topological structures and the properties of the existing signed links to make predictions. However, the available explicit positive links are often sparse and follow powerlaw distributions (Tang et al., 2013). The signed data sparsity problem gets worse as social media users tend to reveal more their positive disposition than their negative one; thus, negative links are often much sparser than positive links in a signed social network. To make a better signed link predictor, we need to overcome the data sparsity problem of the signed links.
As suggested by psychologists (Asendorpf and Wilpers, 1998; Burt et al., 1998), user’s optimism and pessimism are important factors that determine her propensity in establishing the positive/negative social relations. According to Scheier et. al. (Scheier and Carver, 1985), a person is defined as optimist when she is more likely to reinterpret negative events in a positive way and find meaning and growth in stressful situations. On the other hand, an individual is referred to as pessimist when she is preoccupied only with the negative aspects of the environment and overlooks the positive aspects (Scheier and Carver, 1985). For example, optimistic users have better social functioning and relations. Therefore, they actively pursue social relationships and have higher chances in establishing positive links resulting in longer lasting friendships (Geers et al., 1998; Scheier and Carver, 1985). In contrast, pessimists likely practice in the opposite way, i.e., having negative attitudes and expecting the worst of people and situations. Consequently, they often establish negative links with others (Geers et al., 1998; Scheier et al., 2001). People’s personal traits can be observed on social media and serve as a good indicator of their personality (Golbeck et al., 2011). This is because (1) social media websites allow for free interaction and open exchange of viewpoints, and (2) social media data can be aggregated to establish normative behavior of individuals. Previous research (Beigi et al., 2016a) has shown the correlation between users’ personality information and positive/negative links in social networks. In particular it shows that:

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Users with high optimistic behavior are more likely to establish and receive positive links than those with low optimism.

Users who are more pessimistic are more likely to establish and receive negative links than those with low level of pessimism.
These findings are in line with psychology research (Geers et al., 1998; Scheier et al., 2001; Scheier and Carver, 1985) and also suggest that user’s personality, i.e., optimism and pessimism, may have potentials to alleviate the signed link data sparsity problem and improve the performance of signed link prediction. We use optimism and pessimism as a representative aspect of personality.
Although previous research (Beigi et al., 2016a) has taken the first steps to study the correlation between users’ personality and positive/negative links in signed social networks, it is still unclear how such information could be modeled mathematically and incorporated for predicting the positive and negative links, whether the information could help solving signed link data sparsity problem and what the impact of personality information is on signed link prediction problem. In this paper, we study the problem of signed link prediction by exploiting personality information, in particular, users’ optimism and pessimism. In particular, we investigate how to leverage such information for positive and negative link prediction, and then we propose a novel signed link prediction framework SLP. Our main contributions are as follows:

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Provide a principled way to model optimism and pessimism information mathematically;

Propose the framework SLP which deploys personality information for the signed link prediction problem; and

Evaluate extensively SLP on two datasets of realworld signed link networks and explore the impact of personality information on signed link prediction.
2. Problem Statement
We shall first assume is the set of users. We use the matrix to denote useruser positive and negative links where , and represent a positive link, a negative link, and missing (a.k.a unknown) information from to respectively. We also measure users’ optimism and pessimism personality information following previous research (Beigi et al., 2016a)–this is discussed in more details in the next section. We follow psychology literature and consider two separate measures for each user’s optimism and pessimism as they should be conceptualized as two independent dimensions (fischer1986optimism; mroczek1993construct; Beigi et al., 2016a; Chang, 1998)
. This means that being optimistic does not necessarily mean not pessimistic. Let us now assume vectors
and denote the users’ optimism and pessimism respectively, where is the optimism strength of and is her pessimism strength. The higher optimism (pessimism) score is, the more optimistic (pessimistic) is.The problem of signed link prediction by exploiting user’s optimism and pessimism is then formally defined as follows:
Given users’ optimism and pessimism and , and useruser existing positive and negative links matrix , we seek to learn a predictor to find the unknown positive/negative link information by inferring new useruser positive/negative link matrix as follows:
(1) 
The problem of signed link prediction is different than its existing variants, positive link prediction (Tang et al., 2013) and sign prediction (Yang et al., 2012) and more challenging compared to them. In particular, we aim to predict the existence of a link between a pair of nodes and its sign. We also predict both positive and negative links simultaneously. Besides, the vast majority of the existing work for the problem of signed link prediction (Leskovec et al., 2010) leverage only the existing links between users. In our work, we seek to leverage additional resources such as user’s personality to alleviate the data sparsity problem.
3. Computation of Personality Information
Personality information is not readily available on social media. Individuals usually do not label themselves as optimistic or pessimistic. A conventional way of obtaining personality information is to directly ask people whether they expect outcomes in their lives to be good or bad (scheier1992effects), which is often seen to use psychological surveys designed for measuring an individual’s optimism and pessimism (e.g., (Scheier et al., 1994)). However, since social media data is largescale, and mainly observational, it is impractical to ask each and every user for their personality information. The onus is, therefore, on us to find a sensible way to infer if a user is optimistic or pessimistic or neither. An indirect approach is to measure optimism and pessimism based on the idea that people’s expectancies for the future stem from their interpretations of the past (peterson1984causal). Thus, past experiences can reflect an individual’s levels of optimism or pessimism. With social media data, the question is how to define a computational measure of optimism or pessimism. To summarize, individuals do not explicitly offer their personality information, it is infeasible to ask a large number of users about such information, but individual social media users do leave their traces online. We ask if we can aggregate individual user’s data and automatically figure out if a user is optimistic or not.
Scheier et. al. (Scheier and Carver, 1985) defines optimism as reinterpreting negative events in a positive way and pessimism as preoccupying with the negative aspects and overlooking positive events. Following the psychology literature, user’s feedback could be also used to estimate her optimism and pessimism as they are counterparts of each other (Hu and Pu, 2013, 2014). It is shown in (Hu and Pu, 2013, 2014) that on social media websites, optimists are more willing to give more positive feedback while pessimists are more biased toward giving more negative feedback than usual. In previous research (Beigi et al., 2016a), this observation has been utilized to calculate users’ optimism and pessimism by leveraging their feedback to different entities in social media (e.g. posts and items). In this work, we use two different scenarios to illustrate how personality scores can be computed. The two scenarios differ in their user feedback: (1) ratings given by users to items, or (2) opinions expressed by users towards each other.
3.1. Scenario 1: Ratings as Feedback
Here, feedbacks are users’ ratings given to the items. Let be the set of items and assume denotes the rating score given from to with indicating that has not rated yet. Also, consider as the average rating score of the th item rated by users. Following (Beigi et al., 2016a), we treat ratings less than some predefined threshold as low and above it as high. We use to denote the set of items with low average rating scores rated by :
is further used to denote the set of items which have received high ratings from , and meanwhile have low average scores. can be formally defined as:
Intuitively, the more frequently user has rated above the average, the more optimistic she is. Therefore, optimism score for is defined as where is the size of the set (Beigi et al., 2016a).
Similarly, we use to denote the set of items with high average rating scores and rated by ,
Let denotes the subset of items from , which are given low rates by :
The pessimism score for is defined as: (Beigi et al., 2016a).
3.2. Scenario 2: Opinions as Feedback
Here, feedbacks are users’ opinions they expressed towards each other and individuals’ personality is defined based on their positive/negative opinions (Beigi et al., 2016a). Following the work of (Beigi et al., 2016a), we create useruser positive and negative opinion matrices and by computing the number of positive or negative opinions users express toward each other. Let and be the average of positive and negative opinions between all pairs of users, respectively. We also define and as the average of positive and negative opinions received by . Further, we define , as a set of users who have received positive emotions from , but at the same time, have received more negative emotions than the average of negative opinions in the network, i.e. they are among the worst people in the network:
denotes the set of users who belong to and have received more positive emotions from than ,
Intuitively, the more frequently has given positive emotions to the worst users in the network, the more optimistic she is (Beigi et al., 2016a). Thus, the optimism score for is defined as as .
Likewise, we define , as a set of users who have received negative emotions from , but at the same time, have received more positive emotions than the average in the network, i.e. they are better than the average,
We define to denote the set of users who belong to and have received more negative emotions from than ,
Pessimism of could be similarly defined as: (Beigi et al., 2016a).
4. The Proposed Framework  SLP
Readily available information such as user’s personality and its impact on the formation of signed links, motivates us to exploit it to overcome the inherent sparsity of the signed links. We model this information mathematically and then incorporate it for predicting positive and negative links. Here, we introduce our approach for modeling user’s optimism and pessimism and then detail the proposed method SLP for signed link prediction.
4.1. Basic Model for Signed Link Prediction
Users usually establish signed links with only a few set of other users. This results in very sparse and lowrank networks. Therefore, lowrank approximation methods could be deployed for modeling signed links (Hsieh et al., 2012). Moreover, the work of (Hsieh et al., 2012) showed that weak structural balance in signed networks leads to a lowrank approximation method for modeling the network. Let be the lowrank latent representations of users in where is the lowrank latent vector representation of . The matrix factorization model seeks a lowrank representation of via solving the following optimization problem:
(2) 
where is the Frobenius norm of a matrix, is Hadamard product, and captures the correlations among user latent representations. controls the contribution of in the learning process. A typical choice of is to set if , and otherwise. Two smoothness regularization terms are also added to avoid overfitting where and are nonnegative regularization parameters on and , respectively. This standard model is very flexible to add prior knowledge from side information. In the following subsection, we introduce how to incorporate user personality information into the standard model.
4.2. Modeling User Personality Information
The analysis in the previous research (Beigi et al., 2016a) introduces two important findings according to users’ optimism and pessimism: (a) users who are more optimistic tend to create and receive more positive links in comparison to the users with low level of optimism; and (b) users with more pessimism personality are more likely to create and receive more negative links compared to the users who are less pessimistic. To model the user’s optimism and pessimism effect, we consider the following two cases for each pair of users :

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Case 1: and ;

Case 2: and ;
where and are thresholds to consider the significant optimism and pessimism difference between and , respectively. We use and to make the expected total degree comparisons flexible for and .
In Case 1, has a higher level of optimism and has a lower level of optimism, then , which suggests that is more likely to receive positive links in comparison to . This results in a higher degree for , i.e., . To account for this, we impose a penalty if is lesser than 0, when . Similarly, in Case 2, if has a higher pessimistic level while has a lower pessimism, then . This suggests that is more likely to receive negative links in comparison to which results in a higher negative degree (and consequently a lower total degree) for , i.e., . Therefore, we impose a penalty if is greater than 0, when . These two cases align well with the findings in (Beigi et al., 2016a) regarding optimism and pessimism of users. Therefore, we propose the following personality regularizations:
(3) 
(4) 
where . Next, we will show that by minimizing Eq. 3 and Eq. 4, we can model personality information:

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Eq. 3 imposes a penalty when the user contradicts optimism behavior, where and . Minimizing will force to be closer to higher values and to be close to lower values. Thus, is more likely to establish positive links resulting in an increase in its degree while is less likely to have positive links so that its degree will be decreased.

Eq. 4 imposes a penalty when the user contradicts pessimism behavior, where and . Minimizing will force to be closer to lower values and to be closer to higher values. Therefore, is more likely to establish negative links toward others resulting in a decrease in its degree while is less likely and as a consequent its degree will increase.
The above observations show that we can model personality information by minimizing Eq.3 and Eq.4.
4.3. Personality Information for Signed Link Prediction
Having added the personality regularizations, our proposed framework SLP now seeks to solve the following optimization problem:
(5)  
where and is a vector with all elements equal to 1. The additional information related to the optimism and pessimism of users alleviates the data sparsity problem for signed link prediction. If does not have any positive/negative links, learning her latent factor is impossible. However, if we have information on how much is optimistic or pessimistic, we still can learn for via personality regularization.
Since the optimization problem in Eq.5 is not jointly convex with respect to and , there is no neat closed solution for it due to existence of the function. Therefore, it can be rewritten into its matrix form as:
(6) 
where . We define and in the th iteration,
(7) 
Expanding the objective function of Eq. 4.3 in the th iteration can be written as,
(8) 
where the function is defined as,
(9) 
where could be either or . We use the gradient descent method to solve Eq. 8, which has been proven to gain an efficient solution (Hsieh et al., 2012). The partial derivations of w.r.t. and are,
where
(11) 
With the partial derivations of and , an optimal solution of the objective function in Eq. 4.3 can be obtained as shown in Algorithm 1.
The inputs to this algorithm are useruser positive/negative link matrix , expected degree difference matrices and and users’ optimism and pessimism scores. We randomly initialize and in line 1. From line 2 to 8, we update and until they converge. The algorithm will stop when objective function has little change or when it reaches a predefined maximal iterations. The output of algorithm is the estimated positive/negative link matrix which is computed as . shows the likelihood of establishing relation from to and also shows whether the relation is a positive or negative link.
4.4. Time Complexity
The most timeconsuming operations are the calculations of and . We only discuss the time complexity analysis of these two steps. Let the number of nonzero elements of be .

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We first focus on the analysis of which needs to be calculated in each iteration and is . We can keep the difference between users’ optimism scores before running the algorithm. If is considered the number of pair of users , we only need to check whether is satisfied for these pairs or not. Due to the sparsity of , the time complexity of calculating is if is the number of nonzero elements of . The time complexity for comparing number of users is also . The same analysis can be done for . Therefore, the total time complexity of calculating and in each iteration is .

For the analysis of in Eq.4.3, since is very sparse, the time complexity of calculating both and are in which is the number of nonzero elements of . Similarly, since and only need to be computed once, we can get the time complexity of and as and , respectively. and denote the numbers of nonzero elements of and , respectively. For brevity, we omit the detailed analysis of these terms. The time complexity of in each iteration is thus .

Now we discuss the time complexity of in Eq.4.3. Since the number of nonzero elements of is , the cost of calculating is . Thus, the time complexity of is . With the same approach for calculating the time complexities of and , the time complexity of computing and is . Hence, the total time complexity of in each iteration is .
5. Experiments
In this section, we first introduce the datasets we use, and then explore the effectiveness of SLP for signed link prediction. In particular, we design an extensive set of experiments to (1) evaluate the proposed method SLP, (2) investigate the effect of personality information on the performance of SLP and (3) conduct parameter analysis to examine the sensitivity of SLP to the main parameters.
5.1. Datasets
We collect two large datasets of online signed social networks, Epinions and Slashdot. We perform some standard preprocessing steps by filtering out users without either positive or negative links. Table 1 shows the statistics of our datasets.
Epinions. this is a productreview website where users can establish trust and distrust relationships. We treat each trust and distrust relation as positive and negative links and construct useruser matrix where if user trusts user , and if user distrusts user . Also, if the information is missing. Users can rate each item in a scale of 1 to 5. Here we assume , i.e., scores in are treated as low and as high scores (Tang et al., 2014b). We define optimism and pessimism based on the user’s rating behavior in Epinions, following the scenario 1 (Beigi et al., 2016a).
Slashdot. this is a technologyrelated news platform which allows users to tag each other as either ‘friend’ or ‘foe’. Similar to the Epinions, we construct useruser matrix from the positive (friendship) and negative links (foes) in the network. Likewise, users can express their opinions toward each other by annotating the articles posted by each other. We define a user’s optimism and pessimism based on her opinion expressing behavior following scenario 2 (Beigi et al., 2016a).
Epinions  Slashdot  

# of Users  131,828  7,275 
# of Positive Links  717,677  67,705 
# of Negative Links  123,705  20,851 
# of Ratings/Opinions  577,692  403,896 
5.2. Experimental Settings
We use 5fold cross validation for evaluation. Each time, we hold one fold out and treat it as our test set . From the remaining 4 folds, we pick of positive and of negative links to construct our training set . Then we set , and new representation of is fed to each predicator. In this paper, we vary as to investigate how well our model performs with different sizes of training set. As stated before, in signed networks, positive links are often much denser than negative ones; hence signed links are imbalanced in both training and test sets. Therefore we rather use the Area Under Curve (AUC), to assess the performance of signed link predictors on predicted values of links between pairs of users in test set, .
To evaluate the proposed framework SLP, we compare it with the following representative signed link predictors:

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MF (Hsieh et al., 2012): This is a variant of the proposed method and preforms matrix factorization on . This baseline ignores the personality regularization. We select this method to see how signed link prediction method performs in absence of personality information.

DB/OP/RP (Shahriari et al., 2016)
: This method first extracts two sets of topologicalbased features for each pair of users: the first set consists of seven (7) degreebased (DB) features, and the second set contains twelve (12) features describing user’s optimism/reputation (OP/RP), which are derived from the links between users. A total of 19 features. Then, it trains a logistic regression classifier using these features to predict positive/negative links for a given pair.

All23 (Leskovec et al., 2010): This method considers 23 different topological structure features for each pair of relation between users. It then trains a logistic regression classifier to predict positive/negative links. The deployed features could be categorized into two groups. The first category captures the local relations of a node to the rest of the network including positive/negative indegrees and outdegrees. The second category is extracted according to the balance theory.

TDP (Guha et al., 2004): This baseline treats positive (trust)/negative (distrust) link propagation as a repeating sequence of atomic operations. In this propagationbased method, positive link propagates multiple steps while negative link propagates only a single step.

Random: This algorithm assigns a random sign (+ or ) to each user pair.
Note we do not compare SLP with any traditional positive link predictor such as (Jang et al., 2014; Tang et al., 2013). This is because the signed link prediction problem could not be carried out by trivially applying positive link predictors (Tang et al., 2014a), despite existence of several positive link predictors (Jang et al., 2014; Tang et al., 2013). We use crossvalidation to determine the best values for the proposed method and the baselines with parameters. For the proposed framework, we set the parameters as follows: . We also construct the matrices and as follows,
(12) 
where and indicate the difference between the ranks of users and , assuming users are sorted in an descending order according to their optimism and pessimism scores, respectively.
5.3. Performance Comparison
The comparison results are shown in Table 2 and Table 3 for Epinions and Slashdot, respectively. We observe that all methods outperform the baseline Random. The performance of each method improves with the increasing size of the training data. SLP performs the best among all methods. Next, we discuss why SLP did better:

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SLP outperforms TDP since edge signs could be incorporated into the signed link prediction rather than requiring a notion of propagation from fartheroff parts of the network as (Guha et al., 2004) did. Moreover, in contrast to SLP, TDP does not consider imbalance distribution of positive/negative links.

SLP always outperforms All23
since features extracted based on the topological structure, may not be robust due to the sparsity problem, and there might be many pairs of users without features based on balance theory
(Chiang et al., 2011). The imbalance problem of positive/negative links distribution cannot be handled by All23. 
SLP achieves better performance over DB/OP/RP, despite that both of the approaches leverage optimism/reputationbased features. The reason is DB/OP/RP uses topological structure to extract these features and hence suffers from the sparsity problem, similar to All23. Simply put, there could be many pairs of users with zero optimism/reputation, which make leveraging the optimism/reputationbased features less useful in alleviating the imbalance problem of signed links distributions. In contrast, SLP infers users’ personality information from their feedback on different issues other than merely using signed links.

SLP has better performance than MF. This is because SLP incorporates personality information to predict positive/negative links while MF does not. This suggests the importance of personality information in the problem of signed link prediction.
We perform ttest on all comparisons and the ttest results suggest that all improvements are significant. To recap, the proposed framework obtains significant performance improvement by exploiting personality information.
50%  60%  70%  80%  90%  100%  

SLP  0.8097  0.8113  0.8193  0.8258  0.8363  0.8504 
MF  0.6497  0.6585  0.6614  0.6779  0.6884  0.6957 
DB/OP/RP  0.5981  0.6093  0.6107  0.6202  0.6379  0.6426 
All23  0.5699  0.5721  0.5740  0.5797  0.5813  0.5934 
TDP  0.5461  0.5532  0.5591  0.5613  0.5826  0.6001 
Random  0.4939  0.4994  0.5044  0.5024  0.5009  0.4997 
50%  60%  70%  80%  90%  100%  

SLP  0.8308  0.8404  0.8464  0.8518  0.8613  0.8725 
MF  0.6784  0.6810  0.6911  0.7066  0.7177  0.7265 
DB/OP/RP  0.6347  0.6401  0.6476  0.6558  0.6716  0.6811 
All23  0.5913  0.5983  0.6005  0.6094  0.6126  0.6237 
TDP  0.5710  0.5794  0.5816  0.5871  0.5981  0.6013 
Random  0.4924  0.5023  0.4981  0.4993  0.5003  0.5011 
5.4. Further Experiment with Personality Information
In this set of experiments, we probe further if the newly discovered personalitybased features in SLP can be incorporated into other methods such as All23 and DB/OP/RP. The addition of personalitybased features to these two methods results two variants as follows.

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The comparison results are shown in Table 4 and Table 5 for Epinions and Slashdot. We observe the following:

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Both All23+PI and DB/OP/RP+PI outperform their corresponding original methods, i.e., All23 and DB/OP/RP. This performance gain confirms the added value of the proposed personality features extracted from an exogenous source of information, in addition to those inferred from the signed links.

Even with the personalitybased features, All23+PI and DB/OP/RP+PI were outperformed by SLP because SLP uses latent features for signed link prediction problem, while All23+PI and DB/OP/RP+PI both use a manually developed set of features.
5.5. Impact of Personality Information on SLP
We further explore the impact of personality information on signed link prediction, in an attempt to capture the different strength levels of optimism and pessimism that manifest online. First, we assume the size of training set is fixed to throughout this section. Then, using means, we divide the users in the training set into two groups, based on their optimism and pessimism scores: (1) : users with strong personality (both high optimism and pessimism), and (2) : indifferent users (with low optimism and pessimism).
50%  60%  70%  80%  90%  100%  

SLP  0.8097  0.8113  0.8193  0.8258  0.8363  0.8504 
DB/OP/RP+PI  0.6761  0.6839  0.6947  0.7014  0.7177  0.7263 
DB/OP/RP  0.5981  0.6093  0.6107  0.6202  0.6379  0.6426 
All23+PI  0.6531  0.6673  0.6701  0.6848  0.6974  0.7012 
All23  0.5699  0.5721  0.5740  0.5797  0.5813  0.5934 
50%  60%  70%  80%  90%  100%  

SLP  0.8308  0.8404  0.8464  0.8518  0.8613  0.8725 
DB/OP/RP+PI  0.6938  0.7076  0.7188  0.7254  0.7374  0.7513 
DB/OP/RP  0.6347  0.6401  0.6476  0.6558  0.6716  0.6811 
All23+PI  0.6847  0.6918  0.7043  0.7181  0.7203  0.7328 
All23  0.5913  0.5983  0.6005  0.6094  0.6126  0.6237 
To assess the impact of personality information, we train our model on the whole training data, in three different ways by : (1) only considering the personality information (optimism and pessimism scores) of users in (i.e., ), (2) only considering the personality of users in , (3) considering the personality of users in . The results corresponding to these three runs are shown in Table 6 with the following observations:

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By removing users with strong personality, the performance of SLP drastically drops. This can be observed by comparing the performance on and .

The removal of indifferent users’ personality does not have significant influence on the performance of SLP, as we compare the performance on and .


The role of personality information becomes clearer via this study: personality information can help signed link prediction with a caveat– the stronger the personality, the more improvement in performance. In other words, low personality information as indifferent users exhibit, can lead to performance deterioration as shown in the performance on . Moreover, with only a slight difference, the personality information from users in , is worthless compared to the information from . This supports the fact that the information from users in does not make much difference. In other words, the personality information from indifferent users could be treated as irrelevant to the signed link prediction problem.
5.6. Parameter Sensitivity Analysis of SLP
SLP has two important parameters, and which control the contribution from user’s optimism and pessimism, respectively. Here, we discuss their effect by varying both and as when the size of training set is fixed to . The results are shown in Figure 1 with the followings observed.

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In general, the performance of SLP increases with the increase of and , and then it degrades. These patterns ease the parameter selection for SLP.

The performance improves even when and slightly change from to , which confirms the importance of user personality information in signed link prediction.

After reaching to certain values, continuing to increase and will result in the performance reduction. This suggests that large values of and dominate the learning process and the model could learn and inaccurately due to the overfitting of the model to the personality information.

SLP is more sensitive to than since controls the contribution of user’s optimism, which is denser than pessimism information.
6. Related Work
The ease of using the Internet has raised numerous security and privacy issues. Mitigating these concerns has been studied from different aspects such as identifying malicious activities (Alvari and Shakarian, 2019; Alvari et al., 2018, 2017), addressing users’ privacy issues (Beigi et al., 2018, 2019; Beigi and Liu, 2018a) and finding positive/ negative links (i.e., trust/distrust) between users (Tang et al., 2013, 2015; Beigi et al., 2016a, b). Positive link prediction (a.k.a. trust prediction) has been extensively studied (Jang et al., 2014; Tang et al., 2013; Beigi et al., 2014) in which the goal is to predict only positive links from existing ones. The availability of signed networks has motivated the research on signed link prediction (Chiang et al., 2011; Leskovec et al., 2010). The recent advances on signed link prediction demonstrate that negative links have added value in addition to positive links (Tang et al., 2014a). Thus, we focus on the positive/negative link prediction problem which is different from positive link prediction (Tang et al., 2013) and sign prediction (Yang et al., 2012; Javari and Jalili, 2014). It is more challenging compared to them because: first, in contrast to positive link prediction, in signed link prediction, we aim to predict both positive and negative links simultaneously and second, the sign prediction problem only infers the signs of the existing links while, in the signed link prediction, we predict the existence of a link between a pair of nodes as well as its sign.
The existing signed link prediction studies can be divided into two categories: supervised and unsupervised methods. Supervised methods consider the signed link creation problem as a classification problem by using the old links and training a classifier on the features extracted from the signed networks(Chiang et al., 2011; Leskovec et al., 2010). For example, the work of (Leskovec et al., 2010) first extracts indegree and outdegree from signed links and then uses balance and status theory to extract trianglebased features and it then verifies the importance of balance and status theory for signed link prediction. Another work of (Chiang et al., 2011) extends the trianglebased features to the kcyclebased features.
Unsupervised methods often perform predictions based on certain topological properties of signed networks (Hsieh et al., 2012; Symeonidis and Mantas, 2013; Ye et al., 2013). One type of unsupervised methods is node similarity based methods (Symeonidis and Mantas, 2013), which first define similarity metrics to calculate node similarities, and then provide a way to predict the signed relations based on them. Another type of unsupervised methods is propagationbased methods (De Cock and Da Silva, 2005; Guha et al., 2004; Ziegler and Lausen, 2005). Positive sign propagation is treated as a repeating sequence of matrix operations (Guha et al., 2004). Negative sign propagation then stopped after multiple steps of positive sign propagation (Guha et al., 2004). The work of (De Cock and Da Silva, 2005) considers ignorance as well as partial positive/negative links in its proposed positive/negative link propagation method by modeling the network as an intuitive fuzzy relations. Another category of unsupervised methods is based on lowrank matrix factorization (Hsieh et al., 2012; Ye et al., 2013; Wang et al., 2017). The work in (Hsieh et al., 2012) models the signed link prediction problem as a lowrank matrix factorization model, based on the weak structural balance on the signed network. Another study in (Ye et al., 2013) extends the lowrank model to perform link prediction across multiple signed networks. Also the work of Wang et al. (Wang et al., 2017) completes a binary matrix with positive and negative elements in an online setting by penalizing the difference between predicted matrix and the ground truth by logistic loss and matrix maxnorm. Authors of (Tang et al., 2014b) incorporate side information, i.e., helpfulness ratings in a lowrank matrix factorization model to predict negative links. Beigi et al. (Beigi et al., 2016b) incorporates users’ emotional information in a lowrank matrix factorization framework to predict positive and negative links between them. Another work of (Tang et al., 2015) predicts the negative links using positive links and contentcentric user interactions.
Likewise, SLP is also based on the lowrank matrix factorization model. The difference between SLP and the above lowrank matrix factorization models is that we investigate the role of personality information, i.e. optimism/pessimism in signed link prediction. Since optimists tend to establish more positive links than others and pessimists establish more negative links (Geers et al., 1998), we model this fact as a constraint in the lowrank matrix factorization cost function to guide the learning process of and .
Exploiting user’s features such as trustworthiness, bias, and optimism has been discussed in prior studies (Shahriari et al., 2016; Mishra and Bhattacharya, 2011). For example, the work of (Shahriari et al., 2016) addresses the problem of sign prediction based on users’ optimism/reputation. The authors define optimism as users’ voting pattern towards others and the reputation as their popularity. Specifically, their approach calculates the optimism as the difference between the number of user’s positive and negative outlinks. Moreover, they introduce rank based optimism and reputation based on the rank of users in the signed social network. Another work (Mishra and Bhattacharya, 2011) computes bias and prestige of nodes based on the positive links between users in signed social networks. It defines bias as the user’s truthfulness. The prestige is also calculated based on the opinion of other users in the form of inlinks a user gets.
Similarly, we calculate users’ optimism/pessimism and exploit these information for signed link prediction. The difference between our work and the above works is that we infer users’ optimism/pessimism based on a source other than signed links, i.e. users’ feedback and interactions on different entities (items and posts). These additional sources of information could help to overcome the data sparsity and imbalance problem for signed link data.
7. Conclusion and Future Work
In this paper, we study the role of user personality, in particular, optimism and pessimism to mitigate the data sparsity problem in signed link prediction. User’s feedback is further used to estimate optimism/pessimism. We then investigate the incorporation of such information for predicting positive/negative links and solving data sparsity problem for signed link prediction. We propose the framework SLP by mathematically incorporating optimism and pessimism information. We evaluate SLP on realworld datasets and the results demonstrate the complementary role of personality information in the signed link prediction problem. This work also enables us to experiment if incorporating different types of personality information can be relevant or helpful.
One future direction is to consider additional user’s personality traits including extraversion, agreeableness, openness, conscientiousness and neuroticism as suggested in the Big Five Model (McCrae and John, 1998). We also plan to explore more on inferring users personal information by incorporating content information. Furthermore, we can expand our statistic solution of user behavior to a dynamic one as users can evolve over time and they adapt to different situations, though slowly. A nuanced solution is to consider temporal dynamics of user’s personality for dynamic signed link prediction. Another future direction is to explore the impact of users’ personality and signed links on recommendation systems as signed links have previously shown promising results for recommendation task.
Acknowledgements.
This material is based upon the work supported, in part, by NSF #1614576, ARO W911NF1510328 and ONR N000141712605.References
 Alvari et al. (2018) authorpersonHamidreza Alvari, personElham Shaabani, and personPaulo Shakarian. year2018. Early Identification of Pathogenic Social Media Accounts. In booktitle2018 IEEE International Conference on Intelligence and Security Informatics (ISI). IEEE, pages169–174.
 Alvari and Shakarian (2019) authorpersonHamidreza Alvari and personPaulo Shakarian. year2019. Hawkes Process for Understanding the Influence of Pathogenic Social Media Accounts. In booktitle2019 2nd International Conference on Data Intelligence and Security (ICDIS). IEEE.
 Alvari et al. (2017) authorpersonHamidreza Alvari, personPaulo Shakarian, and personJE Kelly Snyder. year2017. Semisupervised learning for detecting human trafficking. journalSecurity Informatics volume6, number1 (year2017), pages1.
 Asendorpf and Wilpers (1998) authorpersonJens B Asendorpf and personSusanne Wilpers. year1998. Personality effects on social relationships. journalJournal of personality and social psychology volume74, number6 (year1998), pages1531.
 Beigi et al. (2019) authorpersonGhazaleh Beigi, personRuocheng Guo, personAlexander Nou, personYanchao Zhang, and personHuan Liu. year2019. Protecting User Privacy: An Approach for Untraceable Web Browsing History and Unambiguous User Profiles. In booktitleProceedings of the Twelfth ACM International Conference on Web Search and Data Mining. ACM, pages213–221.
 Beigi et al. (2014) authorpersonGhazaleh Beigi, personMahdi Jalili, personHamidreza Alvari, and personGita Sukthankar. year2014. Leveraging community detection for accurate trust prediction. (year2014).
 Beigi and Liu (2018a) authorpersonGhazaleh Beigi and personHuan Liu. year2018a. Privacy in social media: Identification, mitigation and applications. journalarXiv preprint arXiv:1808.02191 (year2018).
 Beigi and Liu (2018b) authorpersonGhazaleh Beigi and personHuan Liu. year2018b. Similar but different: Exploiting users’ congruity for recommendation systems. In booktitleInternational Conference on Social Computing, BehavioralCultural Modeling and Prediction and Behavior Representation in Modeling and Simulation. Springer, pages129–140.
 Beigi et al. (2018) authorpersonGhazaleh Beigi, personKai Shu, personYanchao Zhang, and personHuan Liu. year2018. Securing social media user data: An adversarial approach. In booktitleProceedings of the 29th on Hypertext and Social Media. ACM, pages165–173.
 Beigi et al. (2016a) authorpersonGhazaleh Beigi, personJiliang Tang, and personHuan Liu. year2016a. Signed Link Analysis in Social Media Networks. In booktitleTenth International AAAI Conference on Web and Social Media.
 Beigi et al. (2016b) authorpersonGhazaleh Beigi, personJiliang Tang, personSuhang Wang, and personHuan Liu. year2016b. Exploiting emotional information for trust/distrust prediction. In booktitleProceedings of the 2016 SIAM international conference on data mining. SIAM, pages81–89.
 Burt et al. (1998) authorpersonRonald S Burt, personJoseph E Jannotta, and personJames T Mahoney. year1998. Personality correlates of structural holes. journalSocial Networks volume20, number1 (year1998), pages63–87.
 Chang (1998) authorpersonEdward C Chang. year1998. Distinguishing between optimism and pessimism: A second look at the optimism–neuroticism hypothesis.. In booktitleInternational Congress of Psychology. American Psychological Association.
 Chiang et al. (2011) authorpersonKaiYang Chiang, personNagarajan Natarajan, personAmbuj Tewari, and personInderjit S Dhillon. year2011. Exploiting longer cycles for link prediction in signed networks. In booktitleProceedings of international conference on Information and knowledge management.
 Cho (2006) authorpersonJinsook Cho. year2006. The mechanism of trust and distrust formation and their relational outcomes. journalJournal of retailing volume82, number1 (year2006), pages25–35.
 De Cock and Da Silva (2005) authorpersonMartine De Cock and personPaulo Pinheiro Da Silva. year2005. A many valued representation and propagation of trust and distrust. In booktitleInternational Workshop on Fuzzy Logic and Applications. pages114–120.
 Geers et al. (1998) authorpersonAndrew L Geers, personSean P Reilley, and personWilliam N Dember. year1998. Optimism, pessimism, and friendship. journalCurrent Psychology volume17, number1 (year1998), pages3–19.
 Golbeck et al. (2011) authorpersonJennifer Golbeck, personCristina Robles, and personKaren Turner. year2011. Predicting personality with social media. In booktitleCHI extended abstracts on human factors in computing systems.
 Guha et al. (2004) authorpersonRamanthan Guha, personRavi Kumar, personPrabhakar Raghavan, and personAndrew Tomkins. year2004. Propagation of trust and distrust. In booktitleProceedings of WWW.
 Hardin (2004) authorpersonRussell Hardin. year2004. Distrust: Manifestations and management. In booktitleDistrust.
 Hsieh et al. (2012) authorpersonChoJui Hsieh, personKaiYang Chiang, and personInderjit S Dhillon. year2012. Low rank modeling of signed networks. In booktitleProceedings of the 18th ACM SIGKDD.
 Hu and Pu (2013) authorpersonRong Hu and personPearl Pu. year2013. Exploring Relations between Personality and User Rating Behaviors.. In booktitleUMAP Workshops.
 Hu and Pu (2014) authorpersonRong Hu and personPearl Pu. year2014. Exploring personality’s effect on users’ rating behavior. In booktitleCHI’14 Extended Abstracts on Human Factors in Computing Systems.
 Jang et al. (2014) authorpersonMinHee Jang, personChristos Faloutsos, and personSangWook Kim. year2014. Trust prediction using positive, implicit, and negative information. In booktitleProceedings of WWW.
 Javari and Jalili (2014) authorpersonAmin Javari and personMahdi Jalili. year2014. Clusterbased collaborative filtering for sign prediction in social networks with positive and negative links. journalACM TIST (year2014).
 Larson and Hardin (2004) authorpersonDeborah Welch Larson and personRussell Hardin. year2004. Distrust: Prudent, if not always wise. journalDistrust volume8 (year2004), pages34.
 Leskovec et al. (2010) authorpersonJure Leskovec, personDaniel Huttenlocher, and personJon Kleinberg. year2010. Predicting positive and negative links in online social networks. In booktitleProceedings of WWW.
 McCrae and John (1998) authorpersonRobert R McCrae and personOliver P John. year1998. An introduction to the fivefactor model and its applications. journalPersonality: critical concepts in psychology volume60 (year1998).
 McKnight and Chervany (2001) authorpersonD Harrison McKnight and personNorman L Chervany. year2001. Trust and distrust definitions: One bite at a time. In booktitleTrust in Cybersocieties. publisherSpringer, pages27–54.
 Mishra and Bhattacharya (2011) authorpersonAbhinav Mishra and personArnab Bhattacharya. year2011. Finding the bias and prestige of nodes in networks based on trust scores. In booktitleProceedings of WWW.
 Scheier and Carver (1985) authorpersonMichael F Scheier and personCharles S Carver. year1985. Optimism, coping, and health: assessment and implications of generalized outcome expectancies. journalHealth psychology volume4, number3 (year1985).
 Scheier et al. (1994) authorpersonMichael F Scheier, personCharles S Carver, and personMichael W Bridges. year1994. Distinguishing optimism from neuroticism (and trait anxiety, selfmastery, and selfesteem): a reevaluation of the Life Orientation Test. journalJournal of personality and social psychology volume67, number6 (year1994), pages1063.
 Scheier et al. (2001) authorpersonMichael F Scheier, personCharles S Carver, and personMichael W Bridges. year2001. Optimism, pessimism, and psychological wellbeing. journalOptimism and pessimism: Implications for theory, research, and practice volume1 (year2001), pages189–216.
 Shahriari et al. (2016) authorpersonMohsen Shahriari, personOmid Askari Sichani, personJoobin Gharibshah, and personMahdi Jalili. year2016. Sign prediction in social networks based on users reputation and optimism. journalSNAM (year2016).
 Symeonidis and Mantas (2013) authorpersonPanagiotis Symeonidis and personNikolaos Mantas. year2013. Spectral clustering for link prediction in social networks with positive and negative links. journalSocial Network Analysis and Mining volume3, number4 (year2013), pages1433–1447.
 Tang et al. (2015) authorpersonJiliang Tang, personShiyu Chang, personCharu Aggarwal, and personHuan Liu. year2015. Negative link prediction in social media. In booktitleProceedings of WSDM. ACM, pages87–96.
 Tang et al. (2013) authorpersonJiliang Tang, personHuiji Gao, personXia Hu, and personHuan Liu. year2013. Exploiting homophily effect for trust prediction. In booktitleProceedings of WSDM. ACM, pages53–62.
 Tang et al. (2014b) authorpersonJiliang Tang, personXia Hu, personYi Chang, and personHuan Liu. year2014b. Predictability of distrust with interaction data. In booktitleProceedings of CIKM. ACM, pages181–190.
 Tang et al. (2014a) authorpersonJiliang Tang, personXia Hu, and personHuan Liu. year2014a. Is distrust the negation of trust?: the value of distrust in social media. In booktitleProceedings of HT.
 Wang et al. (2017) authorpersonJing Wang, personJie Shen, personPing Li, and personHuan Xu. year2017. Online Matrix Completion for Signed Link Prediction. In booktitleProceedings of WSDM. ACM.
 Xin et al. (2009) authorpersonXin Xin, personIrwin King, personHongbo Deng, and personMichael R Lyu. year2009. A social recommendation framework based on multiscale continuous conditional random fields. In booktitleProceedings of conference on Information and knowledge management.
 Yang et al. (2012) authorpersonShuangHong Yang, personAlexander J Smola, personBo Long, personHongyuan Zha, and personYi Chang. year2012. Friend or frenemy?: predicting signed ties in social networks. In booktitleSIGIR.

Ye
et al. (2013)
authorpersonJihang Ye, personHong Cheng,
personZhe Zhu, and personMinghua Chen.
year2013.
Predicting positive and negative links in signed social networks by transfer learning. In booktitle
WWW.  Ziegler and Lausen (2005) authorpersonCaiNicolas Ziegler and personGeorg Lausen. year2005. Propagation models for trust and distrust in social networks. journalInformation Systems Frontiers volume7, number45 (year2005), pages337–358.
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