A social recommender system based on reliable implicit relationships

Knowledge-Based Systems xxx (xxxx) xxx

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Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys

A social recommender system based on reliable implicit relationships✩ ∗

Sajad Ahmadian a , , Nima Joorabloo b , Mahdi Jalili b , Yongli Ren c , Majid Meghdadi d , Mohsen Afsharchi d a

Faculty of Information Technology, Kermanshah University of Technology, Kermanshah, Iran School of Engineering, RMIT University, Melbourne, Australia c School of Science, RMIT University, Melbourne, Australia d Department of Computer Engineering, University of Zanjan, Zanjan, Iran b

article

info

Article history: Received 26 March 2019 Received in revised form 6 December 2019 Accepted 9 December 2019 Available online xxxx Keywords: Recommender system Social information Reliability Implicit relationship Dempster–Shafer theory

a b s t r a c t Recommender systems attempt to suggest information that is of potential interest to users helping them to quickly find information relevant to them. In addition to historical user–item interaction data, such as users’ ratings on items, social recommendation methods use social relationships between users to improve the accuracy of recommendations. However, the available social relationships are often extremely sparse. Therefore, incorporating implicit relationships into the recommendation process can be effective to improve the performance of social recommender systems, especially for those users whose explicit relationships are insufficient to make accurate recommendations. The existing approaches have not considered reliability of the implicit relationships. In this paper, a social recommender system is proposed based on reliable implicit relationships. To this end, Dempster– Shafer theory is used as a powerful mathematical tool to calculate the implicit relationships. Moreover, a new measure is introduced to evaluate the reliability of predictions, where unreliable predictions are recalculated using a neighborhood improvement mechanism. This mechanism uses a confidence measure between the users to identify ineffective users in the neighborhood set of a target user. Finally, new reliable ratings are calculated by removing the identified ineffective neighbors. Extensive experiments are conducted on three well-known datasets, and the results demonstrate that our approach achieves superior performance to the state-of-the-art recommendation methods. © 2019 Elsevier B.V. All rights reserved.

1. Introduction In recent years, social recommender systems have attracted increasing attention due to ever increasing popularity of social media in everyday applications [1]. Users in online social media share ideas and opinions with their families, friends and colleagues, resulting in rich social relationships such as friendships in Facebook, following in Twitter and trust in Epinions. With increasing access to social information between users, recommender systems can directly incorporate social relationships into the recommendation process. The main idea of social recommender systems is that users connected to each other by social ✩ No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.knosys. 2019.105371. ∗ Corresponding author. E-mail addresses: [email protected] (S. Ahmadian), [email protected] (N. Joorabloo), [email protected] (M. Jalili), [email protected] (Y. Ren), [email protected] (M. Meghdadi), [email protected] (M. Afsharchi).

relationships are correlated rather than being independent and identically distributed [2]. They are built on the assumption that social relationships are formed when users have similar opinions to similar products. Recommender systems often suffer from cold start and data sparsity problems. Users tend to rate only a small number of items, and thus the user–item rating matrix is often heavily sparse with the entries being mostly unknown [3,4]. Social recommender systems can potentially solve these challenging problems of traditional recommender systems by using social relationships between users in the recommendation process. However, the available social relationships are extremely sparse too, and the distribution of the number of social relationships follows a power-law like distribution [5]. A small number of users express most of the social relationships, while a large portion of them express few relationships. Generally, users who have expressed many social relationships are likely to have many ratings as well [6]. Traditional recommender systems can provide accurate recommendations for the users with enough ratings, while for those without sufficient ratings, they fail to produce good recommendations. Such users often have insufficient social relationships, and thus social recommender systems can neither produce

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Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

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accurate recommendations [7,8]. Therefore, a major challenge in designing effective social recommender systems is to provide an accurate approach for predicting implicit relationships. Generally, social relationships between users in social recommender systems can be classified into two main types including explicit and implicit relationships. Users may explicitly express their social relationships with one another. For example, a user explicitly states their trust relationships to other users in Epinions website. On the other hand, implicit social relationships are learnt using available information, such as the frequency, interactions and common neighbors between users. Although several approaches have been proposed to incorporate the implicit social relationships into the recommendation process, they fail to consider the reliability of the predicted implicit relationships [9–12]. Incorporating unreliable implicit relationships into the recommendation process may lead to dramatically affect the performance of social recommender systems. Evaluating the reliability measure can be effective to determine the quality of the predicted implicit relationships. To address the above mentioned problems, a new social recommendation method is proposed in this paper, which is based on reliable implicit relationships. In the proposed method, first user–user interaction network is constructed based on the user– item interaction matrix and explicit trust relationships. The user– user interaction matrix represents the connectivity network between the users. The edges’ weights of the network are calculated as the combination of similarity values and explicit trust relationships between the users. Then, the implicit relationships between the users are predicted using a link prediction approach. To this end, a series of mass functions are used to measure the degrees of similarity between the users. Dempster–Shafer theory is used as a powerful mathematical tool to combine the mass functions and calculate the implicit relationships. This leads to improve the performance of social recommender systems, especially for the users whose explicit relationships are insufficient to make accurate recommendations. The user–item matrix, explicit and implicit trust relationships are used to calculate the final similarity weights between the users. In addition, the reliability of predicted ratings is evaluated using a reliability measure and the initial neighborhood of the users is recalculated for the predicted ratings with low reliability value. For this purpose, ineffective users in the initial neighborhood of the users are identified using a confidence measure, and then removed from the initial neighborhood. Updated reliable ratings are predicted using the improved neighborhood set for the target user. The contributions of the proposed method are summarized as follows:

• An effective link prediction model is proposed based on Dempster–Shafer theory to calculate the implicit relationships between the users in social recommender systems. Both the similarity values and explicit trust relationships between users are considered in the proposed model. • The reliability of the predicted ratings is evaluated using a new reliability measure. This enables to determine the quality of the predicted ratings, and thus to identify unreliable predicted ratings. • A confidence measure is proposed to evaluate the usefulness of the neighbors in the initial neighborhood set of a target user. Ineffective users are removed from the initial neighborhood of the target user to provide more accurate recommendations. The main advantage of this mechanism is to identify unreliable implicit relationships used in the recommendation process. A series of experiments are conducted on three well-known datasets to show the effectiveness of the proposed method in

comparison to other recommendation methods. The results indicate that the proposed method significantly outperforms other compared methods. The rest of the paper is organized as follows. Related works are discussed in Section 2. Dempster–Shafer theory is discussed in Section 3. Section 4 introduces the proposed method in details. The experimental results are represented in Section 5. Finally, the conclusions of the proposed method and also future works are discussed in Section 6. 2. Related work 2.1. Social recommender systems based on explicit relationships Several approaches have been proposed in the literature to improve the performance of social recommender systems using explicit social relationships between users [13–16]. In [13], a social recommendation method is proposed using global rating reputation and local rating similarity, which combines user reputation and social similarity based on ratings. User reputation is obtained by iteratively calculating the correlation of historical ratings of the user and intrinsic qualities of items, which can be used as the user’s global influence on the basic social recommender model. In other words, the users with high reputation have a strong influence on others. In [14], a social recommendation method is proposed based on integration of interactions, trust relationships and product popularity to predict user preferences. The method mainly focuses on analyzing user interactions to infer their latent interactions in accordance with the ratings and corresponding reviews. Moreover, the popularity of products is taken into consideration. A feasible differentially private social mechanism is proposed in [15] to improve link privacy in social recommender systems. This mechanism uses a private graph-link analysis to enhance the accuracy of applying differential privacy to the recommendation. Li et al. [17] proposed a social matrix factorization method to optimize the prediction in both user latent feature space and user–item rating space by employing the individual trust among users. To this end, a context-aware model is considered based on Gaussian mixture model to improve the recommendation performance and alleviate data sparsity problem. In [18], the authors proposed a social recommendation method using matrix factorization technique to ease data sparsity problem meanwhile increasing the accuracy and diversity in complex contexts. The basic idea of the method is to cluster users and consider a variety of complex factors. A trust-based recommendation method is proposed in [19] which integrates the information of trust relationships into the resource-redistribution process. In addition, a tunable parameter is considered to scale the resources received by trusted users before the redistribution process. To achieve the best recommendation accuracy, an optimal scaling value is obtained under several evaluation metrics across different datasets. In [20], a trust-based recommendation method is proposed by applying a graph clustering algorithm and also considering trust statements. The clustering approach is used to obtain the appropriate users/items clusters and consider them as a set of neighbors to recommend unseen items to the target user. 2.2. Social recommender systems based on implicit relationships Although social relationships in social recommender systems can be explicitly expressed by users, a large portion of users specify no or only few relationships [21,22]. Several approaches have been proposed to incorporate implicit social relationships into the recommendation process [9–12,23]. A link prediction method is proposed in [9] based on learning automata to address predicting the emergence of future relationships among nodes in a social network. The method focuses on estimating the weight

Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

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of each test link directly from the weights information in the network using learning automata. In [10], a trust link detection scheme is proposed which includes three aspects: trust scheme, trust link category, and traversal scheme, which are used to build up strong or weak trust links among users. A personalized news recommendation framework is proposed in [11] based on implicit social experts. For this purpose, the opinions of potential influencers on virtual social networks extracted from implicit feedbacks are considered as auxiliary resource for providing recommendations. A social recommender system is proposed in [12] based on implicit social trust and sentiment, which draws user preferences by exploring their online social networks. To this end, the degree of trust level between friends and sentiment rating are identified from micro-reviews using machine learning regression algorithms including linear regression, random forest and support vector regression. In [23], a new social personalized ranking model is proposed which exploits both explicit and implicit trust and ratings. In [24], a latent factor model is proposed based on probabilistic matrix factorization, which incorporates implicit feedback as complementary information. Specifically, a combination of explicit and implicit feedback matrices is used as a shared subspace in the recommendation process. Gao et al. [25] proposed a preference elicitation algorithm based on bipartite graphical correlation and implicit trust. The method first uses an improved single-source shortest path to get the shortest behavior path based on the user–item bipartite graph. Then, the bipartite graphical correlation is calculated and the Markov separation algorithm is employed to separate uncorrelated vertexes and obtain the values of bipartite graphical correlation. Moreover, the implicit trust is used to determine trust relationship between users and items without any historical behaviors. In [26], a method is proposed to predict activity attendance in event-based social networks by discovering a set of factors that connect the physical and cyber spaces and influence individual’s attendance of activities. Zhang et al. proposed a group-based event participation prediction framework for event-based social networks [27]. To this end, personalized random walk with restart on a hybrid event-group category-user network is used to capture intrinsic social relationships. In [28], a group event venue recommendation system is proposed by incorporating mobility via individual location traces and context information into a social-based group decision model. This model is used to provide venue recommendations for groups of mobile users. In [29], a joint personal and social latent factor model is proposed, which extracts the social factor vectors for each user leading to explicitly express the varieties of the social relationships. Nie et al. [30] conducted a case study of recommending YouTube videos to Facebook users based on their social interactions. Moreover, they proposed a video recommendation method that exploits user social interaction information to improve the recommendation accuracy for niche videos. 2.3. Reliability measure in recommender systems Hernando et al. [31] showed that reliability can be incorporated into recommender systems to evaluate the predictions. The main idea of the reliability measure is that the more reliable a prediction is, the less likely to be wrong [32]. A matrix factorization-based method is proposed in [33] that provides a reliability value to each prediction. In [34], a confidence-weighted bias model is proposed for online collaborative filtering which adds bias into collaborative filtering and further introduces confidence weights to improve the stability and accuracy of recommender systems. A trust-based recommendation method is proposed in [35] to identify implicit trust statements by applying a specific reliability measure. Moreover, Pareto dominance

3

and confidence concepts are used to identify the most prominent users of which opinions are employed in the recommendation process. In [36], an adaptive neighbor selection mechanism is proposed for social recommender systems based on reliability and confidence measures. Gohari et al. [37] proposed a confidence-based recommendation method, which employs four different confidence models that derive the users’ and items’ confidence values from both local and global perspectives. In [38], a method is proposed to evaluate the performance of six different confidence estimation algorithms. 3. Dempster–Shafer theory Dempster–Shafer Theory (DST) is a mathematical tool for reasoning with uncertainty [39]. This theory can be used to combine evidences from different sources and arrive at a degree of belief taking into account all the available evidences. The prior data needed in DST can be obtained more intuitive and easier than probability theory. Suppose Ω is the set of mutually exclusive variables ωi called the Frame of Discernment (FOD). FOD describes all circumstances of variable ωi as follows:

Ω = {ω1 , ω2 , . . . , ωi , . . . , ωN }

(1)

where N is the number of elements in set Ω . The power set of Ω is shown as 2Ω and can be expressed as follows: 2Ω = {∅, {ω1 } , . . . , {ωN } , {ω1 , ω2 } , . . . , {ω1 , ω2 , . . . , ωi } , . . . , Ω }

(2) where ∅ indicates an empty set. A value m(ε ) ∈ [0, 1] can be assigned to each subset ε ⊆ 2Ω using a mass function satisfying the following conditions:

∑

m (∅) = 0 and

m (ε) = 1, 0 ≤ m (ε) ≤ 1.

(3)

ε⊆2Ω

In the theory of evidence, belief function Bel(A) measures the strength of the evidence in favor of a proposition A which ranges from 0 (no evidence) to 1 (certainty). On the other hand, plausibility function Pl(A) determines the potential specific support for the proposition A, which can be obtained as the sum of the masses of all sets whose intersection with the proposition is not empty. Bel(A) and Pl(A) are mathematically defined as follows: Bel(A) =

∑

m (B)

(4)

B⊆A

∑

Pl(A) =

m (B)

(5)

B∩A̸ =∅

Fusion operators can be used to combine the beliefs obtained from different sources to model specific situations of belief fusion. Dempster’s rule of combination provides a mechanism to combine belief constraints, which are dictated by independent belief sources. Suppose m1 and m2 are two independent Basic Probability Assignments (BPA) obtained by different sources. The combination of these two BPAs can be calculated by Dempster’s rule as follows: m (A) =

{1 ∑ M

B∩C =A

m1 (B) m2 (C ) A ̸ = ∅

0

A=∅

(6)

where M=

∑

m1 (B)m2 (C )

(7)

B∩C ̸ =∅

Pignistic transformation [40] is used to transform a basic belief assignment over Ω into a probability function. The Pignistic

Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

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probability function for a basic belief assignment m on set Ω is defined as follows: BetPm (ωi ) =

1

∑ A⊆Ω ,ωi ∈A

m(A)

|A| 1 − m(∅)

, m(∅) ̸= 1

(8)

where BetPm is the Pignistic transformation and |A| is the cardinality of subset A. The main idea of the Pignistic probability function is to assign a probability value to each transferable belief model. 4. Social recommender method based on reliable implicit relationships This section presents a new social recommender method called Social recommender based on Reliable Implicit Relationships (SoRIR). The proposed method consists of five main steps:

• Step 1: The user–item rating matrix and explicit trust rela-

•

• •

•

tionships among users are used to construct a network. To this end, the users are considered as the nodes of the network and the weights on the edges are calculated by integrating the similarity values and explicit trust relationships between the users. Step 2: A link prediction approach is used to predict the implicit relationships among the users based on Dempster– Shafer theory. This theory is a powerful mathematical tool to combine mass functions and calculate the implicit relationships. To this end, a series of mass functions are used to measure the degrees of similarity weights between the users. The main advantage of the approach is to improve the performance of social recommender systems especially about the users with insufficient relationships with others. The predicted implicit relationships are used as additional information in the recommendation process. In other words, the final similarity weights between the users are calculated using the user–item rating matrix, explicit trust relations, and implicit trust relationships. Step 3: The quality of predicted ratings is evaluated using a reliability measure. Step 4: The initial neighborhood of the users is updated for the predicted ratings that show low reliability value so as to improve recommendation quality here. To this end, a confidence measure is used to identify ineffective users in the initial neighborhood of the users, which are then removed from the initial neighborhood. Step 5: Finally, the new reliable ratings are predicted using the improved neighborhoods and a list of recommendations is provided for the target user.

The overview of the proposed method is shown in Fig. 1. 4.1. Users’ network construction In this step, a network is constructed based on the combination of user–item rating matrix and explicit trust relationships between users. To this end, the users’ network is represented as a graph G = (U , E , W ) where U is the set of users, E indicates the set of edges between the user pairs, and W denotes the weights of the edges. The similarity values and trust relationships between the users are combined to calculate the edge weights W . The user–item rating matrix is used to calculate similarity values between the users based on Pearson correlation coefficient function, as follows:

∑ sim (u, v) = √∑

i∈Iu,v (ru,i

i∈Iu,v (ru,i

− r u )(rv,i − r v ) √∑ 2

− r u)

i∈Iu,v (rv,i

(9)

− r v )2

where ru,i is the rating of item i provided by user u, r u is the average of ratings provided by user u, and Iu,v is the set of common items which are rated by both of the users u and v . In addition to the user–item rating matrix, the explicit trust relationships between the users are used to calculate the similarity weights in the users’ network. To this end, the trust network of the users is used as additional information for calculating the similarity weights. It should be noted that these trust relationships are explicitly expressed by the users based on the similarity of their preferences to other users. The trust values between the users u and v can be calculated using the trust network as follows: tu,v =

dmax − du,v + 1

(10)

dmax

where du,v is the trust propagation distance indicating the number of edges on the path between the nodes u and v [41], and dmax indicates the maximum allowable propagation distance between two users calculated as follows: dmax =

ln (n)

(11)

ln (k)

where n and k are the size and the average degree of the trust networks in the system, respectively [42]. Finally, the similarity values and trust relationships between the users are combined to calculate the final similarity weights in the graph G. Therefore, the final similarity weights are calculated as follows:

wu,v =

⎧ 2×sim(u,v)×t u,v ⎪ ⎪ ⎪ sim(u,v)+tu,v ⎨

if sim (u, v) > 0 and tu,v > 0

⎪ sim (u, v) ⎪ ⎪ ⎩

if sim (u, v) > 0 and tu,v ≤ 0

tu,v

if sim (u, v) ≤ 0 and tu,v > 0

0

if sim (u, v) ≤ 0 and tu,v ≤ 0

(12)

where sim(u, v ) and tu,v are the similarity and trust values between users u and v , respectively. It should be noted that the positive correlations between the users are considered to calculate the similarity weights because the negative correlations can be ignored to form the neighborhoods. 4.2. Predicting implicit relationships in users’ network In this section, an effective approach is applied on the users’ network to predict implicit relationships between the users. The main advantage of this approach is to consider further relationships in the recommendation process leading to improve the performance of recommender systems especially for the users with few relationships. Insufficient relationships between a user and others might lead to provide unreliable predictions, because the system cannot find sufficient neighbors for the users. To this end, a similarity transferring approach is used to predict the implicit relationships in the users’ network [43]. The main idea of the approach is to use DST to obtain the implicit relationships with high efficiency and accuracy. DST is an efficient mathematical technique to handle uncertainty and information fusion problem [44]. To apply DST, the correlation coefficient between the users is calculated based on their common neighbors in the users’ network. The common neighbors refer to the users who have direct relationships with both of the target users in the users’ network. The similarity values between the users and their common neighbors are used to calculate the correlation coefficient value. Suppose that x is a common neighbor for the target users u and v . The correlation coefficient value based on the common neighbor x can be calculated as follows: Corrx (u, v) = [Min_Corrx (u, v ), Max_Corrx (u, v )]

(13)

Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

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Fig. 1. Overview of the proposed recommender system including its overall steps.

where Min_Corrx (u, v ) and Max_Corrx (u, v ) are respectively the minimum and maximum values of the correlation coefficient between the target users u and v based on the common neighbor x, which are calculated as follows: Min_Corrx (u, v) = wu,x × wv,x −

√

Max_Corrx (u, v) = wu,x × wv,x +

√

1 − wu2,x ×

√

1 − wu2,x ×

√

2 1 − wv, x 2 1 − wv, x

(14) (15)

where wu,x and wv,x are calculated using Eq. (12). Min_Corrx (u, v ) and Max_Corrx (u, v ) can be any real number in the interval [−1, 1]. It can be concluded from Eq. (13) that the correlation coefficient is calculated as an interval instead of a unique real value. In other words, the correlation coefficient is bounded to a specific range of values. However, recommender systems need to have the similarity values between the users as a real number to perform the recommendation process. Therefore, DST is used to

transform the correlation coefficient intervals to a real number as the similarity value between the users. To this end, a set of possible correlations is used with three concepts including Positivecorrelation (P), Uncorrelated (U), and Negative-correlation (N). Then, a membership degree to each subset of possible correlations can be calculated based on the correlation coefficient values between the users. A series of mass functions are defined to measure the membership degree of the correlation coefficient values to the considered subsets. The mass functions are defined based on the correlation coefficient value between users u and v according the common neighbor x as in Box I . It should be noted that mu,v,x ({N , P }) = 0, mu,v,x ({N , P , U }) = 0, and mu,v,x ({∅}) = 0. The membership degrees based on all common neighbors of users u and v can be calculated using Eqs. (16)–(20) in Box I. The final mass function for each subset can be determined using the combination of the membership degrees. To this end, Dempster’s rule of combination is used to calculate

Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

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if Min_Corrx (u, v) > −0.65

⎧ 0 ⎪ ⎪ ⎪ ⎨

−0.65 − Min_Corrx (u, v) mu,v,x ({N }) = ⎪ Max_Corrx (u, v) − Min_Corrx (u, v) ⎪ ⎪ ⎩ 1

else if Max_Corrx (u, v) > −0.65

(16)

else

⎧ 0 if Min_Corrx (u, v) > 0.35 or Max_Corrx (u, v) < −0.35 ⎪ ⎪ ⎪ ⎪ 0.35−Min_Corrx (u,v) ⎪ ⎪ else if Max_Corrx (u, v) > 0.35 and Min_Corrx (u, v) > −0.35 ⎪ ⎨ Max_Corrx (u,v)−Min_Corrx (u,v) Max_Corrx (u,v)+0.35 mu,v,x ({U }) = Max_Corrx (u,v)−Min_Corrx (u,v) else if Min_Corrx (u, v) < −0.35 and Max_Corrx (u, v) < 0.35 ⎪ ⎪ ⎪ 0 .7 ⎪ Max_Corr (u,v)− else if Min_Corrx (u, v) < −0.35 and Max_Corrx (u, v) > 0.35 ⎪ Min_Corrx (u,v) x ⎪ ⎪ ⎩ 1 else ⎧ 0 if Max_Corrx (u, v) < 0.65 ⎪ ⎪ ⎪ ⎨ Max_Corrx (u, v) − 0.65 else if Min_Corrx (u, v) < 0.65 mu,v,x ({P }) = ⎪ Max_Corr x (u, v) − Min_Corrx (u, v) ⎪ ⎪ ⎩ 1

(17)

(18)

else

⎧ 0 if Min_Corrx (u, v) > −0.35 or Max_Corrx (u, v) < −0.65 ⎪ ⎪ ⎪ ⎪ −0.35−Min_Corrx (u,v) ⎪ ⎪ else if Max_Corrx (u, v) > −0.35 and Min_Corrx (u, v) > −0.65 ⎪ ⎨ Max_Corrx (u,v)−Min_Corrx (u,v) Max_Corrx (u,v)+0.65 mu,v,x (N , U ) = Max_Corrx (u,v)−Min_Corrx (u,v) else if Min_Corrx (u, v) < −0.65 and Max_Corrx (u, v) < −0.35 ⎪ ⎪ ⎪ 0.3 ⎪ else if Min_Corrx (u, v) < −0.65 and Max_Corrx (u, v) > −0.35 ⎪ Max_Corrx (u,v)−Min_Corrx (u,v) ⎪ ⎪ ⎩

(19)

⎧ 0 if Min_Corrx (u, v) > 0.65 or Max_Corrx (u, v) < 0.35 ⎪ ⎪ ⎪ ⎪ 0.65−Min_Corrx (u,v) ⎪ ⎪ else if Max_Corrx (u, v) > 0.65 and Min_Corrx (u, v) > 0.35 ⎪ ⎨ Max_Corrx (u,v)−Min_Corrx (u,v) Max_Corrx (u,v)−0.35 else if Min_Corrx (u, v) < 0.35 and Max_Corrx (u, v) < 0.65 mu,v,x (P , U ) = Max_Corrx (u,v)− Min_Corrx (u,v) ⎪ ⎪ ⎪ 0.3 ⎪ else if Min_Corrx (u, v) < 0.35 and Max_Corrx (u, v) > 0.65 ⎪ Max_Corrx (u,v)−Min_Corrx (u,v) ⎪ ⎪ ⎩

(20)

1

else

1

else

Box I.

the final mass functions, as follows:

follows:

⎡

⎡ 1

m′u,v ({P }) =

M

×⎣

∑

∑ [(

mu,v,x ({P }) × mu,v,y ({P , U })

)

x∈CNu,v y∈CNu,v

) + mu,v,x ({P , U }) × mu,v,y ({P }) ⎤ ( )] + mu,v,x ({P }) × mu,v,y ({P }) ⎦ (

(21)

m′u,v ({P , U })

⎡ =

1 M

×⎣

∑

⎤ )] mu,v,x ({P , U }) × mu,v,y ({P , U }) ⎦

∑ [(

x∈CNu,v y∈CNu,v

(22) where CNu,v is the set of the common neighbors for users u and v , which can be calculated as follows: CNu,v = x ∈ U |wu,x > 0 and wv,x > 0 ,

{

}

(23)

where U is the set of all users in the system and wu,x is the similarity weight between users u and x, which is calculated using Eq. (12). The parameter M in Eqs. (21) and (22) is calculated as

M=

∑

∑ ⎣

x∈CNu,v y∈CNu,v

∑ (

⎤ ) mu,v,x (A) × mu,v,y (B) ⎦ ,

(24)

A∩B̸ =∅

where A, B ∈ {{N } , {U } , {P } , {N , U } , {P , U }}. Eqs. (21) and (22) indicate that the final mass functions are calculated only for the subsets related to the positive correlations, as the main purpose of the proposed method is to use the implicit relationships between the users into the recommendation process. On the other hand, the neighborhood of the users can be obtained based on the positive correlations between the users to predict unseen items. Dempster’s rule of combination is used to calculate the final mass functions based on the positive correlations. Finally, the weight of the positive correlation between the users is calculated using the Pignistic probability function [40] based on the combination of the positive mass functions, as follows:

wu′ ,v = m′u,v ({P }) +

m′u,v ({P , U }) 2

,

(25)

where wu′ ,v is the weight of the positive implicit relationship between users u and v . The implicit relationships between the users can be used into the recommendation process to predict unseen items. It should be noted that these relationships are calculated only between the user pairs without any explicit relationships. After obtaining the implicit and explicit relationships between the

Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

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where rmax and rmin are respectively the maximum and minimum of the ratings in the system, and Va,i is calculated as follows:

users, the final similarity weight is calculated as follows:

⎧ ⎨wu,v if wu,v ̸= 0 = wu′ ,v else if wu′ ,v ̸= 0 ⎩ 0 other w ise

f wu,v

(26)

where wu,v and wu′ ,v are the explicit and implicit similarity weights between users u and v calculated using Eqs. (12) and (25), respectively. 4.3. Evaluating the reliability of predicted ratings The unknown items can be predicted based on the final similarity values between the users calculated using Eq. (26). The reliability of predictions is one of the issues that one can raise about the recommendation process. It can even be more critical when the ratings are predicted using the implicit relationships obtained by the proposed link prediction approach. To address this problem, a reliability measure [31] is used to evaluate the quality of the predicted ratings for the users. The main idea of this step is to evaluate the performance of the implicit relationships in the recommendation process. Incorporating implicit relationships with low reliability into the recommendation process might lead to reduce the accuracy of the predictions, and this step tries to find unreliable predictions by considering the reliability measure. The rating given to item i by user a is predicted as follows:

∑ pa,i = r a +

v∈Ka,i

f wa,v · (rv,i − r v )

∑

v∈Ka,i

f wa,v

,

(27)

where r a is the average of ratings provided by user a, rv,i is the rating of item i provided by user v , f wa,v represents the final similarity weight between users a and v calculated using Eq. (26), and Ka,i indicates a subset of users in the nearest neighborhood of user a who have rated item i. The nearest neighborhood of user a is obtained using the following equation: Ka = v ∈ U ⏐f wa,v > θ ,

⏐

{

}

(28)

where U is the set of all users in the system and θ is a threshold value for the final similarity weights between users. The reliability of the predicted ratings is calculated based on two positive and negative factors. The positive factor is based on the summation of the final similarity weights between the target user a and those in the nearest neighbors set. This factor has a positive effect on the reliability measure, in which the higher value of the positive factor makes a higher score for the reliability measure, and vice versa. Therefore, the following equation is used to calculate the positive factor:

(

S

)

fS Sa,i = 1 −

S + Sa,i

,

(29)

where S is the median of Sa,i values, and Sa,i indicates the summation of final similarity weights between user a and those in its nearest neighborhood who have rated item i. Therefore, the value of Sa,i can be calculated as follows: Sa,i =

∑

f wa,v .

(30)

v∈Ka,i

The negative factor is calculated based on the variance of the ratings provided by users in the nearest neighbors set. This factor has a negative effect on the reliability measure; its higher values lead to reduce the value of the reliability measure. Therefore, the following equation is used to calculate the negative factor:

( fV (Va,i ) =

rmax − rmin − Va,i rmax − rmin

7

)γ (31)

f wa,v · (rv,i − r v − Pa,i + r a )2

∑

v∈Ka,i

Va,i =

∑

v∈Ka,i

f wa,v

(32)

and the value of parameter γ is calculated as follows: ln 0.5

γ = ln

(33)

rmax −rmin −V rmax −rmin

where V denotes the median of Va,i values in the system. Finally, the combination of the positive and negative factors is used to calculate the reliability measure. For this purpose, the geometric average of the factors is used to calculate the reliability measure, as follows:

( (

)

(

Ra,i = fS Sa,i · fV Va,i

)fS (Sa,i ) ) 1+f (1S ) S a ,i

(34)

where Ra,i is the reliability value of the predicted rating pa,i obtained using Eq. (27). The calculated reliability values can be used to evaluate the quality of the predicted ratings; higher reliability value indicates the higher quality for a predicted rating. Thus, the accuracy of the predictions depends on the value of the reliability measure. 4.4. Improving initial neighborhood using confidence measure After calculating the reliability values of the predicted ratings, a new mechanism is proposed to enhance the quality of the ratings with low reliability. The predicted ratings for which reliability values are less than a threshold value can be identified as unreliable ratings. The aim of the proposed neighborhood improvement mechanism is to identify ineffective users from the nearest neighbors set of the users. To this end, a confidence measure is introduced which is calculated using the reliability values of the predicted ratings. The effectiveness of the users in the target user’s neighborhood is evaluated using the confidence measure. The main idea of the proposed mechanism is that some of the users in the neighborhood set might not provide enough information for the prediction process. Moreover, the proposed mechanism can help to find unreliable implicit relationships between the users by identifying the ineffective users. Such ineffective users can be removed from the initial neighborhood set to improve the accuracy of the predictions. To this end, a threshold value (α ) is used in the proposed method to decide unreliable predicted ratings, i.e. the ratings with reliability value less than the threshold α are denoted as unreliable, and thus will be recalculated by the proposed mechanism. The unreliable predicted ratings are determined as follows: UR = {pa,i |Ra,i < α}

(35)

where UR denotes the set of the unreliable predicted ratings and Ra,i is the reliability value for user a and item i calculated using Eq. (34). The confidence value between the target user and those in its neighborhood is calculated as follows:

∑ Ca,v = √∑

i∈Ia,v

i∈Ia,v

Ra,i (ra,i − r a )Rv,i (rv,i − r v )

R2a,i (ra,i − r a )2

√∑

i∈Ia,v

(36)

R2v,i (rv,i − r v )2

where Ca,v is the confidence value between the users a and v . A threshold value (β ) is used to evaluate the confidence values of the users in the neighborhood set, and those with confidence values less than the threshold β are removed from the neighborhood set of the target user. Thus, a new neighborhood is obtained for recalculating the predicted rating pa,i ∈ UR, as follows: Kane,i w = v ∈ Ka,i |Ca,v > β ,

{

}

(37)

Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

8

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where Kane,i w is the new neighborhood of user a for target item i, and Ka,i is the initial neighbors set of the user a calculated using Eq. (28). The main advantage of the proposed mechanism is to evaluate the predicted ratings calculated based on the explicit and implicit relationships between the users. The performance of social recommender systems can be improved by using the reliability and confidence measures. Moreover, this leads to remove unreliable implicit relationships obtained by using the proposed link prediction approach. 4.5. Recommendation In this step, the improved neighborhood of the target user is used to recalculate the predicted ratings with low reliability values. The new rating of item i given by user a is calculated as follows:

∑ w pne a ,i

= ra +

w v∈Kane ,i

∑

f wa,v rv,i − r v

w v∈Kane ,i

(

f wa,v

) ,

(38)

where Kane,i w is the new neighborhood set of the user a calculated using Eq. (37). Finally, a set of items with the highest predicted ratings is suggested to the target user as the recommendations list. The pseudo code of the proposed method is shown in Fig. 2. 4.6. Computational complexity analysis The proposed method consists of five main steps:

• (1) Users’ network construction: the user–item rating matrix and explicit trust relationships between users ( are )used to construct a network, with complexity of O |U |2 |I | where |U | and |I | are the number of users and items, respectively. • (2) Predicting implicit relationships in users’ network: a link prediction approach is used to predict the implicit relationships between users based on Dempster–Shafer theory. To this end, the correlation coefficient between users and their common neighbors is used to calculate the implicit relationships, for which the complexity depends on the number of ˆ is the average number common neighbors. Suppose that CN of common neighbors; thus, the complexity of the second ( ) ˆ . step is O |U |2 CN • (3) Evaluating the reliability of predicted ratings: the quality of predicted ratings is evaluated using a reliability measure, with complexity of O(|U | |I |). • (4) Improving initial neighborhood using confidence measure: a confidence measure is used to identify ineffective users in the initial neighborhood of the users, which are then removed from this (neighborhood. Thus, the complexity of ) the fourth step is O |U |2 |I | . • (5) Recommendation: the new reliable ratings are predicted using Eq. (38) for which the complexity is O(|U | |I |). Moreover, these predicted ratings should be sorted to obtain a list of recommendations, for which the complexity is O(|U | |I | log |I |). Therefore, the complexity of the fifth step is O(|U | |I | + |U | |I | log |I |). Finally, the total complexity of the proposed method can be calculated by summing the complexity of all steps which is equal ˆ + |U | |I | (2 + log |I |)). to O(2 |U |2 |I | + |U |2 CN 5. Experiments Several experiments are conducted in this section to compare the performance of the proposed method (SoRIR) with other recommendation methods. The algorithms are applied on three well-known datasets and their performance is compared in terms

of seven evaluation metrics. The details of the datasets, evaluation measures, and sensitivity analysis of the proposed algorithm on its controllable parameters are discussed in the following. 5.1. Datasets Three datasets including Epinions,1 Flixster,2 and FilmTrust3 are used to conduct the experiments. Epinions is a dataset collected from a website where people can review products across multiple categories such as movies, computers and sports. The users can assign a rating to each item in the range of 1 (bad) to 5 (excellent) with step 1. Moreover, the users can express their trust statements with others. This dataset contains 49,290 users and 139,738 different items. Flixster dataset is a social movie site, in which the users can make friendship relationships and assign their rates to the movies in the range of 0.5 (min) to 4.0 (max) with step 0.5. For simplicity, a subset of Flixster dataset with 10,000 users and their corresponding ratings and friendship relationships is randomly selected in the experiments. FilmTrust dataset consists of 1986 users, 2071 items, and 35,497 ratings. The users can express their interests by assigning ratings to the items in the range of 0.5 (min) to 4.0 (max). Moreover, the link information among the users is used as social information in FilmTrust dataset. In the experiments, 5-fold cross validation approach is used to split the datasets into five different folds. To conduct the experiments, four folds are considered as training set and the remaining fold as test set in each run. This procedure is repeated in five runs and the average of the results is reported as the final result. 5.2. Evaluation metrics Seven evaluation metrics are considered, including mean absolute error (MAE), root mean square error (RMSE), precision, recall, catalog coverage (CC), diversity, and novelty. MAE and RMSE are two common evaluation measures in the field of recommender systems to calculate the accuracy of predictions. To this end, the average of differences between predicted ratings and real ratings are considered as the prediction error. These evaluation metrics can be calculated as follows:

∑n MAE =

i=1

|ri − pi |

 n  n 1 ∑ RMSE = √ (ri − pi )2 n

(39)

(40)

i=1

where ri and pi are respectively the real and predicted rating of item i, and n is the number of all ratings predicted by the recommendation method. It should be noted that lower MAE and RMSE values indicate better performance for the recommendation method. Precision evaluates the proportion of the number of relevant recommended items to the length of the recommendation list. On the other hand, recall evaluates the proportion of the number of relevant recommended items to the number of items that are relevant in the test set. The higher values of the precision and recall show better performance for the recommendation method. To calculate precision and recall metrics, we need to transform the ratings into a binary scale including relevant and non-relevant items [45]. It should be noted that Epinions dataset contains 1 http://www.trustlet.org/datasets/download_epinions 2 http://www.cs.sfu.ca/~sja25/personal/datasets/ 3 http://trust.mindswap.org/FilmTrust

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Fig. 2. The pseudo-code of the proposed recommender system.

5-point scale ratings, while Flixster and FilmTrust datasets provide the ratings in the range of 0.5 to 4.0. Therefore, in the experiments, the ratings that are larger than 3 are considered as relevant and the remaining ones are considered as non-relevant. Precision and recall metrics are calculated as follows:

|relev ant items recommended| (41) |all items retriev ed and recommended| |relev ant items recommended| Recall = (42) |all relev ant items retriev ed and not recommended| Precision =

It should be noted that CC measure, which is expressed as the percentage of the items in the catalog that are ever recommended to users, has been less often used to evaluate the performance of recommendation methods [45]. This measure is usually calculated on a set of recommendations formed at a single point in time by taking the union of the top-N recommendations for each user. In the simplest case, to compute CC, first the top-N recommendation list for each user is obtained by the recommendation method, and then the union of all the recommended items is formed as a set of distinct items. Finally, the size of this set is divided by the total number of available items in the system. Therefore, CC refers to the percentage of distinct items in the top-N recommendation lists of users which indicates that how the recommender system uses all the available items in the recommendation process [46,47]. This measure is calculated as follows: CC =

Ir n

(43)

where Ir is the total number of distinct items provided for the users in the recommendations list. The higher value of CC shows better performance for the recommendation method.

Diversity is another important measure used to evaluate the degree of differences between the items recommended to a user that is calculated by evaluating the similarity values between the item pairs in the recommendation lists. The following equation is used to calculate the diversity measure:

∑|U |

Div ersity =

u=1

div ersityu

(44)

|U |

where div ersityu =

1

∑ ∑

|Lu | (|Lu | − 1)

[1 − s (i, j)]

(45)

i∈Lu j∈Lu ,j̸ =i

and Lu is the recommendations list provided for user u. s (i, j) indicates the similarity value between items i and j, which can be calculated using the cosine similarity function, as follows:

∑

s (i, j) = √∑

u∈U

ru,i .ru,j

2 u∈U ru,i

∑

u∈U

ru2,j

.

(46)

Novelty metric refers to the degree of difference between the items recommended to users and the items already experienced by the users. This measure is calculated using the Shannon entropy [48] as follows: Nov elty = −

∑

p(i|s) log 2p(i|s),

(47)

i∈I

where p(i|s) is the probability of item i being drawn from all of the recommendations lists generated by system s, which is calculated as follows: p (i|s) = ∑

|{u ∈ U |i ∈ Lu }| . j∈I |{u ∈ U |j ∈ Lu }|

(48)

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Fig. 3. The performance of the proposed algorithm as a function of parameter θ for the case when all users are considered.

5.3. Sensitivity analysis of the parameters In this section, several experiments are conducted based on different values of the tunable parameters of the proposed method. The parameter θ is used as a threshold value of the final similarity weights between the users to calculate the initial neighbors set using Eq. (28). Figs. 3 and 4 show the performance of the algorithm in terms of different evaluation metrics for different values of θ for all users and cold start users, respectively. Cold start users are those with less than five ratings made on the items. As it can be seen from these results, increasing the value of θ results in decreasing MAE and RMSE values, and thus improving the performance. One might expect such results, as increasing the value of θ leads to increasing the similarity weights between the target user and those in its neighborhood set. On the other hand, diversity, novelty and CC values decrease when the value of θ increases from 0.1 to 0.9. Increasing θ leads to reduce the number of users in the neighborhood set of the target user, which impacts diversity, novelty and CC measures. Finally, increasing the value of θ has a positive effect on precision and recall metrics. In the proposed method, a reliability measure is used to evaluate the quality of predicted ratings (see Eq. (34)). Some experiments are conducted to show the correlation between the

reliability values and the accuracy of the predicted ratings. To this end, first the predicted ratings are divided into several intervals based on their reliability values, where each predicted rating belongs to one of the considered intervals based on its reliability value. Then, the prediction error (MAE) of each interval is calculated by considering all the predicted ratings belonging to that interval and calculating MAE measure for them. Fig. 5 shows MAE values of the predicted ratings based on their reliability values. These results indicate that the predicted ratings with higher reliability values have a lower prediction error. Therefore, one may argue that the accuracy of the predicted ratings depends on the reliability measure. In other words, there is a positive correlation between the reliability value and the accuracy of the predicted rating. The parameter α is used as a threshold value in the neighborhood improvement step of the proposed method (Eq. (35)) to decide the unreliable predicted ratings. The ratings with reliability value less than α are denoted as unreliable and recalculated based on an updated neighborhood set. The performance of the proposed algorithm for different values of α is shown in Figs. 6 and 7 for all users and cold start users, respectively. These results indicate that MAE and RMSE decrease and precision and recall increase as α increases from 0.1 to 0.9 for both cases with all users

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Fig. 4. The performance of the proposed algorithm as a function of parameter θ for the case when only cold start users are considered.

Fig. 5. MAE for different intervals of reliability values of the predicted ratings.

and cold start ones. Thus higher values of α have a positive effect on the accuracy of the predictions. However, the performance of the proposed method is decreased in terms of diversity, novelty and CC measures, by increasing α . In the proposed neighborhood improvement mechanism, a confidence measure (Eq. (36)) is used to identify ineffective users from the nearest neighbors set of the users. The ineffective users

are those of the neighbors who have negative effect on the accuracy of the predicted rating. Our hypothesis is that the neighbors with higher confidence value with the target user can predict more accurate ratings. To prove this, some experiments are conducted to show the correlation between the confidence values and the accuracy of the predicted ratings. First, the neighborhood sets of the users are divided into several intervals based on their confidence values. Then, the unseen items of the users are calculated for all intervals based on the neighbors belonging to each interval. Finally, the prediction error of each interval is calculated by considering all the predicted ratings belonging to this interval and calculating MAE measure for them (Fig. 8). As it can be seen from these results, the predicted ratings which are calculated using the neighbors with higher confidence values have lower prediction error. Therefore, it is clear that the accuracy of the predicted ratings depends on the confidence values of the neighbors and there is a positive correlation between the confidence value and the accuracy of the predicted ratings. The experiments are repeated to evaluate the effects of different values of the parameter β on the performance of the proposed method. This parameter is used as a threshold value for the confidence measure to remove ineffective users from the neighborhood set of a target user. Figs. 9 and 10 study this for

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Fig. 6. The performance of the proposed algorithm as a function of parameter α for the case when all users are considered.

the cases with all users and only cold start users, respectively. These results indicate that MAE, RMSE, diversity, novelty and CC measures decline by increasing β , and thus higher values for β have positive effect on MAE and RMSE measures, while being negative for diversity, novelty and CC measures. Also, higher values of the parameter β lead to increase the performance of the proposed method based on precision and recall metrics. It should be noted that the number of users who can be removed from the neighborhood set increases when the value of β is increased from 0.1 to 0.9. This leads to increase the reliability and also the accuracy of the predictions, which is also seen by reduction in MAE and RMSE metrics. However, diversity, novelty and CC depend on the number of users in the neighborhood set. 5.4. Performance comparison with other recommender systems In this section, experimental results are reported to show the effectiveness of the proposed method in comparison with other recommendation algorithms. To this end, the proposed method is compared with several state-of-the-art recommendation methods including TARS [41], SoRec [49], SoReg [50], TrustMF [51], SocialMF [52], TrustSVD [53], Merge [54], RTCF [55], IPG [56],

CETrust [57], CALA-WLP [9], and SPR_SVD++ [23]. It should be noted that MAE and RMSE evaluate the accuracy of predicted ratings (see Eqs. (39) and (40)). However, SPR_SVD++ is a personalized ranking model that predicts the rank of recommended items in the recommendations list instead of predicting unknown ratings. Therefore, the results of MAE and RMSE metrics are not reported for SPR_SVD++. In the proposed method, parameter θ is used as a threshold value for the final similarity weights between users to obtain the nearest neighbors using Eq. (28). Moreover, parameter α is used as a threshold value for the reliability values to obtain unreliable predicted ratings using Eq. (35). Finally, parameter β is used as a threshold value for the confidence values between users to obtain the new neighborhood of users using Eq. (37). These are critical parameters for the proposed method, and as the results show (Figs. 3–10), recommendation performance depends on their proper choices. Such a numerical procedure is required to choose the best values for these parameters. To this end, 5-fold cross validation approach is used to obtain the optimal values for parameters θ , α , and β as a trade-off between different evaluation measures. Therefore, for the proposed method, the value of the parameter θ is set to θ = 0.6 for Epinions and Flixster datasets

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Fig. 7. The performance of the proposed algorithm as a function of parameter α for the case when only cold start users are considered. Table 1 Experiment results on the Epinions dataset for all users. The top-performing algorithm is denoted by bold font, while the one with the second-top performance is denoted by underlined font. The recommendations list length is set to top-10.

Fig. 8. MAE for different intervals of confidence values for the neighbors of target users.

and θ = 0.5 for FilmTrust dataset. In addition, the value of the parameter α is set to α = 0.7 for Epinions dataset and α = 0.6 for Flixster and FilmTrust datasets. Finally, the value of the parameter β is set to β = 0.6 for Epinions dataset and β = 0.7 for Flixster and FilmTrust datasets.

Methods

MAE

RMSE

Precision

Recall

CC

Diversity

Novelty

TARS SoRec SoReg TrustMF SocialMF TrustSVD Merge RTCF IPG CETrust CALA-WLP SPR_SVD++ SoRIR

0.826 0.874 0.926 0.804 0.813 0.786 0.798 0.638 0.781 0.812 0.809 – 0.552

1.143 1.112 1.216 1.048 1.054 1.021 1.032 0.925 1.018 1.051 1.049 – 0.873

0.078 0.089 0.093 0.231 0.283 0.352 0.338 0.315 0.327 0.319 0.296 0.378 0.412

0.263 0.361 0.397 0.497 0.572 0.597 0.568 0.542 0.572 0.536 0.564 0.623 0.651

0.291 0.343 0.349 0.389 0.412 0.435 0.368 0.307 0.311 0.326 0.339 0.372 0.514

0.415 0.415 0.425 0.435 0.441 0.482 0.503 0.463 0.423 0.467 0.452 0.473 0.491

7.068 6.935 6.973 7.236 7.459 7.968 8.176 7.784 7.218 7.382 7.012 7.567 8.415

The results of the experiments on Epinions dataset are reported in Tables 1 and 2 for all users and cold start ones, respectively. It is seen that the proposed method (SoRIR) obtains

Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

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Fig. 9. The performance of the proposed algorithm as a function of parameter β for the case when all users are considered.

the best results in terms of MAE, RMSE, precision, recall, CC and novelty measures. RTCF has the second best MAE and RMSE, while TrustSVD and Merge are the second best for CC and novelty measures, respectively. These results indicate that the proposed method is the second best performer on diversity measure for all users, while the best-performer algorithm is Merge. The experiments are repeated for cold start users and the results are shown in Table 2. SoRIR is the top-performer in terms of all evaluation metrics. It has significantly better performance than the second-top performer. For example, MAE of SoRIR is 0.608 that is almost 20% lower than RTCF (0.725) with the second-best performance. CC of SoRIR in almost 30% higher than TrustSVD, which is the second top-performer after SoRIR in terms of this metric. Therefore, incorporating reliable implicit relationships into the recommendation process significantly boost the recommendation performance by providing more effective recommendations for the users. Table 3 shows the results of the experiments based on Flixster dataset for all users. The proposed method obtains the best results for all evaluation measures, followed by CETrust for MAE, RMSE, diversity and novelty measures, and TrustSVD for CC measure. Moreover, Merge and SPR_SVD++ obtain the second best performance for precision and recall metrics, respectively. Table 4 shows the results on the same dataset when only cold start users

Table 2 Experiment results on the Epinions dataset for cold start users. The topperforming algorithm is denoted by bold font, while the one with the second-top performance is denoted by underlined font. The recommendations list length is set to top-5. Methods

MAE

RMSE

Precision

Recall

CC

Diversity

Novelty

TARS SoRec SoReg TrustMF SocialMF TrustSVD Merge RTCF IPG CETrust CALA-WLP SPR_SVD++ SoRIR

0.864 0.892 1.104 0.835 0.846 0.825 0.837 0.725 0.839 0.851 0.843 – 0.608

1.158 1.136 1.412 1.114 1.127 1.102 1.123 0.997 1.125 1.131 1.126 – 0.936

0.097 0.126 0.159 0.198 0.215 0.321 0.292 0.274 0.254 0.284 0.269 0.345 0.372

0.201 0.327 0.368 0.472 0.493 0.517 0.486 0.465 0.462 0.459 0.478 0.504 0.563

0.182 0.239 0.246 0.273 0.324 0.332 0.258 0.195 0.217 0.231 0.235 0.269 0.445

0.242 0.241 0.245 0.247 0.253 0.289 0.307 0.264 0.257 0.249 0.268 0.271 0.337

5.912 5.856 6.029 6.243 6.489 7.125 7.586 6.861 7.059 6.713 6.894 6.937 8.024

are considered. SoRIR obtains the best results in all evaluation measures except for diversity measure, in which it has the second best performance after TrustSVD. CETrust is the second best in MAE and RMSE measures, while TrustSVD obtains the second

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Fig. 10. The performance of the proposed algorithm as a function of parameter β for the case when only cold start users are considered. Table 3 Experiment results on the Flixster dataset for all users. The top-performing algorithm is denoted by bold font, while the one with the second-top performance is denoted by underlined font. The recommendations list length is set to top-10. Methods

MAE

RMSE

Precision

Recall

CC

Diversity

Novelty

TARS SoRec SoReg TrustMF SocialMF TrustSVD Merge RTCF IPG CETrust CALA-WLP SPR_SVD++ SoRIR

0.873 0.735 0.762 0.864 0.756 0.719 0.885 0.725 0.735 0.657 0.749 – 0.618

1.134 0.962 1.013 1.126 0.978 0.935 1.157 0.952 0.958 0.897 0.971 – 0.834

0.297 0.304 0.325 0.452 0.503 0.531 0.581 0.564 0.546 0.567 0.559 0.572 0.635

0.521 0.576 0.594 0.642 0.701 0.754 0.698 0.686 0.768 0.786 0.743 0.791 0.847

0.213 0.235 0.219 0.288 0.292 0.337 0.269 0.284 0.246 0.253 0.264 0.283 0.419

0.283 0.293 0.295 0.302 0.318 0.374 0.353 0.291 0.352 0.391 0.348 0.361 0.398

5.230 5.214 5.247 5.312 5.394 5.689 5.425 5.259 5.476 5.786 5.419 5.536 6.053

best CC and novelty measures. Also, SPR_SVD++ is the second top-performer based on precision and recall metrics. Finally, the experiments are conducted on FilmTrust dataset and the results are reported in Tables 5 and 6 for all users and cold start users, respectively. When the experiments are performed on all users, SoRIR has the best performance in terms of MAE, RMSE,

precision, recall, CC and novelty measures, while having the third rank for diversity measure (Table 5). In this case, TrustSVD and IPG are the best and second best performers, respectively. The results on FilmTrust dataset are shown in Table 6 for cold start users. These results indicate that MAE, RMSE, precision, CC and novelty values of the proposed method are significantly better

Please cite this article as: S. Ahmadian, N. Joorabloo, M. Jalili et al., A social recommender system based on reliable implicit relationships, Knowledge-Based Systems (2019) 105371, https://doi.org/10.1016/j.knosys.2019.105371.

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S. Ahmadian, N. Joorabloo, M. Jalili et al. / Knowledge-Based Systems xxx (xxxx) xxx

Table 4 Experiment results on the Flixster dataset for cold start users. The topperforming algorithm is denoted by bold font, while the one with the second-top performance is denoted by underlined font. The recommendations list length is set to top-5. Methods

MAE

RMSE

Precision

Recall

CC

Diversity

Novelty

TARS SoRec SoReg TrustMF SocialMF TrustSVD Merge RTCF IPG CETrust CALA-WLP SPR_SVD++ SoRIR

0.952 0.863 0.937 0.891 0.877 0.823 0.965 0.814 0.862 0.796 0.872 – 0.752

1.154 1.079 1.151 1.125 1.086 1.028 1.173 0.996 1.072 0.985 1.081 – 0.947

0.379 0.397 0.435 0.571 0.594 0.625 0.605 0.589 0.581 0.611 0.568 0.643 0.659

0.436 0.488 0.511 0.591 0.637 0.685 0.638 0.617 0.628 0.652 0.627 0.691 0.723

0.164 0.185 0.173 0.241 0.246 0.271 0.217 0.235 0.192 0.213 0.216 0.229 0.358

0.228 0.231 0.235 0.245 0.263 0.296 0.281 0.237 0.274 0.278 0.251 0.264 0.287

3.559 3.573 3.611 3.712 3.768 3.976 3.893 3.647 3.914 3.815 3.697 3.758 4.216

Table 5 Experiment results on the FilmTrust dataset for all users. The top-performing algorithm is denoted by bold font, while the one with the second-top performance is denoted by underlined font. The recommendations list length is set to top-10. Methods

MAE

RMSE

Precision

Recall

CC

Diversity

Novelty

TARS SoRec SoReg TrustMF SocialMF TrustSVD Merge RTCF IPG CETrust CALA-WLP SPR_SVD++ SoRIR

0.763 0.628 0.668 0.631 0.638 0.607 0.696 0.648 0.684 0.626 0.658 – 0.531

0.924 0.810 0.875 0.810 0.837 0.787 0.858 0.852 0.879 0.803 0.862 – 0.726

0.292 0.298 0.301 0.284 0.315 0.302 0.375 0.352 0.297 0.361 0.334 0.356 0.397

0.556 0.598 0.601 0.592 0.634 0.614 0.651 0.645 0.582 0.572 0.629 0.638 0.665

0.312 0.351 0.334 0.384 0.391 0.416 0.423 0.369 0.348 0.362 0.367 0.383 0.497

0.219 0.234 0.242 0.235 0.251 0.267 0.263 0.229 0.265 0.261 0.249 0.256 0.264

5.043 4.935 5.068 5.279 5.362 5.897 5.724 5.213 5.991 5.983 5.761 5.842 6.271

Table 6 Experiment results on the FilmTrust dataset for cold start users. The topperforming algorithm is denoted by bold font, while the one with the second-top performance is denoted by underlined font. The recommendations list length is set to top-5. Methods

MAE

RMSE

Precision

Recall

CC

Diversity

Novelty

TARS SoRec SoReg TrustMF SocialMF TrustSVD Merge RTCF IPG CETrust CALA-WLP SPR_SVD++ SoRIR

0.827 0.670 0.771 0.674 0.680 0.661 0.745 0.729 0.726 0.653 0.756 – 0.579

1.098 0.857 1.034 0.867 0.907 0.853 0.914 0.925 0.911 0.837 1.018 – 0.798

0.171 0.187 0.193 0.215 0.223 0.224 0.265 0.246 0.211 0.208 0.237 0.254 0.281

0.449 0.454 0.469 0.678 0.703 0.615 0.588 0.574 0.572 0.556 0.597 0.625 0.659

0.195 0.229 0.214 0.272 0.289 0.327 0.334 0.256 0.223 0.241 0.252 0.265 0.381

0.069 0.076 0.072 0.075 0.079 0.084 0.082 0.072 0.078 0.082 0.073 0.076 0.083

3.636 4.346 4.285 4.124 4.318 4.956 4.867 3.952 4.223 4.694 4.431 4.675 5.126

than other recommendation methods. TrustSVD obtains the best diversity value, followed by the proposed method. Moreover, the proposed method has the third rank for recall metric after SocialMF and TrustMF as the best and second best performers, respectively. 6. Conclusions This paper proposed a social recommender system based on reliable implicit relationships among users. To this end, the user– item rating matrix and also the explicit trust relationships are used to construct a graph hosing connections between users. The

users are considered as the nodes of the graph and the edge weights are determined based on the combination of the similarity and trust values between them. A link prediction approach is applied on the graph to find implicit relationships among the users. To this end, Dempster–Shafer theory is used to calculate the implicit relationships by combining a series of mass functions. Moreover, the reliability of the predicted ratings is evaluated using a reliability measure. The unreliable ratings are recalculated using an effective mechanism by removing ineffective users from the neighborhood of the target user. The ineffective users are identified using a confidence measure between the users. Experimental results on three well-known datasets showed that the proposed method outperforms other recommendation methods in terms of different evaluation metrics including mean absolute error, root mean square error, precision, recall, catalog coverage, novelty, and diversity. CRediT authorship contribution statement Sajad Ahmadian: Conceptualization, Methodology, Software, Writing - original draft, Visualization. Nima Joorabloo: Conceptualization, Methodology, Writing - original draft, Visualization. Mahdi Jalili: Conceptualization, Methodology, Validation, Writing - review & editing, Visualization, Supervision. Yongli Ren: Methodology, Validation, Writing - review & editing, Visualization. Majid Meghdadi: Methodology, Validation, Supervision. Mohsen Afsharchi: Methodology, Validation, Supervision. Acknowledgment This research is supported in part by Australian Research Council through project No. DP170102303. References [1] H. Wu, K. Yue, Y. Pei, B. Li, Y. Zhao, F. Dong, Collaborative Topic Regression with social trust ensemble for recommendation in social media systems, Knowl.-Based Syst. 97 (2016) 111–122. [2] S. Ahmadian, M. Meghdadi, M. Afsharchi, Incorporating reliable virtual ratings into social recommendation systems, Appl. Intell. 48 (2018) 4448–4469. [3] M. Mao, J. Lu, G. Zhang, J. Zhang, Multirelational social recommendations via multigraph ranking, IEEE Trans. Cybern. 47 (2017) 4049–4061. [4] W. Wang, G. Zhang, J. Lu, Member contribution-based group recommender system, Decis. Support Syst. 87 (2016) 80–93. [5] M.E.J. Newman, Power laws Pareto distributions and Zipf’s law, Contemp. Phys. 46 (2005) 323–351. [6] J. Tang, H. Gao, X. Hu, H. Liu, Exploiting homophily effect for trust prediction, in: Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, 2013, pp. 53–62. [7] E. Cho, S.A. Myers, J. Leskovec, Friendship and mobility: user movement in location-based social networks, in: Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2011, pp. 1082–1090. [8] J. Leskovec, L.A. Adamic, B.A. Huberman, The dynamics of viral marketing, ACM Trans. Web 1 (2007). [9] B. Moradabadi, M.R. Meybodi, Link prediction in weighted social networks using learning automata, Eng. Appl. Artif. Intell. 70 (2018) 16–24. [10] B. Zhang, H. Zhang, M. Li, Q. Zhao, J. Huang, Trust traversal: A trust link detection scheme in social network, Comput. Netw. 120 (2017) 105–125. [11] C. Lin, R. Xie, X. Guan, L. Li, T. Li, Personalized news recommendation via implicit social experts, Inform. Sci. 254 (2014) 1–18. [12] D.H. Alahmadi, X.J. Zeng, ISTS: Implicit social trust and sentiment based approach to recommender systems, Expert Syst. Appl. 42 (2015) 8840–8849. [13] F. Qian, S. Zhao, J. Tang, Y. Zhang, SoRS: Social recommendation using global rating reputation and local rating similarity, Physica A 461 (2016) 61–72. [14] L.C. Hui, L.S. Jye, H.H. Ling, A social recommendation method based on the integration of social relationship and product popularity, Int. J. Hum. Comput. Stud. (2018). [15] T. Guo, J. Luo, K. Dong, M. Yang, Differentially private graph-link analysis based social recommendation, Inform. Sci. 463 (2018) 214–226.

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