Enhanced recommender system using predictive network approach

Accepted Manuscript Enhanced recommender system using predictive network approach Hadi Zare, Mina Abd Nikooie, Parham Moradi

PII: DOI: Reference:

S0378-4371(19)30055-X https://doi.org/10.1016/j.physa.2019.01.053 PHYSA 20484

To appear in:

Physica A

Received date : 15 August 2018 Revised date : 8 November 2018 Please cite this article as: H. Zare, M.A. Nikooie and P. Moradi, Enhanced recommender system using predictive network approach, Physica A (2019), https://doi.org/10.1016/j.physa.2019.01.053 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Highlights (for review)

Highlights 

A predictive network based approach to alleviate the sparsity problem



Compute the similarity network based on information network ideas



Employ the hidden connections and unknown ratings of users via link prediction and

diffusion rules 

Experimental results are performed on benchmark datasets



The results show that the proposed approach outperformed the earlier methods.

*Manuscript Click here to view linked References

Enhanced Recommender System using Predictive Network Approach Hadi Zarea,∗, Mina Abd Nikooieb , Parham Moradic a b

Department of Network Science and Technologies, University of Tehran, Tehran, Iran Department of Network Science and Technologies, University of Tehran, Tehran, Iran c Department of Computer Engineering, University of Kurdistan, Sanandaj, Iran

Abstract Recommender systems have a unique role in on-line trading companies due to building relationships among users and items to reduce big information load. There exist several successful algorithms in the recommender systems like collaborative filtering (CF), although most of them suffer from the sparsity problem. Here, we propose a novel integrated recommendation approach based on the tools of network science to mitigate the sparsity problem. The link prediction approach is used to extract hidden structures among users, and diffusion of information is applied to enhance the rating matrix in our proposed framework. Not only, the sparsity problem is alleviated through a more efficient way, but the proposed approach also can be applied in a hybrid way with the well-known algorithms. The proposed approach is examined on several datasets via standard evaluation criteria. The experimental results show that the proposed approach outperforms the earlier methods. ∗

Corresponding author Email addresses: [email protected] (Hadi Zare ), [email protected] (Mina Abd Nikooie), [email protected] (Parham Moradi) Preprint submitted to Physica A

November 8, 2018

Keywords: Recommender Systems, Diffusion, Complex Networks, Link Prediction. 1. Introduction Intelligent recommender systems introduce an ingenious tool to facilitate users in selection of relevant information in the world of web applications like e-commerce, social networking services, and online watching and reading among the large available information in Internet [1]. The process of designing of recommender systems depends on several elements such as, type of data, filtering method, choice of model, type of prediction algorithms, scalability, and performance of the system [2]. Initially the data contain different types of inputs like users’ ratings and profiles meta-data, items attributes, users’ connections, and contextual information. Filtering algorithms characterize the internal properties of recommender systems by finding relations among users and items where this primary step can be classified into “Collaborative Filtering” (CF), “Content Based Filtering” (CBF), and “Hybrid Filtering”. The choice of model depends on either explicitly using data for recommendation “memory-based”, or implicitly applying the data through a generative learned model from them “model-based”. A variety of predictive techniques are applied in recommender systems such as Bayesian networks, nearest neighbors classifier, and matrix factorization approach [3], [48]. The scalability and sparsity are two important factors in planning a recommendation system. 2

CF approach is one of the successful filtering algorithms that is initiated by the tendency of users with similar patterns to express common interests in the future [4]. There have been a multitude of works to improve significantly the performance of a recommender system using CF approach using the connections between users and items, which is denoted by U-I matrix [2]. The input of many recommender systems is U-I matrix which suffers from the sparsity and cold start issues. There exist a variety of different approaches to deal with these problems which are typically adding useful information such as employing the prior ratings [5], trust propagation [6], community based recommendation [7]. Here, the idea is to exploit the social network tools to alleviate the sparsity problem of recommender systems. Our motivation is based on the link prediction approach to discover the hidden relationships in the induced similarity network among users to mitigate the sparsity problem. In addition, a novel similarity measure is used along with the concept of meta-paths on information networks to evaluate the similarity between pair of users. Moreover, the diffusion of information is devised to predict the unknown ratings of users in the rating matrix. Hence, the proposed approach is built via link prediction and diffusion of information to relieve deficiencies of the earlier ones’. This framework can be considered as an assistant for any memory based recommender algorithms to enhance their accuracy without adding significant computational costs. The proposed approach enables us to improve the recommendation methods significantly as compared to the earlier 3

ones. Our contribution in this work is summarized as: • Investigate a novel approach to remedy the sparsity problem in recommender systems via the predictive network tools • Compute the similarity network by applying the meta-paths concept of the information networks • Detect the hidden connections and discover the unknown ratings among the users via link prediction and diffusion techniques • Demonstrate an enriched rating information that can be aligned with any recommender systems The rest of this article is organized as follows. Section 2 introduces related works. Section 3 describes the proposed approach through a stage-wise framework. Section 4 discusses the sensitivity analysis of the method. Section 5 presents the experimental settings and results. Finally, Section 6 concludes the paper and discusses some challenges for future works. 2. Related works Recently, several works are introduced to improve CF approach using the other aspects of existing information in the input data. There are two types of additional data sources. There exist large amount of side information of users and items and visible (or hidden) interconnections between users and

4

items and their characteristics such as time, location, and type of relationships. Marginal information on users and items along with the U-I matrix are explored in the earlier works including the attribute features in a latent based model [8], demographic information via ontological approach [9], and music context features [10]. A variety of works are considered the idea that user preferences would be affected by the context such as time of the purchase, location, season, and planned options by the system that relates the users and items at a special event [16]. Several attempts are developed by applying the contextual information in the recommender systems such as the situation of user rating on food deliveries [17], adopting augmented reality by users contextual information [18] and exploiting the adjective features from user reviews [19]. The aforementioned works are based on the additional sources in the input U-I data, e.g. a branch of works are developed on implicit trust based recommender systems [20], [47]. Moreover, The performance of recommender systems are improved by using social friendship of users in social networks from the users trust (distrust) among themselves and contextual information on users (items) [11]. Moreover, the social network provides a useful framework to extract users (or items) behavior and similarities that can be applied them to find the most similar users in memory and model-based recommender algorithms [3]. Several researchers proposed the user-user connections in a network based recommendation such as random walk approach on bipartite user-item net5

work [12], heat diffusion method [13], graph clustering approach on similarity network [14], time aware recommendation [46] and a review on network based recommendation [15]. There are some works based on exploiting the heterogeneous information network (HIN) in recommendation models. In [40], a linear-weighted hybrid model is presented for recommendation by defined meta-path in HIN. This approach is applied for networks with additional information other than just user and item. SemRec [41] uses of weighted meta-paths for considering rating scores of users to items. In [39] and [44] link prediction approaches based on meta-paths has been proposed. In [42], an interest diffusion methodology in HIN is proposed to deal with sparseness of data. For this purpose, they have used of meta-information of items to personalized recommendations of top-N items and produce a HIN for items. In some recommender systems there isn’t explicit feedback and only the implicit feedback is available. To discover hidden relations among users and items, diffusion is used through implicit feedback data to get users preferences by different meta-paths [43]. In these work the diffusion is used as a concept for using meta-path based similarity approach for finding relation between users and items. In most of the works, accessing to additional information like item’s attributes is necessary. In our work, we exploited the user-item information as our resource to alleviate the sparsity problem through applying network tools. Furthermore, the integration of link prediction with diffusion rules enables us to enrich the available information. Also, we have applied the diffusion rules to enhance 6

the ratings, whereas it was used for similarity computations in the earlier works. 3. Proposed approach

Input User-Item Dataset

Initialization of User-Item Network

Similarity Computation

Compute Meta-Path Similarity in the User-Item Network

Applying Link Prediction in Similarity Network

Edge Prediction Between Users

Update Similarity Matrix by Discovered Connections

Produce Features for Each User Propagate the Rating Information

Applying Diffusion Rules

Enhanced Similarity Matrix and Rating Information

Output of the Algorithm

Figure 1: The flow-graph of the proposed approach

The proposed approach (LDRS) “Link prediction and Diffusion of infor7

mation in Recommender Systems” is outlined by the following main steps, (i) Computing pairwise similarity between users using the meta-paths (ii) Discovering the hidden connections in the induced similarity network through link prediction approach (iii) Propagating the rating information by applying the diffusion rules to predict hidden user’s ratings The aim of first step is to enhance the similarity computation among users by applying the meta-paths. In second step, a link prediction method is applied to discover the hidden interconnections among users to relieve the sparsity problem. Finally, the diffusion rules are applied to predict the hidden ratings with the propagation among similar users in the built-up network. After the above stages, we can apply a CF method on this enriched input to produce more accurate recommendations. The overall scheme of the proposed approach is presented in Figure 1. More details of each step are described in their corresponding sections. User 1

User 2

User 3

5

User 4

1

1

5 2 3

Item 1

4

5

Item 2

2

4

Item 3

3

Item 4

5

Item 5

Figure 2: The network of users and items

8

3

1

Item 6

3.1. Computing Meta-Path based Similarity Most of the memory-based recommender systems are primarily dependent on the way of similarity computation between users. The similarity is measured typically by the available ratings of users. Cosine, Pearson correlation coefficient and nonparametric Spearman association are well-known similarity measures that do not consider the additional information available on the induced networks of users and items [49]. By exploiting the side information of users and items, we can construct a HIN as a generalized network when there exist different types of nodes or links or both of them. In our scenario, users and items is represented as a heterogeneous network with two types of nodes, user and item, along with weighted links which represent users ratings at different items on U-I matrix. A typical example is presented in Figure 2 with 4 users and 6 items with the ratings as weights of links in the network. There are different kinds of nodes and links in the heterogeneous network. The generalized paths named as meta-paths are defined by considering the different types of nodes and links in traversing the paths between two nodes in heterogeneous networks [21]. While the exploitation of whole entities in the network on meta-paths computations is caused more accurate lens on the network, it induces heavy computational complexity to afford in the recommendation algorithm [22]. In this work, the user and item nodes are given in the meta-path computation based on their types. By representing the rating information as a network, one can use the meta-paths for similarity computation among the 9

users. With network traversal via the defined meta-paths, user-user paths by crossing from common items would be generated. The weights of links in the meta-paths improve the accuracy of similarity computation between users.

User Rate Item Rate User Rate ∈ [1−5]

{1,2} User {1,2} Item User

𝐏𝟏

User {3,4} Item {3,4} User

𝐏𝟐

User

{5}

Item

{5}

User

𝐏𝟑

Figure 3: Schematic description of the meta-paths division for similarity computation

We consider the user-item-user “SPSim” meta-paths aligned with the rating information wights in similarity computations. The proposed SPSim method is a similarity computation approach through the weighted meta-paths. Considering the fact that rating information is in range of {1, 2, 3, 4, 5}, we divided the rating information to three groups, R1 = {1, 2} “low scores”, R2 = {3, 4} “average scores”, R3 = {5} “high scores” to get more meaningful results. Figure 3 shows the details of this scenario. The main user-item-user meta-path is divided to three weighted sub meta-paths,{P 1 , P 2 , P 3 }, based on ratings that is denoted in Figure 3. For example, P 1 is the sub meta-path along with the rating values in R1 group. By considering this division in rating information, the network of User-Item can be divided to three subnetworks which is depicted in Figure 4. Indeed, the proportions of each users on rating information are captured along these groups to attain better insight on the nearness of the users to each other. The proposed similarity approach

10

User 1 Item 1

Item 1

2

2

3

3

4

3

3

4

2

4

5

Scores 1 & 2 Scores 3 & 4 Score 5

6

U-I Matrix of Scores 3 & 4

U-I Matrix of Scores 1 & 2

User 1

2

4

5

User 1 6

Item 1

2

3

2

U-I Matrix of Score 5

User 1

4

3

4

5

6

Item 1

2

3

2

4

3

User

1

2

3

4

User

1

2

3

4

User

1

2

3

4

1

0

0

2

0

1

0

0

1

0

1

0

1

0

0

2

0

0

0

0

2

0

0

0

1

2

1

0

0

1

3

2

0

0

0

3

1

0

0

0

3

0

0

0

0

4

0

0

0

0

4

0

1

0

0

4

0

1

0

0

4

5

6

+ User

1

2

3

4

1

0

1

3

0

2

1

0

0

2

3

3

0

0

0

4

0

2

0

0

Figure 4: Similarity computing through the division of U-I network in 3-fold and counting the number of meta-paths between users in each network

is given as, SimSP Sim (u, v) =

3 X

i Puv

(1)

i=1

i denotes the ith weighted sub meta-path between users u and where the Puv

v and i consists of the three sub meta-paths on our rating groups. 3.2. Link Prediction in Similarity Network of Users Here, we employ a link prediction method to discover the hidden connections among users from the similarity matrix to address the data sparsity problem of U-I matrix. There are several methods on link prediction, which are mainly dependent on topological features of the network. Common neighbors, Jaccard, Adamic–Adar and Preferential Attachment [23], and weighted proximity measure [24] are the well-known methods for computing the similarity score score(u, v) between two nodes u and v. In our proposed

11

User 2

User 2

User 1

User 1

User 4

0.37

User 3

User 6

User 4

0.9

0.9

0.41

User 6

User 3

Use r5

User 5 User 7

User 7

(a)

(b)

Figure 5: Weighted Similarity network of users: (a) before link prediction, (b) after link prediction (predicted links are shown in red color)

approach, we apply the wighted Adamic–Adar (WAA) method [24] on the weighted similarity network of users. This method is configured on the structural properties of the network and weights on links that is presented in (2),

score(u, v) =

X

z∈Γ(u)∩Γ(v)

W (u, z) + W (v, z) P 2 log( z0 ∈Γ(z) W (z, z 0 ))

(2)

where for users u and v, Γ(u), W (u, v) and Γ(u) ∩ Γ(v) denote the set of neighbors of u in the network, the similarity between u and v as the weights link of network, and the set of common neighbors of u and v. Figure 5 represents the effect of link prediction on the similarity network among users, where the links in built-in network means the positive or negative tendency between users. 3.3. Enhancing Rating Information via Diffusion Users’ ratings information is regarded as one of the important ingredients on recommender systems. The main challenge is how to discover and exploit 12

Positive Neighbors of Desired User

19 41 12

19

50 6 89 2

0.1

0.1

0.5

0.5

0.56 0.9

19 2

Desired User

0.56

Diffused items

19 41 50

41 50

+

19 2

0.9

Figure 6: The diffusion process on item propagation where the items 41 and 50 are added to the red user’s rating information due to the impact of diffusion on PN

existing patterns in user’s ratings to spread them in an efficient way to enrich the rating information. Spreading information in networks is an important concept that can help us to extract more information [45] . We proposed the diffusion of innovations approach on the rating information to predict the unknown user’s ratings. The diffusion behaves like an epidemic propagation from one node to another considering an acceptance threshold which is applied in many domains like opinion, rumor and technology adoption [25]. By defining a threshold for diffusion, θd , user u will accept item i if N (u, i) ≥ θd where N (u, i) is the number of neighbors of user u who accepted item i. The rating information can be expanded by exploiting the enhanced similarity matrix. To this aim, the similarity matrix is considered as a network of users along with the rating information as nodes features. We denote the set of “Positive Neighbors” (PN ) for a given user u to represent its neighbors with the property of positive similarity score with u. In order to enhance rating

13

information, a process applies on each user by employing on its PN to consider only the opinion influence of its neighbors with the same direction of the desired user. The effect of diffusion is depicted in Figure 6 which represents a similarity network of seven users (nodes) with the rating information as nodes’ features. The red colored user accepts items with corresponding id numbers 41 and 50 by the impact of diffusion from its PN. Each user would accept items that are rated by at least θd percent of his positive neighbors. In proposed method, we set the θd = 0.1 from the empirical results. The ratings of user u to diffused item i, is computed as,

ru,i =

P

v∈C(u,i) P

sim(u, v).rv,i

v∈C(u,i)

sim(u, v)

, ∀i ∈ Items(u).

(3)

Where in (3), sim(u,v) is the similarity between users u and v and ru,i is the rating of u on item i. The (3) implies that important users have more effect on the ratings prediction. The C(u,i) is the positive neighbors of user u who have rated item i and Items(u) is the union of items that user u has not rated with at least rating to θd percent of PN of u. Finally, enhanced ratings and similarity networks of users can be used as an enriched input of any recommendation method. Here, we report the effect of link prediction and diffusion on three wellknown dataset, Filmtrust, Epinion and Flixster [34]. The number of the added links after link prediction is presented in Table 1. Indeed the link

14

prediction is used for predict relation between users to exploit the enriched network in the next step. In the next step, user-user network is applied for enhancing user-item information by using item diffusions in the network (Table 2). These results reveal that the positive impact on extraction of hidden connections among users and user’s behavior diffusing on ratings value. Table 1: Effect of link prediction on similarity network of users on three benchmark datasets

DataSet

Before LP

After LP

predicted links(number)

predicted links(%)

Filmtrust Epinion Flixster

2,133,518 21,449,662 24,331,456

2,239,380 21,525,000 24,585,000

105,586 73,338 253,544

5% 0.4% 1%

Table 2: Effect of diffusion on Ratings (User-Item) based on three well-known datasets

DataSet

Ratings before diffusion

Ratings after diffusion

Added information (%)

Filmtrust Epinion Flixster

30,496 67,149 216,695

98,827 988,342 2,560,035

2.5% 1% 4%

3.4. The proposed algorithm Algorithm 1 describes the LDRS approach. The Input is original user ratings (R) that is accessible in all recommender systems. The output of the LDRS are the enhanced rating information (Re ) and similarity matrix (Se ). In lines 5 and 6, the number of paths between users is computed from three weighted sub meta-paths as in Figure 3. Then, the similarity between users (Smain ) is calculated by SPSim approach in line 7. Lines 9–14 show the link 15

Algorithm 1 LDRS algorithm 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20:

Input: Ratings Information (R) Output: Enhanced Rating Information Re and Similarity Matrix Se NI = Number of Items in R NU = Number of Users in R Consider sub meta-paths {P 1 , P 2 , P 3 } (Fig. 3) Construct U-U matrices via each meta-path (Fig. 4) Calculate Smain by Eq.1 Normalize Smain to [-1,1] for each u, v ∈ {1, ..., N U } do if Smain (u, v) = 0 and u 6= v do Calculate Se (u, v) by Eq.2 end if end for Se = Smain + Se for each u ∈ {1, ..., N U } do Find (Items(u)) set Calculate Re (u, Item(u)) by Eq. 3 end for Re = R + Re return Re and Se

prediction operation on similarity network Smain . The next step, lines 15-18, is devoted to enrich the rating information via diffusion rules. The definition of (Items(u)) is given in 3.3. Then by Re = R + Re , the enhanced rating information is integrated with main rating information. The final line of the LDRS produces the output Re and Se , that can be aligned with a common recommendation approach such as CF based methods. 3.5. The Computational Complexity of LDRS The computational complexity of LDRS is computed based on Algorithm 1. Where N , k and M denote the number of users, average degree 16

of network, number of items and m << M is the number of items that meet the acceptance decision of diffusion respectively. Similarity computation is done one time in O(N 2 ). Then link prediction should be applied for the elements of similarity matrix by (O(N k 2 ). The final stage is for enhancing rating through diffusion operation by using updated similarity matrix, which the time complexity is O(N m). Therefore, The computational time complexity of LDRS would be O(N 2 + N m + N k 2 ) for enhancing inputs of recommender method. Due to the common factor of similarity computation in any recommendation method, LDRS just adds a linear time complexity O(N (m + k 2 )). 4. Sensitivity Analysis The proposed approach mainly depends on computation of the link prediction approach that may influence on the robustness and performance of the LDRS. We conducted a bunch of experiments to examine the sensitivity of the LDRS to initialization of link prediction methods. The well-known link prediction methods are employed in our sensitivity experiments namely Adamic-Adar (AA), Preferential Attachment (PA), Common Neighbor (CN), and Resource Allocation (RA). Due to applying weighted network in our procedure, the weighted version of each method is used (denoted by WAA, WPA , WCN and WRA) [24], [35]. Table 3 presents the formula and computational complexity of each link prediction method [36]. Initially, we investigate the effect of link prediction methods on ratings 17

and similarity network based on FilmTrust dataset. According to the results in Figure 7, while there is a slight difference among the different link prediction methods on adding information to the ratings and edges to similarity network, the performance of WPA and WAA are somewhat better than the others. Table 3: Used link prediction methods for selection in LDRS Method

Formula (score(x, y)) X

WAA

z∈Γ(x)∩Γ(y)

WPA 0

X

0

x ∈Γ(x)

WCN

W (x , x) ×

0

X

0

y ∈Γ(y)

O(N K 2 )

X

W (x, z) + W (y, z) P W (z 0 , z) 0 z ∈Γ(z)

O(N K 2 )

Effect of Link Prediction Methods on Similarity Network Number of Available Links (106 )

Number of Available Ratings (104 )

Effect of Link Prediction Methods on Ratings 10 8 6 4 2

Main

WAA

WPA

O(N 2 K 2 )

W (y , y)

W (x, z) + W (y, z) 2

z∈Γ(x)∩Γ(y)

0

O(N K 2 )

X

z∈Γ(x)∩Γ(y)

WRA

Computation Complexity

W (x, z) + W (y, z) P 2 × log( z0 ∈Γ(z) W (z 0 , z))

WCN

Link Prediction Methods

2.0

1.5

1.0

0.5

0.0

WRA

Main

WAA

WPA

WCN

Link Prediction Methods

WRA

Figure 7: Comparison of link prediction Methods effect in FilmTrust on Ratings and Similarity Network

Then, the performance of LDRS with four link prediction method are 18

compared on FilmTrust dataset based on RMSE and RC as standard evaluation criteria[26]. Figure 8 represents the results based on integrated LDRS on CF by considering different link prediction methods. The obtained results show that LDRS attains similar results based on these four link prediction methods with a slight differences among them. Due to the similar behavior of WAA and WPA and superiority of them than the others, we examine the effect of them on LDRS through the Epinions dataset[4]. The results of the integrated LDRS with CF along with the main CF approach are reported in Figure 9. The RMSE results reveal that a significant impact of employing WAA method versus WPA. Furthermore, the attained RC values verifies the strength of WAA method than the WPA on this dataset. Due to the lower computational complexity and equal or better performance of WAA link prediction method than the other well-known link prediction methods, this method is selected as initial link prediction approach in our procedure. 2.0 1.8

FilmTrust dataset

FilmTrust dataset

1.00

Main WAA WPA WCN WRA

0.95 0.90

1.6 RC

RMSE

0.85 0.80

1.4

0.75 1.2 1.0 0.0

0.70 0.1

0.2

0.3 0.4 0.5 0.6 Neighborhood Threshold CF

0.7

0.8

0.9

0.65 0.0

Main WAA WPA WCN WRA 0.1

0.2

0.3 0.4 0.5 0.6 Neighborhood Threshold CF

0.7

0.8

0.9

Figure 8: Comparison of LDRS with different link prediction methods in FilmTrust by RMSE and RC

19

Epinion dataset

3.6

Epinion dataset

0.70

Main WAA WPA

0.65

3.4

0.60 0.55

3.0

RC

MAE

3.2

0.45

2.8

0.40

Main WAA WPA

2.6 2.4 0.0

0.50

0.1

0.2

0.3 0.4 0.5 0.6 Neighborhood Threshold CF

0.7

0.8

0.35 0.9

0.30 0.0

0.1

0.2

0.3 0.4 0.5 0.6 Neighborhood Threshold CF

0.7

0.8

0.9

Figure 9: The effect of WAA and WPA on LDRS in Epinions dataset by RMSE and RC evaluation criteria

5. Experiments The details of implementation and experimental results are described in this section. We demonstrate the strength of the proposed approach via the benchmark datasets and standard evaluation measures. A variety of wellknown recommender techniques [26] are investigated to verify the benefits of LDRS approach. 5.1. Experimental Setup We employ three real-world datasets, namely FilmTrust [26], Epinions [4] and Flixster [6] in our experiments. FilmTrust contains user’s ratings on a variety of different movies. Epinions is a dataset of a general review Epinions.com website where users express their opinions about products and their trust about each other’s. Flixster contains the rating information of

20

Table 4: The main characteristics of the datasets

DataSet

Users

Items

Ratings

Density

FilmTrust Epinions Flixster

1508 40,163 53,213

2,071 139,738 18,197

35,497 664,824 409,803

1.14% 0.051% 0.04%

users of Flixster.com website on movies and their interests. Table 4 presents a brief summary of the datasets. The 5-fold cross-validation is applied for training and testing. Each data is randomly divided into five folds and four folds are applied in training set and the remaining as the test. We iterate this process for five times to test on all of the folds and report the average performance on test data sets in the result. There exist several metrics for evaluating recommender systems including mean absolute error (MAE ), root mean square error (RMSE ) [4], diversity [37], novelty [38]. The mean absolute error (MAE ) and root mean square error (RMSE ) are well-known and more common evaluation measures on recommender algorithms which are employed to compare with different techniques in this work. The MAE and RMSE are defined as,

M AE =

RM SE =

P

u,i∈Ω

sP

|ru,i − pu,i | |Ω|

u,i∈Ω (ru,i

21

|Ω|

− pu,i )2

(4)

(5)

Table 5: Overview of the state-of-the-art methods

Methods

Description

Reference

PMF MCFM RSTE BiasedMF SoReg TrustSVD TrustMF

Probabilistic Matrix Factorization Multifaceted Collaborative Filtering Model Recommendation with Social Trust Ensemble Biased Matrix Factorization Social Regularized recommender Trust-based matrix factorization Social collaborative filtering by trust

[27] [28] [29] [30] [31] [32] [33]

where Ω is the test set and |Ω| is the size of test set. The actual and predicted rating of user u to item i are denoted by ru,i and pu,i . Moreover, we use Rating Coverage (RC) measure in our evaluations that represents ratio of the predictable ratings (PR) over size of test dataset. At first, we use base CF methods to see the effect of proposed approach namely the base Collaborative Filtering “CF ” method, the clustering kmedoids CF based approach “ KCF ”, and the modified version of KCF based method “KCFT ” [26]. Then, we employ a bunch of state-of-the-art recommender methods to evaluate the effectiveness of the proposed method in comparison with probabilistic matrix factorization “PMF ” [27], multifaceted collaborative filtering model “ MCFM ” [28], recommendation with social trust ensemble “ RSTE ” [29], biased matrix factorization “ BiasedMF ” [30], social regularized recommender “SoReg” [31], trust-based matrix factorization technique “TrustSVD” [32], and social collaborative filtering by trust “ TrustMF ” [33]. All methods summarized in Table 5 along with Baseline “UserAvg” method are implemented using LibRec, a Java library for recom-

22

mendation algorithms [34]. 5.2. Experimental Results In this Subsection, we first test the effect of the proposed approach on base CF methods and then report the results of an integrated version of it in compare with the state-of-the-art methods. 5.2.1. Comparison with base CF FilmTrust Dataset

2.0 1.8

Epinion Dataset

3.6

CF LDRS

Flixster Dataset

3.0

CF LDRS

3.4 2.5 3.2

1.4

RMSE

RMSE

RMSE

1.6 3.0

2.0

2.8 1.5

1.2 1.0 0.0

2.6 0.1

0.2

0.3

0.4

0.5

0.6

0.7

Neighborhood Threshold CF

0.8

0.9

2.4 0.0

CF LDRS 0.1

0.2

0.3

0.4

0.5

0.6

0.7

Neighborhood Threshold CF

0.8

0.9

1.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Neighborhood Threshold CF

0.8

0.9

Figure 10: RMSE performance results of LDRS on CF versus the base one.

Initially, the proposed approach is examined on original CF and results are reported in Figure 10. The results reveal that LDRS integrated on CF can effectively decrease the value of RMSE as compared to CF and improves the accuracy on each dataset. Indeed, exploiting the LDRS approach is yielded to produce enriched neighborhood set to be used on rating prediction in CF. Figure 10 indicates that more differences exist between CF and LDRS on Epinions and Flixster than FilmTrust. In addition, there exist less sensitivity of the integrated LDRS approach to threshold parameter than CF method. It is demonstrated the effect of LDRS on CF approach through the MAE

23

FilmTrust Dataset

1.2

2.4

MAE

MAE

2.6

1.1

2.0

0.9

1.8 0.1

0.2

0.3

0.4

0.5

0.6

0.7

Neighborhood Threshold CF

0.8

0.9

1.6 0.0

CF LDRS

2.2 2.0

2.2

1.0

Flixster Dataset

2.6 2.4

2.8

1.3

0.8 0.0

Epinion Dataset

3.0

CF LDRS

MAE

1.5 1.4

1.8 1.6 1.4 1.2

CF LDRS 0.1

0.2

0.3

0.4

0.5

0.6

0.7

Neighborhood Threshold CF

0.8

1.0 0.9

0.8 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Neighborhood Threshold CF

0.8

0.9

Figure 11: MAE performance results of LDRS on CF versus the base one

measure in Figure 11 which shows the positive impact of the proposed approach. In the same way, we compare the LDRS integrated with KCF and KCFT methods versus the original ones’ by varying the number of clusters from 10 to 100 and the results are reported in Figure 12. The results show positive impact of LDRS on significant reduction of RMSE values. Actually enhancing the rating information in user’s clusters is caused to predictions that are more precise. According to Figure 12, LDRS has more impact on FilmTrust and Flixster datasets compared to Epinions in terms of RMSE results. It is mainly due to the exploiting of clustering techniques in KCF and KCFT and the existing true categories in Epinions that could not be truly uncovered by a clustering approach. In addition, the items in Epinions dataset are from different categories, while the items in FilmTrust and Flixster dataset are just movies. Furthermore, we examine the LDRS integrated on KCF and KCFT methods through the MAE evaluation measure in Figure 13. As this figure shows more significant reductions in MAE error rates occurred on FilmTrust and 24

FilmTrust Dataset

1.65 1.60

KCFT LDRS

1.60 1.55

1.55

1.50

RMSE

1.50

RMSE

FilmTrust Dataset

1.65

KCF LDRS

1.45 1.40

1.45 1.40 1.35

1.35

1.30

1.30

1.25

1.25 10

1.20 10

20

30

40

50

60

70

Number of Clusters

80

90

100

20

30

Epinion Dataset

70

80

90

100

70

80

90

100

70

80

90

100

3.8

RMSE

RMSE

60

KCFT LDRS

3.9

3.8

3.7

3.6

3.5 10

50

Epinion Dataset

KCF LDRS

3.9

40

Number of Clusters

3.7

3.6

20

30

40

50

60

70

Number of Clusters

80

90

3.5 10

100

Flixster Dataset

2.2

20

50

60

KCFT LDRS

2.1

2.0

40

Number of Clusters Flixster Dataset

2.2

KCF LDRS

30

2.0

RMSE

RMSE

1.9 1.8

1.8 1.7

1.6

1.6 1.5

1.4 10

20

30

40

50

60

70

Number of Clusters

80

90

100

1.4 10

20

30

40

50

60

Number of Clusters

Figure 12: RMSE performance results of LDRS on KCF and KCFT versus the base ones on FilmTrust, Epinion and Flixter Datasets.

25

FilmTrust Dataset

1.20

1.10

1.10

1.05

1.05

1.00

1.00

0.95

0.95

0.90

0.90

0.85 10

20

40

50

60

70

Number of Clusters

80

90

100

0.85 10

Epinion Dataset

3.7

3.4

3.4

MAE

3.5

3.3

3.2

3.1

3.1 30

40

50

60

70

Number of Clusters

80

90

3.0 10

100

Flixster Dataset

1.6

70

80

90

100

20

30

40

50

60

70

80

90

100

70

80

90

100

Number of Clusters Flixster Dataset

KCFT LDRS

1.4

MAE

MAE

60

KCFT LDRS

1.5

1.4 1.3

1.3

1.2

1.2

1.1

1.1

1.0 10

50

Epinion Dataset

1.6

KCF LDRS

1.5

40

Number of Clusters

3.3

3.2

20

30

3.6

3.5

3.0 10

20

3.7

KCF LDRS

3.6

MAE

30

KCFT LDRS

1.15

MAE

MAE

1.15

FilmTrust Dataset

1.20

KCF LDRS

20

30

40

50

60

70

Number of Clusters

80

90

100

1.0 10

20

30

40

50

60

Number of Clusters

Figure 13: MAE performance results of LDRS on KCF and KCFT versus the base ones on FilmTrust, Epinion and Flixter Datasets.

26

Flixster datasets than the Epinions dataset which is probably due to the existing different categories in the Epinions. FilmTrust Dataset

1.00

Epinion Dataset

0.70 0.65

0.95

0.9

0.60

0.90

0.8

0.55

0.80

0.50

RC

RC

RC

0.85

0.45

0.75

0.7 0.6

0.40

CF LDRS

0.70 0.65 0.0

0.1

0.2

0.5

0.35 0.3

0.4

0.5

0.6

0.7

Neighborhood Threshold CF

0.8

0.9

0.30 0.0

0.1

0.2

0.4

0.5

0.6

0.7

0.8

0.4 0.0

0.9

CF LDRS 0.1

0.2

0.92

0.4

0.5

0.6

0.7

0.8

0.9

70

80

90

100

70

80

90

100

(c)

Epinion Dataset

0.6

0.3

Neighborhood Threshold CF

(b)

FilmTrust Dataset

0.94

0.3

Neighborhood Threshold CF

(a) 0.5

Flixster Dataset

0.95

KCF LDRS

0.90

0.90

RC

0.86

RC

0.4

0.88

RC

Flixster Dataset

1.0

CF LDRS

0.85

0.3

0.84

0.80 10

20

30

0.80

0.2

KCF LDRS

0.82

40

50

60

70

Number of Clusters

80

90

0.1 10

100

20

30

(d)

50

60

70

Number of Clusters

80

90

100

0.75 10

KCF LDRS 20

30

(e)

FilmTrust Dataset

0.94

40

50

60

(f)

Epinion Dataset

0.6

0.92

40

Number of Clusters

0.5

Flixster Dataset

1.00

KCFT LDRS

0.95

0.90

RC

RC

0.90

RC

0.4

0.88 0.86

0.3

0.85

0.2

0.80

0.84

KCFT LDRS

0.82 0.80 10

20

30

40

50

60

70

Number of Clusters

(g)

80

90

100

0.1 10

20

30

40

50

60

70

Number of Clusters

(h)

80

90

100

0.75 10

KCFT LDRS 20

30

40

50

60

Number of Clusters

(i)

Figure 14: The RC results of LDRS integrated on CF, KCF and KCFT on datasets in Table 4, where (a-c) CF, (d-f) KCF and (g-i) KCFT based results

RC is the other widely used measure to see the relative frequency of items predicted by the recommender systems. We examine our approach along with the CF, KCF, and KCFT to evaluate their performances. The 27

obtained results in Figure 14 show us the effect of LDRS approach on significant improvement of RC values in comparison with the base approaches. In addition, it is observed that the robustness of the integrated approach on CF versus the threshold effect as well as less decrease in RC than the original one according to Figure 14a to 14c. The similar increasing values in RC is achieved by applying LDRS on KCF and KCFT methods versus the base ones’ (Figure 14d to 14i). Moreover, these figures verify the effect of the proposed approach on the reducing the sparsity problem due to the less sensitivity of RC values with LDRS exploitation. 3.0 2.5

SoReg PMF RSTE

BiasedMF UserAvg TrustSVD

2.5

TrustMF MCFM LDRS

SoReg PMF RSTE

2.0

BiasedMF UserAvg TrustSVD

TrustMF MCFM LDRS

1.5

MAE

RMSE

2.0 1.5

1.0 1.0 0.5

0.5 0.0

FilmTrust

Epinion

0.0

Flixster

FilmTrust

Epinion

Flixster

Figure 15: Performance comparison of the integrated LDRS on MCFM versus the stateof-the-art methods of Table 5

5.2.2. Comparison with the well-known approaches Here, we examine the effect of integration of LDRS on a well-known method MCFM [28] due to its simplicity of the base method to reveal the benefits of enhancement of rating information. Our aim is to introduce an

28

FilmTrust Dataset

1.0

Main Approaches

FilmTrust Dataset LDRS

Main Approaches

1.2

0.8

LDRS

1.0

MAE

RMSE

0.6 0.4

0.8 0.6 0.4

0.2 0.0

0.2

g PMF

SoRe

0.0

RSTE BiasedMFUserAvgTrustSVDTrustMF MCFM

g PMF

SoRe

Epinion Dataset Main Approaches

RSTE BiasedMFUserAvgTrustSVDTrustMF MCFM

Epinion Dataset LDRS

Main Approaches

LDRS

2.0 1.5

RMSE

MAE

1.5 1.0

0.5

0.0

1.0

0.5

g PMF

SoRe

0.0

RSTE BiasedMFUserAvgTrustSVDTrustMF MCFM

g PMF

SoRe

Flixster Dataset Main Approaches

1.0

RSTE BiasedMFUserAvgTrustSVDTrustMF MCFM

Flixster Dataset LDRS

Main Approaches

1.4

LDRS

1.2 1.0

0.6

RMSE

MAE

0.8

0.4

0.8 0.6 0.4

0.2 0.0

0.2

g PMF

SoRe

0.0

RSTE BiasedMFUserAvgTrustSVDTrustMF MCFM

g PMF

SoRe

RSTE BiasedMFUserAvgTrustSVDTrustMF MCFM

Figure 16: Performance comparison of the methods versus the integrated LDRS

effective hybrid method that can be applied in variety of datasets and domains. The state-of-the-arts techniques in Table 5 are deployed to study the strength of LDRS with MCFM approach. The MAE and RMSE comparison measures are applied in our investigation. Figure 15 represents the values of RMSE and MAE via the integrated LDRS on MCFM method versus

29

the state-of-the-art methods in Table 5 on Flixter, FilmTrust and Epinions datasets. The obtained results in these figures reveal that applying of LDRS on MCFM resulted in the improvement of it versus the other well-known approaches on FilmTrust, Epinions and Flixster datasets. In addition, we can apply our approach to the other well-known techniques in Table 5 to examine the usefulness of the LDRS on the performance of those ones’. The Figure 16 shows MAE and RMSE results of these techniques along with the integrated LDRS on each ones. The attained results demonstrate the significant impact of our proposed approach on these recommender techniques to reduce the MAE and RMSE of each technique by as much as the 50% as compared to its base ones. 6. Conclusion and Future Works In this paper, we proposed a novel approach by applying network predictive tools such as link prediction and diffusion rules to remedy the sparsity problem of the user-item data. Experimental results on real-world datasets demonstrated that the proposed approach aligned with the typical simple recommender techniques could effectively improve the performance of recommendation approaches than the base one’s in terms of accuracy and rating coverage. Moreover, exploiting the social network tools on the recommender algorithms yielded to reduce the error rate and promoted their performance significantly. The obtained results on the standard evaluation measures verified that the proposed approach was effective to alleviate the main sparsity 30

problem of the U–I matrix. There are some directions for further investigation on this interesting ongoing research field including, applying the proposed approach to relieve the cold-start problem, incorporating trust and other meta-path definitions in similarity measure computations, and exploiting graph embedding (or representational learning) approaches on meta-path networks. Furthermore, the probabilistic modeling on the density of user–user connections and item-item relations is another direction for further works in this interesting domain. References [1] J. B. Schafer, J. A. Konstan, J. Riedl, E-Commerce Recommendation Applications, Data Mining and Knowledge Discovery 5 (1-2) (2001) 115– 153. [2] J. Bobadilla, F. Ortega, A. Hernando, A. Guti´errez, Recommender systems survey, Knowledge-Based Systems 46 (2013) 109–132. [3] Y. Shi, M. Larson, A. Hanjalic, Collaborative Filtering Beyond the UserItem Matrix: A Survey of the State of the Art and Future Challenges, ACM Comput. Surv. 47 (1) (2014) 3:1–3:45. [4] M. D. Ekstrand, J. T. Riedl, J. A. Konstan, Collaborative Filtering Recommender Systems, Found. Trends Hum.-Comput. Interact. 4 (2) (2011) 81–173.

31

[5] G. Guo, J. Zhang, D. Thalmann, N. Yorke-Smith, Leveraging prior ratings for recommender systems in e-commerce, Electronic Commerce Research and Applications 13 (6) (2014) 440–455. [6] M. Jamali, M. Ester, A Matrix Factorization Technique with Trust Propagation for Recommendation in Social Networks, in: Proceedings of the Fourth ACM Conference on Recommender Systems, RecSys ’10, ACM, New York, NY, USA, 2010, pp. 135–142. [7] P. Zhang, D. Wang, J. Xiao, Improving the recommender algorithms with the detected communities in bipartite networks, Physica A: Statistical Mechanics and its Applications 471 (2017) 147–153. [8] D. Agarwal, B.-C. Chen, Regression-based Latent Factor Models, in: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’09, ACM, New York, NY, USA, 2009, pp. 19–28. [9] N. Ranjbar Kermany, S. H. Alizadeh, A hybrid multi-criteria recommender system using ontology and neuro-fuzzy techniques, Electronic Commerce Research and Applications 21 (2017) 50–64. [10] P. Knees, M. Schedl, A Survey of Music Similarity and Recommendation from Music Context Data, ACM Trans. Multimedia Comput. Commun. Appl. 10 (1) (2013) 2:1–2:21.

32

[11] I. Konstas, V. Stathopoulos, J. M. Jose, On Social Networks and Collaborative Recommendation, in: Proceedings of the 32Nd International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR ’09, ACM, New York, NY, USA, 2009, pp. 195–202. [12] T. Zhou, J. Ren, M. Medo, Y.-C. Zhang, Bipartite network projection and personal recommendation, Physical Review E 76 (4) (2007) 046115. [13] T. Zhou, Z. Kuscsik, J.-G. Liu, M. Medo, J. R. Wakeling, Y.-C. Zhang, Solving the apparent diversity-accuracy dilemma of recommender systems, Proceedings of the National Academy of Sciences 107 (10) (2010) 4511–4515. [14] P. Moradi, S. Ahmadian, F. Akhlaghian, An effective trust-based recommendation method using a novel graph clustering algorithm, Physica A: Statistical Mechanics and its Applications 436 (2015) 462–481. [15] F. Yu, A. Zeng, S. Gillard, M. Medo, Network-based recommendation algorithms: A review, Physica A: Statistical Mechanics and its Applications 452 (2016) 192–208. [16] G. Adomavicius, B. Mobasher, F. Ricci, A. Tuzhilin, Context-Aware Recommender Systems, AI Magazine 32 (3) (2011) 67–80. [17] C. Ono, Y. Takishima, Y. Motomura, H. Asoh, Context-Aware Preference Model Based on a Study of Difference between Real and Supposed

33

Situation Data, in: User Modeling, Adaptation, and Personalization, Springer, Berlin, Heidelberg, 2009, pp. 102–113. [18] J. Grubert, T. Langlotz, S. Zollmann, H. Regenbrecht, Towards Pervasive Augmented Reality: Context-Awareness in Augmented Reality, IEEE Transactions on Visualization and Computer Graphics PP (99) (2016) 1–1. [19] X. Xu, K. Dutta, C. Ge, Do adjective features from user reviews address sparsity and transparency in recommender systems?, Electronic Commerce Research and Applications 29 (2018) 113–123. [20] R. Andersen, C. Borgs, J. Chayes, U. Feige, A. Flaxman, A. Kalai, V. Mirrokni, M. Tennenholtz, Trust-based Recommendation Systems: An Axiomatic Approach, in: Proceedings of the 17th International Conference on World Wide Web, WWW ’08, ACM, New York, NY, USA, 2008, pp. 199–208. [21] Y. Sun, J. Han, X. Yan, P. S. Yu, T. Wu, PathSim: Meta path-based top-k similarity search in heterogeneous information networks, in: Proceedings of the VLDB Endowment 4 (11), VLDB Endowment, 2011, pp. 992–1003. [22] Y. Gu, B. Zhao, D. Hardtke, Y. Sun, Learning Global Term Weights for Content-based Recommender Systems, in: Proceedings of the 25th In-

34

ternational Conference on World Wide Web, International World Wide Web Conferences Steering Committee, 2016, pp. 391–400. [23] D. Liben-Nowell, J. Kleinberg, The link-prediction problem for social networks, Journal of the American society for information science and technology 58 (7) (2007) 1019–1031. [24] T. Murata, S. Moriyasu, Link prediction of social networks based on weighted proximity measures, in: Web Intelligence, IEEE/WIC/ACM International Conference On, IEEE, 2007, pp. 85–88. [25] J. Kleinberg, Cascading behavior in networks: Algorithmic and economic issues, Algorithmic game theory 24 (2007) 613–632. [26] G. Guo, J. Zhang, N. Yorke-Smith, Leveraging multiviews of trust and similarity to enhance clustering-based recommender systems, Knowledge-Based Systems 74 (2015) 14–27. [27] R. Salakhutdinov, A. Mnih, Probabilistic Matrix Factorization, in: Proceedings of the 20th International Conference on Neural Information Processing Systems, NIPS’07, Curran Associates Inc., USA, 2007, pp. 1257–1264. [28] Y. Koren, Factorization Meets the Neighborhood: A Multifaceted Collaborative Filtering Model, in: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’08, ACM, New York, NY, USA, 2008, pp. 426–434. 35

[29] H. Ma, I. King, M. R. Lyu, Learning to Recommend with Social Trust Ensemble, in: Proceedings of the 32Nd International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR ’09, ACM, New York, NY, USA, 2009, pp. 203–210. [30] Y. Koren, R. Bell, C. Volinsky, others, Matrix factorization techniques for recommender systems, Computer 42 (8) (2009) 30–37. [31] H. Ma, D. Zhou, C. Liu, M. R. Lyu, I. King, Recommender Systems with Social Regularization, in: Proceedings of the Fourth ACM International Conference on Web Search and Data Mining, WSDM ’11, ACM, New York, NY, USA, 2011, pp. 287–296. [32] G. Guo, J. Zhang, N. Yorke-Smith, A novel recommendation model regularized with user trust and item ratings, IEEE Transactions on Knowledge and Data Engineering 28 (7) (2016) 1607–1620. [33] B. Yang, Y. Lei, J. Liu, W. Li, Social Collaborative Filtering by Trust, IEEE Transactions on Pattern Analysis and Machine Intelligence 39 (8) (2017) 1633–1647. [34] G. Guo, J. Zhang, Z. Sun, N. Yorke-Smith, Librec: A java library for recommender systems, in: Posters, Demos, Late-breaking Results and Workshop Proceedings of the 23rd Conference on User Modelling, Adaptation and Personalization (UMAP), 2015.

36

[35] B. Zhu, Y. Xia, Link prediction in weighted networks: A weighted mutual information model, PloS one 11 (2) (2016) e0148265. [36] F. Gao, K. Musial, C. Cooper, S. Tsoka, Link Prediction Methods and Their Accuracy for Different Social Networks and Network Metrics, https://www.hindawi.com/journals/sp/2015/172879/ (2015). doi: 10.1155/2015/172879. [37] A. Javari, M. Jalili, A Probabilistic Model to Resolve Diversity—accuracy Challenge of Recommendation Systems, Knowl. Inf. Syst. 44 (3) (2015) 609–627. [38] A. Javari, M. Jalili, Accurate and Novel Recommendations: An Algorithm Based on Popularity Forecasting, ACM Transactions on Intelligent Systems and Technology (TIST) 5 (4) (2015) 56. [39] M. Jalili, Y. Orouskhani, M. Asgari, N. Alipourfard, M. Perc, Link prediction in multiplex online social networks, Royal Society Open Science 4 (2) (2017) 160863. [40] F. Vahedian, R. Burke, B. Mobasher, Multirelational Recommendation in Heterogeneous Networks, ACM Trans. Web 11 (3) (2017) 15:1–15:34. [41] C. Shi, Z. Zhang, Y. Ji, W. Wang, P. S. Yu, Z. Shi, SemRec: A personalized semantic recommendation method based on weighted heterogeneous information networks, World Wide Webdoi:10.1007/ s11280-018-0553-6. 37

[42] M. Gupta, P. Kumar, R. Mishra, Interest Diffusion in Heterogeneous Information Network for Personalized Item Ranking, in: Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, CIKM ’17, ACM, New York, NY, USA, 2017, pp. 2087–2090. [43] X. Wang, X. Liu, X. Xu, A recommendation algorithm for collaborative denoising auto-encoders based on user preference diffusion, in: 2017 8th IEEE International Conference on Software Engineering and Service Science (ICSESS), 2017, pp. 447–450. [44] A. Javari, M. Jalili, Cluster-Based Collaborative Filtering for Sign Prediction in Social Networks with Positive and Negative Links, ACM Transactions on Intelligent Systems and Technology (TIST) 5 (2) (2014) 24. [45] M. Jalili, M. Perc, Information cascades in complex networks, Journal of Complex Networks 5 (5) (2017) 665–693. [46] F. Rezaeimehr, P. Moradi, S. Ahmadian, N. N. Qader, M. Jalili, TCARS: Time- and Community-Aware Recommendation System, Future Generation Computer Systems 78 (2018) 419–429. [47] M. M. Azadjalal, P. Moradi, A. Abdollahpouri, M. Jalili, A trust-aware recommendation method based on Pareto dominance and confidence concepts, Knowledge-Based Systems 116 (2017) 130–143.

38

[48] M. Ranjbar, P. Moradi, M. Azami, M. Jalili, An imputation-based matrix factorization method for improving accuracy of collaborative filtering systems, Engineering Applications of Artificial Intelligence 46, Part A (2015) 58–66. [49] G. Adomavicius, A. Tuzhilin, Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions, IEEE transactions on knowledge and data engineering 17 (6) (2005) 734–749.

39