Modeling Trust-Aware Recommendations With Temporal Dynamics in Social Networks

In recent years, user’s trust has gained attention in recommender systems. Trust plays a vital role in the recommendation of online products. Trust is a dynamic feature which evolves with passage of time and varies from person to person. Trust-based cross domain recommender systems suggest items to the users usually by ratings, provided by similar users, often not available in the same domain. However, due to the sparse rating scores, recommender systems cannot generate up-to-the-mark recommendations. In this research, we solved a user cold start problem, mainly by modeling preference drift on a temporal basis. We tried to solve this problem by adopting one of the scenarios of cross domain of ‘No Overlap’ using cross domain information. In this work, we proposed a model called Trust Aware Cross Domain Temporal Recommendations (TrustCTR) that predict the rating of an item about an active user from the most recent time. We generated user features and item features by using latent factor model and trained the proposed model. We also introduced the concept of trust relevancy that shows the degree of trust, computed the trusted neighbors in target domain for an active user belonging to a source domain, and predicted the ratings of items for cold start users. We performed experiments on public datasets Ciao and Epinions and used these datasets in cross domain form such as the categories of Ciao as source domain and Epinions as the target domain. We selected five different domains, having a higher proportion of rating sparsity, for observing the performance of our approach using MAE, RMSE, and F-measure. Our approach is a viable solution of cold start problem and offers effective recommendations We also compared the model with state-of-the-art methods; the model generates satisfactory results.


I. INTRODUCTION
In the recent era, the information over the web is growing day by day and it is difficult for the users to find out the relevant information. The social networks and e-commerce applications such as Amazon, Alibaba, Epinions, Aliexpress, eBay, Walmart, and many others, shifted the information retrieval problem to filter out the personalized information. Recommender systems were developed in 90s to employ community opinions and identify the exciting content from a potentially overwhelming set of choices [51]. The recommender systems The associate editor coordinating the review of this manuscript and approving it for publication was Dezhong Peng.
should have the ability to recommend a new item, based on (i) users' recommendations, and (ii) purchase history of other items belonging to the same category. In the case of a new user, since there is no history, recommender systems may depend upon the way that how new users behave and interact with the new items. The objective is to analyze items in which new users have possibly interested.
Collaborative-filtering methods estimate the ratings and recommend the items to users with similar preferences by considering previous recommendations [46]. The collaborative filtering techniques usually have lacks of information about user's behavior which limits their learning and predictive ability for generating quality recommendations [22].
The recommender systems are also suffered because of change in trust relationship among the users, with time [11]. Besides that, users' ratings about items by the recommender systems might be out-of-date and become noisy [12]. Matrix factorization techniques are better to compute the accuracy and popularity of preferences. They are based on latent factorized models [25]. However, these models have limitations; (i) they consider value of item features favored by all users [8], (ii) do not take into account the conditional preferences [35], and (iii) do not consider social effects on user preferences such that social relationships, social influence among peers and homophily effect [32], [75].
Data sparsity makes it difficult for collaborative filtering systems to generate accurate predictions [24]. The recommender systems usually provide recommendations in a particular domain facing sparsity problem, in addition to issues associated with new users and items [53]. In data sparsity, users can rate the few items or cannot assign a rating to them. It also refers to a new community problem, where ratings assigned to the items are low as compared to the number of items, so the useful recommendations are not possible [4].
Nowadays, the cold start problem is the key challenge faced by recommender systems [52]. In the cold start problem, the system cannot produce a recommended list of items to the users [56]. The cold start problem is associated with the situation, i.e., new user, item, and community [52], [80], [4]. This problem occurs when a new user arrives to the system and system do not have adequate information for performing similarity measures which degrades the quality of recommendations. In recent years, the cold start problem is addressed by employing hybrid models. Cold start recommender systems make use of auxiliary information, multimodal information, and side information to overcome the recommendation problems.
In a cross-domain scenario, trust-based recommenders recommend the items to the source users by exploiting target domains. Cross domain recommender systems introduce a new dimension to solve the mentioned problems; this can be done by transferring knowledge from a source domain to the target domain [8], [23]. Cross-domain recommender systems recommend the items to the users from items rating provided by similar users, which are not available in the same domain.
The more advanced types of recommender systems address cross-domain recommendation scenarios, where items related to source domains have been recommended in the target domains and vice versa [8]. In a cross-domain systems, two domains are considered distinct, and knowledge is transferred from a dense to sparse domain. Cross domain recommendation systems are based on four different scenarios; categorized into user overlap, item overlap, full overlap, and no overlap. In user overlap, some users are familiar with the source and target domains and have assigned ratings to items. In item overlap, some items are common in both domains and some user's rate items. In full overlap, all users and items are overlapped. In no overlap, there exists no common users and items across two domains [8].
According to sociology, trust is a set of expectations shared by all those involved in an interactions or networks [109]. The recommender systems based on trust are helpful in improvement of quality recommendations, solve data sparsity problem, and cold start problem.
In recommender systems, preferences are grouped into six main types; feature preferences [44], [77], feature value preferences [79], temporal dynamics [27], social influence [21], [38], [40], [76], [84], conditional preferences [35], user biases, and item biases [28]. Feature value preferences show the favorability of item values by users. Temporal dynamics refer to drift of user-items rating with time. Social influence is an effect of social communities on user preferences. Conditional preferences are the dependencies between the item features and their respective values. User biases and item biases give a higher rating to the items then other users and some items receive higher ratings than others, respectively. Ziegler et al. observed that trust and user preference similarity has a strong correlation [83]. If the two persons are more similar then there exists greater trust between them. For example, if people are interested in 'Book' on time at t 1 then they trust the experts in that domain, then after some time, say t 2 , their preferences are changed and shifted to some other domain say 'Movies', then at that time, people trust experts in this domain. In the rating system, users can establish new trust relations and can add new ratings.
Our contributions are as under: • In this paper, we propose a trust aware recommendation model using cross domain information for rating prediction, that solves a user cold start and sparsity problem in cross-domain scenario of 'No Overlap'. • We propose a hybrid model called Trust-Aware Cross Domain Temporal Recommendations (TrustCTR) by integrating the neighborhood model and latent factor model with baseline estimates, and distance metric to understand the dynamics of user preferences in cross domain social networks.
• We improve the rating prediction process by relating the time with user preferences and learning the features of users, and items using proposed model. • We propose a novel trust metric called Trust Relevancy that measures the degree of trust between two users by incorporating the trust information and the rating information and integrated this trust relevancy in rating prediction.
• We construct a trust network using implicit and explicit trust relationships w.r.t time and then find trustworthy neighbors for an active user, using Ant colony meta-heuristics.
• We train TrustCTR model by selecting the data on a time range t 1 , and predict the ratings for test set from the most recent time that is t 2.
• We also investigated the applications for TrustCTR model such as trust prediction and rating prediction.
• The proposed model is evaluated on two public datasets that are Epinions and Ciao, using the categories of VOLUME 8, 2020 these datasets in cross domain forms. We divide each domain in different views of users and is compare with well-known state-of-the-art methods and present improved results. The main properties of the proposed model are listed as follows: • Likewise, the latent factor model [25], TrustCTR also utilizes the user preferences but the latent factor model does not consider the trusted network and their influences whereas proposed model incorporates trust information, explicitly and implicitly, making it more effective.
• In [61], the neighborhood model has not incorporated the item characteristics and user preferences whereas the TrustCTR consider the user-item preferences, although both models take into account the trust information.
• The existing baseline estimates [26] and social recommendation model based on distance metric [74] have not included the time-sensitive information. Whereas the TrustCTR not only accounts for the time-sensitivity but it also integrates the distance metric with baseline estimates, that learns the data points (locations) closer to each other. The distance propagation shows that how users and items are located inside space by integrating distance metric learning and latent factor model. These locations of users and items are helpful in determining the users who have few ratings.
• TARS [3] is a trust-based recommendation framework based on ACO, that utilizes the rating values for creating an implicit trust graph. It does not consider the explicit trust relationship in generating recommendations that effect its performance when facing sparse data. While the TrustCTR incorporates explicit trust relationship among users from social networks for improving prediction process and implicit trust relationships in the form of cosine similarity and pheromones, this improving the ability of proposed model to tackle the sparsity issue, by choosing best neighbors.
• TCFACO [49] is a trust aware recommendation model that incorporated both explicit and implicit trust information with user-item preferences but it does not account for the dynamicity of trust and users' preferences. While the TrustCTR model has the capability for generating recommendations from most recent times and incorporated the up-to-date trust and rating information.
• One of the modules of TrustCTR is 'Discovering Neighbors' that finds the best neighbors for an active user using ACO. We choose ACO because it is dominant over genetic algorithms and simulated annealing approaches, as the convergence time of metaheuristics algorithm is faster than genetic algorithms and simulated annealing approaches. ACO has the capability of adapting the changes continuously when the graph changes dynamically. Ants can find a high-quality solution in a solution space and they share their knowledge in the form of pheromone as update strategy and solve the problem efficiently. Following is the organization of the article. Section 2 discusses the background and the motivation behind our research. We describe the architecture for proposed model in section 3. Applications of TrustCTR Model are described in Section 4. The experimental setup is described in section 5. Evaluation and experimental results are discussed in Section 6 and finally, we describe conclusion in Section 7.

II. BACKGROUND AND MOTIVATION
In this section, we discuss the recommendation tasks and scenarios; give details of the state-of-the-art in trust-based and cross-domain recommendations; issues in existing recommender systems and motivation behind our research work.

A. RECOMMENDATION TASKS AND SCENARIOS
Recommendation task refers to the method required to give recommendations for user tasks. The recommendation tasks can be performed for both source and/or target domains. In recommendation scenarios, knowledge is transferred from source to target domain based on similarity between users and items. The recommendation systems are continuously evolving. The features related to items, users, and ratings are utilized in the development of recommender systems. Recommendations can be divided into three scenarios namely single, cross, and multi-domains (i) single domain recommendation considers the items belong to target domain, and are recommended to the users of target domain by learning knowledge or profile information available in source domain, (ii) cross domain recommendations consider items belong to source domain, are recommended to the target domain users or if items belong to target domain, are recommended to the users of source domain. (iii) multi-domain, recommends the items to the users of source domain from more than one target domain [8]. A domain can also be categorized into the system, data, and time scenarios; (i) in system domain scenario, two domains are considered as distinct if knowledge is transferred from dense domain to sparse domain; (ii) in the data domain, users interact with items in the form of ratings or likes/dislikes from multiple dimensions related to different data domains; (iii) in time domain rating matrix has timestamps, divided into time slices [70], [48]. Each time slice is called a temporal domain [34]. A domain can be defined at item/category, type, or attribute level (i) item level or category domain, majority of item characteristics are different, (ii) type level attributes of two items are different from each other and some attributes are similar, (iii) attribute level, two items are considered as an indifferent domain when they have different attribute values [58].
This research work is limited to cross domain scenario at item level (category) and temporal domains.

B. CROSS DOMAIN RECOMMENDER SYSTEMS
Xu et al. proposed a method for solving a cold start problem in cross-domain recommendation scenario [71]. The method predicted the rating of items for source users via target domain items using trust relations. Gao et al. developed a latent factor model based on clustering and improved the cross-domain recommendations to learn the patterns of rating using a non-negative tri-factorization matrix [16]. Cremonesi et al. solved the problem of sparsity by transfer learning from the source to the target domain to improve recommendation accuracy and observed that item-based approaches provide better recommendation quality, then user-based approaches [9]. Sahebi et al. addressed a cold start problem in a cross-domain scenario and found that cross-domain recommender systems give more accurate results as compared to multi-domain recommendation systems [53]. Kotkov et al. generated recommendations when items overlapping occur in cross domains at system level and observed that source domain could increase the performance of recommendations in the target domain when there is item overlap, but performance is decreased when items overlap occurs in different domains [29]. Moe et al. developed a context-based cross domain recommender system to recommend cosmetics products using contextual features of the customer [45]. Li et al. solved the problem of data sparsity by transferring patterns from auxiliary domain to other domains [33]. Abdollahi et al. proposed a cross-modal recommendation framework called Asymmetric Non-Negative Factorization (NMF), for solving a new item problem by utilizing multiple domains [1]. Elkahky et al. introduced a multi-view deep learning approach in which they modeled user preferences in cross-domain recommendation systems [15]. Zhuang et al. developed a framework known as TRACER that predicted the rating for cold-start users by transferring knowledge from multiple source domains [82]. Ma et al. developed a joint cross domain recommendation framework that incorporated transitive trust relations among users with context dependency for solving a data sparsity problem [37]. Li et al transferred the latent information through orthogonal mapping function between two domains via dual learning mechanism using autoencoder [95]. He et al. proposed a cross domain model by learning user and items latent information across domains for knowledge transfer and improved the prediction process by embedding the probabilistic modeling with Bayesian neural network [96]. Lin et al. given the concept of cross platform in social e-commerce systems and recommended the items to the active user when they shop the items via social media [97]. In 2019, Liu et al. proposed a cross domain recommendation model called Joint Spectral Convolutional Network and utilized the neighborhood information across domains and improved the recommendation process [98]. In 2018, Hu et al. developed a model called CoNet that used the hidden layers of neural network in cross-connections form and transfer the knowledge across domains for improving the performance of recommendation systems and overcome the issue of data sparsity [99]. Yuan et al. proposed a cross domain framework called deep domain adaptation model that extracts the features shared from two domains using autoencoder and then the rating predictor split the ratings of each domain [100].

C. TRUST-BASED RECOMMENDATION SYSTEMS
Lathia et al. proposed trust-based recommender systems by using the k-nearest neighborhood algorithm and the utility of rating information and trust information [31]. Goldback et al. have determined trust among users based on features extracting from profile similarity [17]. Dohetry et al. investigated trust-based recommendations using traditional algorithms and trust-based models [47]. Jamali et al. overcome the problem of cold-start users who are connected to a trusted network. They applied trust-based methods to generate item recommendations and suggested that few ratings give low precision because there exists weak trust when considering the rating of indirect neighbors [20]. Bedi et al., proposed a model called TARS using an ant system to measure the dynamic trust between users using pheromones activity among ants and select the best neighborhoods [3]. Massa et al. proposed a model that used the trust metric to solve the data sparsity problem in recommendation systems [42]. Deng et al. applied a deep learning technique and developed a model called DLMF and solved the cold start problem in trust-aware recommendation systems [12]. Than et al. overcome the weaknesses of the collaborative filtering algorithms and proposed the architecture for the recommendation system that integrated the similarity with trust and reputation [65]. Carrasco et al. developed a trust-aware model using a direct/indirect trust relationship to overcome the problem of data sparsity [6]. Tang et al. performed a trust evaluation of product review sites and proposed a framework called eTrust by incorporating the user preferences that change with time [62]. Deng et al. developed a model called Relevant Trust Walker that solves the user cold-start problem [11]. Massa et al. presented the architecture for Ski mountaineering application that reported the users about snow conditions by incorporating trust [41]. Chen et al. proposed a recommended method to solve the cold start problem for new users of e-commerce by including trust/distrust network model [7]. Walter et al. introduced an ensemble model to integrate the trust of users and their friends to overwhelm the problem of data sparsity. They highlighted factors such as knowledge sparseness and network density, which affects the performance of recommender systems [67]. Zou et al. analyzed the review contents based on sentiments and items rating to find the purchasing actions on items of the user [84]. A trust-based recommender system was developed by incorporating Ant colony optimization and kmeans [54]. Yuan et al. proposed a trust-aware recommendation model based on genetic algorithms that gives a better prediction, maximum coverage, and minimum maintenance cost [73]. Parvin et al. proposed a trust aware model called TCFACO and predicted the rating for cold-start users by using the ACO [49]. Rezaeimehr et al. proposed a model based on time-aware recommendations called TCARS. They first predicted initial ratings and then identify neighbors VOLUME 8, 2020 using community detection methods and overcome the challenges of sparsity [85]. In 2018, Yadhav et al. tried to solve the data sparsity problem and address the issue of how to prevent malicious attacks [86]. Pan et al. proposed a deep learning-based trust aware recommendation corelative denoising autoencoder. They used autoencoder to learn useful features from ratings and incorporated the social information [87]. In 2018, Parvin et al. integrated the trust and distrust relations and non-negative matrix factorization approach and solves the problem of cold start and data sparsity [88]. In work [89], Jiang et al. constructed a slope one algorithm for e-commerce recommendation systems by fusing user similarity and trust information. In 2020, AutoTrustRec is proposed by Bathla et al. that incorporated the directed and undirected trust information with autoencoder by learning the nonlinear relationship of neural networks present between the ratings and trust information [90]. Dong et al. describe the survey based on deep learning techniques for trust-based recommendations with three aspects such as explainable, social awareness, and robustness in recommender systems [91]. Son et al. proposed a trust aware model for social IoT. They incorporated implicit trust to overcome the limitations of explicit trust relation using environment of social IoT for prediction process [92]. Belkhadir et al. combined social trust information with social regularization by discovering an aggregate path from the multiple trust paths for generating recommendations [93]. Moradi et al. developed a trust based collaborative filtering model that incorporated trust information and predicted ratings about items [94]. Davoudi et al. proposed a social trust model for recommender systems and analyzed the impact of social ties, preference similarity, and different centrality measures on rating prediction. They observed that more similar users trust more on each other [101]. Deebak et al. developed community-based recommendation framework over IoT and solve the issues of cold start and data sparsity. The recommendations systems in IoT which contain applications related to big data allows to analyze a large amount of data to select suitable information. They learned the trusted neighborhood information for active users by finding similar preferences of target users within a community [102]. Lee et al. address a cold start problem by discovering the latent features between the trustor and trustees. They noticed that those trustors who follow the same trustee, having similar tastes and shared common features that improve the performance of social-based recommendations [103]. Ardissono proposed a LOCABAL + model that is a trust-based recommendation model by defining a multifaceted trust by users feedback and generated top N recommendations [108]. Noh et al. developed a trust aware model and studied the impact of power users available in social networks and exploited the trust cluster and observed that clusters with normal user provided better results [104]. Guo et al. developed a support vector regression model based on multiview clustering method to form clusters from user's similarity and trust information for solving cold start problem [107]. Sheugh et al. proposed a recommendation model to reduce the data sparsity issue and observed that with the increase of number of clusters, the coverage values decrease monotonically [105]. Zhang et al. developed a recommendation model by utilizing a two-layer neighborhood scheme for selecting trusted neighbors and improved recommendation accuracy [106].

D. ISSUES AND MOTIVATION
Data sparsity is one of the main issues in generating recommendations, also referred to as a new community problem [4]. Users rate only a few items due to which the resultant user-item rating matrix may be sparse, which leads to poor quality of recommendations [84]. Another problem is the user and item cold start. The new item problem occurs when a new item is added to the recommender system without any ratings. As it does not have any ratings, it cannot be compared to other items, which leads to the item not being included in any recommendations. The new user problem occurs when a new user joins the recommender system. The new user has not provided any preferences in the form of ratings, and so there are no preferences to compare the new user to existing users or items and the recommender system not able to generate any recommendations [56]. Providing recommendations to users with limited history becomes a difficult problem for collaborative filtering models because of their learning and predictive ability due to data sparsity [22]. Locating people with similar neighbors is also a challenge since rating prediction depends upon these neighbors [84]. Trustworthiness is another issue, for example, fake feedback or noisy information for malicious purposes harm the prediction accuracy [11]. Nowadays, time sensitivity is one of the critical issues that occur in personalized recommendation systems. Trust relationship can change with time and ratings assigned by users, is also vary with time and may become noise or out of date [11], [12].
Based on the literature review and above-mentioned challenges, our motivation is to provide quality recommendations to a new user available at source domain from up-to-date rating profile of his/her neighbours present in target domain. We assumed that these recommendations are generated by incorporating trust from cross-domain information available in social networks by following a cross-domain scenario of 'No Overlap'.

III. PROPOSED MODEL ARCHITECTURE
Mostly the recommender systems cannot consider the temporal preferences and trust drifts [76]. We assumed that user and item biases, temporal dynamics, and social influence over features could be subjected to temporal preference drift. Thus, we addressed one major question in this research; ''How can we model the rating prediction while incorporating the influence of contextual factors such as time, preferences, and trust when there exists no common users or items across two domains, for solving user cold start problem?''.
We propose architecture for Trust Aware Cross Domain Temporal Recommendations (TrustCTR) model, as shown in Fig. 1. This architecture consists of four main modules   For trust network at time t 1 , we constructed an undirected trust graph at time t 1 , since we assumed that there is no overlap between source domain and a target domain and there exists a joint factorization of source domain and target domain rating matrices. Therefore, we have [NU S t 1 ×NU T t 1 ] matrix, where NU S t 1 is the number of common users in source domain and WOT (Web of Trust), NU T t 1 be the number of common users in target domain and WOT, that is weighted trust matrix creation. Similarly, we have created the undirected trust graph from a trust network at time t 2 such that [NU S t 2 ×NU T t 2 ].
New users may be added and assigned a rating to the existing or new item at time t 2 , thus I S t 1 ⊆ I S t 2 and I T t 1 ⊆ I T t 2 , similarly, there are new trust relations that can be established, thus We can formulate a user cold start problem for a source user belonging to U S t 2 there exists some trustable neighbours from U T t 2 who have ratings related to a particular item in the target domain at time t 2 . Then, for each active user U S ∈ U S t 2 , the goal is to predict the rating of item from target domain at time t 2 , by incorporating trust. For training of our proposed model, we have used the rating system at t 1 as shown in Fig. 2(a) and for test set, we utilized the rating system to generate recommendations for the active user, at time t 2 , as shown in Fig. 2(b).

B. GENERATE FEATURES
This module randomly initializes the user feature and item feature vectors. After initialization, d-dimensional user feature and item feature vectors are updated for both source and target domains. Algorithm 1 describes the procedure of feature generation for both source and target domains.
In recommendation systems, the large size rating matrix also increases the dimensionality of the user rating vector, so most of the users have assigned a few ratings or missing data scores. In this situation, we have adopted a technique of matrix factorization mainly to reduce dimensions in user rating data. Matrix factorization [44], [27], [18], [57] decomposes M × N rating matrix R into two latent feature matrices of users P and items Q with reduced dimensionality d such that both users and items are present in a single latent feature space and modeled the user-item interactions as inner products in latent feature space as given in equation (1). These two matrices are P u and Q i .
where P u ∈ R Mxd is the latent feature matrix of users and Q i ∈ R Nxd is the latent feature matrix of items. For example, if we have a given matrix of user's rating that is described in Fig. 3, then the resultant matrix R gives the predicted or observed rating which is missing in the user-rating matrix by using these features. Initial values of P u and Q i are produced randomly or assigned manually. For example, the elements of P u and Q i are given in the form of a matrix. These elements of P u are obtained randomly or assigned manually for each item i and update user latent vector using equation (5). 14: end for 15: return user feature vector P and item feature vector Q user u, which shows that how much user is interested in items and Q i having the degree to which item i keep those features, Q i value is also generated randomly or assigned randomly. Then the predicted rating matrix is obtained by dot product of P u and Q i . After the initialization step, item feature and user feature vectors are updated using equation (4) and (5), respectively. So, after multiple iterations, we obtained accurate feature vectors for both source and target domains.
Algorithm 1 describes the process of learning latent feature vectors for users and items. Latent features are constructed for items and users of both source and target domains. To avoid over-fitting, a regularized model is used during the learning of feature vectors to minimize the squared error. Matrix factorization learns these latent features by reducing the following term that is a stochastic gradient algorithm [26], where, R ui is the known ratings and learned parameter, λ controls the degree of regularization and can be deduced by cross-validation. Equation (2) is minimized by using stochastic gradient descent (SGD) and equation (3) is used for computing the error in true rating and the observed rating.
Then SGD model adapts the parameters by a magnitude proportional to γ in opposite direction of the gradient: The output of the module'Generate Feature' gives d-dimensional feature vectors for users and items for both source and target domains.

C. COMPUTE TRUST RELEVANCY
The process of this module is computing trust relevancy between the users of the source domain and target domain.
In social networks, a direct trust relationship between two users does not necessarily improve the prediction accuracy [11]. The active users present in the source domain and trusted users of target domain might differ in preferences, interests, and perception, therefore, we defined trust relevancy that shows the degree of trust present between two users. We estimated the cosine similarity [59] between two users, i.e., the user of the source domain and user of the target domain by incorporating the user feature vectors of both domains. We computed the similarity using equation (6).
Here u is the user feature vector of source domain and and v is the user feature vector available at target domain. Both of these feature vectors are obtained as an output of Algorithm 1.
The domain interest similarity between pair of users for source and target domains shows that how many people belong to two different domains who trust with each other and they have more similar domain interests. So, we considered both domains for finding domain interest similarity. In equation (7), fd u (k) shows the probability that user u is interested in domain k. n u represents the number of products rated by user u and n u (k) is number of products rated by user u, available from kth domain.
For finding, domain interest similarity between the source and target users, we used Jensen Shannon Divergence [10] between users of two domains in the form of domain interest distributions that is fd S ,fd T : Here 'm' shows the average of two domain distributions and is computed using equation (9), as: Algorithm 2 Trust Relevancy Input: (u S , u T , sim) Output: (trust relevancy between u S andu T ) 1: compute fd S (k) according to equation (7). 2: compute fd T (k) according to equation (7). 3: calculate m using equation (9). 4: estimate domain interest similarity i.e. f dist (u S , u T ) betweenu S and u T using equation (8). 5: compute trust relevancy using equation (11).
And D KL is the Kullback-Leibler Divergence [30] and is computed as: Thus, we defined the concept of trust relevancy between the user u S belongs to source domain and user u T of target domain at time t 1 that is tR t 1 (u S , u T ). It is the product of simf , the domain interest similaritybetween user u S and user u T before time t 1 , the trust relationship that exists between users u S and u T at time t 1 , and sim t 1 (u S , u T ), the cosine similarity between the two users before time t 1 . The trust relationship shows the degree of trust that is provided by users, explicitly or can be calculated using some algorithms. In this work, we considered the degree of trust directly from the datasets. Algorithm 2 describes the steps involved in computing trust relevancy. We have formulated the equation (11), for trust relevancy, 0 ≤ tR ≤ 1, as:

D. DISCOVERING NEIGHBORS
In this module, we find trusted neighbors of an active user using ant colony optimization in target domain. We presented a trust network in the form of a weighted undirected bipartite graph. We incorporated the implicit trust relationship among the users in the form of cosine similarity as trust weight computed using equation (6). This trust weight is updated in the form of a pheromone update strategy. For applying ACO, it is required to represent trust network as an undirected bipartite graph G = (V,E), where V represents the user(node), and E represents the undirected edge having initial trust value computed using equation (12). Fig. 4 shows the user's connectivity as an undirected weighted bipartite trust graph. This graph consists of six users; source user and target users. Each edge has the trust weight in the form of similarity value, between two nodes. Ants move back-and-forth in trust graph for constructing solutions [110]. We have considered the initial trust value for trust as initial pheromone value, which is computed by using modified equation (12). Algorithm 3 is derived from the ant colony system proposed by Dorigo et al. [14]. In ACO method, ants start search process in a solution space by investigating the population of ants to find the best quality solution. In this algorithm, the number of k ants are placed at active user node u in source domain towards users exist in target domain.
τ xy is the trust value from user x to user y, nu x is the number of users present in the web of trust for user x and WOT x is the web of trust for user x. We utilized the initial pheromone value for initializing the trail t i with respect to user trust for each ant k. Each k ant moves from current node x to neighbor node y by calculating the probability of ρ k xy of crossing the edge using the following equation (13), where N k x are the neighbors of ant k. The probability ρ k xy from node x to node y depends upon two parameters, one is pheromone level τ xy and other is desirability of moves from node x to y, which is denoted by η xy . α and β are used to control the influence of τ xy τ xy and η xy . After calculating the probability, the ant k moves along with the edge that has highest probability. The ants stop their solution if there exist no more edges for traversing. This process is repeated up to a certain number of iterations when solution converges. In last iteration, each k ant preserves the record of trusted neighbors in N V (u). Only the best solution, globally updated after iteration is completed. The global pheromone level is computed using equation (14).
where m is number of ants and τ k xy is the amount of pheromone deposited by ant k at edge xy in one iteration. L k is the length of trail t i that the kth ant constructed. To find trusted neighbors we set different parameters in Algorithm 3 which are ants k=4, maxIter = 100, α = 3, β = 2, and ρ = 0.01. These parameter settings are chosen on the basis of convergence of proposed algorithm. Algorithm 3 describes the process that how we chose the quality raters for an active user available in the source domain, by incorporating trust between the users of the source and target domains.

Algorithm 3 Trusted Neighbors Discovery
Input: (trust matrix or undirected bipartite trust graph, ants, iteration, α, β, ρ, Q) ants: number of ants, α: pheromone influence factor, β:local node influence factor, ρ: pheromone evaporation coefficient, Q:pheromone deposit factor, TaBU k (u) is a list that maintains the record of each visited node by ant k and prevents the ant k to visit the node again in each trail t i . Output:(list of trusted neighbors for an active user u) 1: Initialize u ← sourcenode 2: m ← numofants 3: Place m ants on source node u. 4: Set iteration ← 0 5: while iteration < maxIter do 6: Create a trail t i by initializing k ant for each trail t i 7: Generate random order of target trusted users in the trail for each ant k using Fisher-Yates shuffle. 8: Initialize pheromones to each trail t i by using equation (12), at time t. 9: Place the starting node u in TaBU k (u), where k =1 to m. 10: Compute the probability of ant k in Graph G from active user node u to select node j using equation (13). 11: Select trustworthy neighbors for active user u on the basis of probability and store these into N V (u). 12: Update pheromones and increase the value of trust at time t + 1 using equation (14). 13: end while 14: return list of trusted neighbors N V (u), for an active user u. VOLUME  if predictedvalue = Null then 10: error ← rating-predictedvalue // compute using equation (26)  A baseline model that is a latent factor model for rating prediction is discussed in [25], which depends on user preferences p t u and characteristics of an item q i .
Tang et al. presented a model for rating prediction for an item j of user i, by incorporating multifaceted trust in the neighborhood model [61].
Here in Eq. (16), N t i represents the group of people trusted by users i at time t at facet k. w t ivk is the trust strength between two user i and trusted users v at time t. r vj is the decay rate
where value of η i ≥ 0 that controls the user-specific decay rate computed by using equation (17) for u i and is learned from the data. The effect of u v to u i on rating given to item j at time t is the distance between t vj and t that is formulated as r t vj vj (t vj < t). It means that earlier ratings show the users earlier preferences and has fewer influences on current ratings when t and t vj are so closed then the more impact of r t vj vj on r t ij [13]. Equation (18) shows the baseline estimates that are used to obtain the interactions between users and items, which give different rating values [26]. These variations in rating values are related to users and items called user and item biases, respectively. These variations exist due to system tendencies such that some items received higher ratings than others and some received lower ratings than others. So, the recommendation system identifies the true portion of interactive values and for which first-order approximation of bias included in the rating r ui is defined as: The predicted rating consists of average rating, item bias and user bias denoted by µ, b i and b u , respectively, where b u and b i shows the observed deviations of user u and item i, from the average. Equation (19), gives us the distance metric described by Wu et al. which shows that the optimal distance metric can increase the performance of learning features [68], [69]. The distance metric is divided into two categories: first is the local distance metric, and the second is the global distance metric [72]. Matrix 'A' calculates the distance between two points x and y, where A ≥ 0 denotes that A is a positive definite matrix.
where x u is the latent factor of user u and y i is the latent factor of item i. 'A' is a positive semi-definite matrix, and A R kxk and k is the dimensions of x and y, instead of learning a matrix 'A', model learns the A = HH T and H is not a positive semi-definite matrix and H R kxk .
The latent factor model is not considered the trusted network and their influences, and the neighborhood model has not incorporated the item characteristics and user preferences. Previous work [2], [25], [60] shows that by combining these two models, we can improve the rating prediction. We also integrated the baseline estimates [26] and distance metric [72] in our TrustCTR model because the distance metric learns the data points closer to each other. We have integrated the distance propagation in TrustCTR model likewise work presented in the literature [38] that used trust propagation and similarity propagation in collaborative filtering. So, we estimated the rating of item i about active user u at time t 1 as: Herer t 1 ui is the predicted or observed rating of item i about active user u, at time t 1 , where 1 ≤ t 1 ≤ 10. α is the learning parameter. Equation (16) represents the neighborhood model and is integrated into equation (20). q T i p t 1 u is the baseline model on the basis of user preferences p t1 u and item characteristics q i at time t 1 . N t 1 u represents the group of people trusted by users u at time t 1 . tR t 1 uvk is the trust relevancy between user u and trusted user v at time t 1 and is estimated using equation (11). r vj is the decay rate and is calculated by using equation (21).
We usually used the value of η i = 0.4 that is the effect of u v to u i on rating given to item i at time t 1 , is the distance between t 1vi and t 1 is formulated as r t1 vi vi (t 1vi < t 1 ). It means that more previous ratings show the users earlier preferences and has fewer influences on current ratings [13]. When t 1 and t 1 vi are so closed then the more impact of r t1 vi vi on r t1 ui . For decaying gradually, the influence of past rating we used the exponential function [13], [26].
We modified the baseline estimate i.e. µ + b t 1 u + b t 1 i which is a part of equation (20), that shows the interactions between users and items where µ represents the average rating, b t 1 u is the user biases at time t 1 and b t 1 i is the item biases at time t 1 . We used the Mahalanobis distance for computing distance between users and items using equation (22), as where p t 1 u is the latent factor of user u and q t 1 i is the latent factor of item i. 'A' is a positive semi-definite matrix and A R kxk and k is the dimension of p and q.
If there is a user u likes an item i and has friend f , then distance propagation model not only placed user u and item i close to each other but also find the close friend f that likes an item i of user u. This propagation of distance supports to overwhelmed a problem of data sparsity, for example, if user v has rated few items then the propagation distance recommends the items of user u likes, to user v. So, by using the distance metric we can discover the potential desired items and friends. The main reason for using distance metrics is to bring closer the data points and the data points that are discriminant in different sets with larger distances.
We integrated the baseline model with distance metric to minimize the distance between the user and the ratings given by the user to the items and their friends. For example, in baseline estimate, the users desired item may be distributed over a large area that fails to establish the meaning of latent factors, but after using distance metric with baseline estimates, the desired items for active users, are available in a smaller area, that captured fine-grained preferences.
If training data contains user and item then the rating for an item is predicted using equation (20), otherwise, we have considered the global mean. This global mean denoted by µ that is the average of users present in the training data and is incorporated to minimize the error between the true rating and observed rating.
The objective minimization function is achieved by computing the loss function that solves the following optimization problem using the gradient descent method as computed using equation (23).
We updated the user biases and item biases using the equation (24) and (25), respectively, where λ is the learning rate or control the magnitudes of latent factors, e t 1 ui is the error between observed rating and predicted rating at time t 1 that is computed using equation (26). The regU , regB, and regI are the regularization parameters.
We updated the user latent features and item latent features by equation (27) and (28).
In equation (29), H is updated as H R kxk is learned with A = HH T but H is not a positive definite matrix. k is the dimension of p u and q i . α is the parameter that is the influence of user-item distance and η controls the influence of constraints.
Stochastic gradient descent is an optimization technique that is used to estimates the error gradient by reading the current state of TrustCTR model [26]. So, during the training phase, the weights which are updated is called the learning rate. The value that we usually assign to learning rate is in the range between [0, 1] intervals; this learning rate controls how quickly the TrustCTR model is adjusted to the problem. The model converges too quickly to the optimum solution if the learning rate is large, and if the learning rate is too small, then the model is converged, too slowly. The second module of proposed framework is 'Trust Relevancy' as described in Algorithm 2. First, we find the cosine similarity between users of source and target domains which takes O(N 2 ). After that the domain interest similarity is computed and it takes O(N 2 ) and then trust relation between two users is extracted from trust graph that is computed within O (N ) times. So, the time complexity of Algorithm 2 is given where N is the total number of nodes (users) present in a trust graph.
Algorithm 3 describes the process of finding neighbors using ACO, so a fully connected undirected graph with n users is created. Some parameters are initialized from Line 1 to 4 which takes O (1). Line 5 is iterated up to O (N ) times. In Line 6, 'K' ants are initialized at trail so its computational time is O (k). Then, the initial weight is assigned as pheromones value to each edge present among nodes (n users) and then probability is computed so Line 7 to 10 takes O(n + N ). After that we find the trusted neighbors and then the pheromones are updated, from Lines 11 to 14 that takes O (N ) time. The overall time complexity of Algorithm 3 is O (1 + N + k + n + N + N ) that is O (N ).
The fourth module of proposed framework is 'Rating Prediction' as described in

IV. APPLICATIONS OF TrustCTR MODEL
In this section, we analysed the role of TrustCTR model in product review applications, which can be helpful to enhance the performance of rating prediction and trust prediction.

A. TRUST PREDICTION
Guha et al. proposed a trust propagation model that discovered trust relationships based on known trust relations but these propagation models cannot predict the trust relationship for the cold start users or users who have little information [19]. Previous studies show that by incorporating trust information with rating similarity, better performance can be achieved than trust propagation model [5], [36]. Therefore, equation (31) can be utilized for trust prediction in the form of trust relevancy.
For recommending trust at time t 2 , where 10 < t 2 ≤ 11, Given that the previous ratings {O t 1 }, and trust networks before time t 1 , TrustCTR learns its parameters by solving the minimization problem using equation (23). Then the trust relevancy between user u S and user u T is calculated using equation (31). Therefore, the trust relevancy at t 2 between user u S and user u T can be computed as

B. RATING PREDICTION
Rating prediction is one of the significant tasks of recommendation systems for estimating rating about an active user u for item i based on previous rating history or profile information. In social networks, people rely on their close friends, sharing information with trusted friends, so trust networks are mainly used for improving rating prediction. However, people place trust differently with different people with different interests across domains, which shows that heterogeneous trust relations exist in various domains. Thus, in product review sites rating systems are dynamic where the preferences of users and interest of users change with time that shows the development of trust relations. Thus, TrustCTR models the trust development for the people who have similar domain interests and can be used for improving the performance of prediction.
Given that the earlier rating {O t 1 }, the objective of trust prediction is to estimate the ratings at time t 2 from test set{O t 2 }. Therefore, the rating of item i about active user u at time t 2 can be predicted aŝ For existing item i, the feature vector q i does not evolve and for an active user u, b i and n i are independent on time and can be directly applied to time t 2 .  [43]. So, for the new user, we first find the trusted neighbors in the target domain for the new user using Algorithm 3. Then compute the trust relevancy at tim t 2 e. If user u S is a new user appears in the source domain and Nu T contains his trusted neighbors available in target domain at time t 2 , then preferences for new user u S at time t 2 can be computed as: where tR t 2 (u S , u T ) is trust relevancy between user u S in the source domain and user u T in target domain at time t 2 , and p t2 T are the preferences for trusted neighbors in the target domain.

V. EXPERIMENTAL SETUP
We used the Ciao dataset published by Tang et al. [61] and Yu et al. [74]. Ciao contains the users that provide the reviews against items in different domains such as books, movies, cars, music, etc., and assigns the rating to these items in the range [1], [5]. In a social network, users express their trust with other users in the form of binary [0, 1]. If trust is present, the user assigns a value 1, otherwise 0. The trust statements are explicitly issued by users on the web of trust (WOT). For trust prediction and measuring the impact of social influence analysis, these trust relations have been used. We have also evaluated our results on another public dataset called Epinions which is a social network dataset [37], [41], [61], [74]. These datasets contain reviews about similar categories. We used these categories (item level) as a domain in the cross-domain scenario. We selected social network datasets 'Ciao' as a source domain and 'Epinions' as the target domain.

A. SETTING RANGE OF TIMESTAMPS
TrustCTR model predicted the ratings at time t 2 after training the model at time t 1 . The rating matrix has timestamps, and these timestamps are divided into time slices, each time slice is referred to as a separate temporal domain, in both Epinions dataset and Ciao dataset. For Epinions dataset, in rating, we split the timestamps into eleven-time slices that is T ={T 1 . . . .. T 11 }, where each T contains one-year data that is T 1 covers data before January 11, 2001, T 11 covers data after January 11, 2010. T 2 covers data from January 12, 2001 to January 11, 2002 and so on. For training of TrustCTR model at time t 1 we choose the time t 1 whose range lies t 1 ={T 1, . . . . T 10 } and for tests we set the time t 2 i.e., t 1 ={T 11 }. Similarly, the same time slices are set for trust relations as given in Epinions dataset. For Ciao dataset, the whole dataset has timestamps and is divided into eleven-time slices where each time slice has range given in Ciao dataset and contains the preferences and trust information dated from 1 st January 1970 to onwards.

B. DATASET STATISTICS
Since our experimental study is about four views of users, 'All User','Cold Start Users','Opinion User' and'Heavy Raters' related to the source and target domains. We selected the categories of Ciao dataset as a source domain and the categories available in Epinions dataset as target domains as we are trying to solve the cold start problem in a cross-domain scenario. Table 1 and Table 2 shows five categories and their statistics about both source and target datasets, respectively. The average ratings per item and average ratings per user concerning each source domain and target domain are also given in Tables I and II, respectively.

C. COMPUTING RATING SPARSITY
Categories are chosen as a domain [8] based on rating sparsity [66] present in a rating matrix of both datasets, as shown in Fig. 5. Sparsity can be measured, quantitatively as where R is the total number of user-item interactions, u is the total number of unique users, and i is the total number of unique items present in a dataset. We have chosen these categories as these categories have high rate of data sparsity. We aimed to choose categories from source domain that has high sparsity rate and categories from the target domain that has a dense data matrix, but we did not find such a combination. But despite a high rate of rating sparsity that is more than 99% our TrustCTR model performed well. Table 3 shows the statistics about trust network related to Ciao and Epinions datasets. A user 1 trusts user 2 if there exists 1 that shows the trust relationship and if the relationship is 0 then it means that user 1 does not trust user 2 . We incorporated the direct trust relationship in TrustCTR model.   Trust relationships among the users usually follow a powerlaw distribution. The degree is the number of edges that one node has with other nodes. Degree distribution shows the fraction of nodes in a social network with degree k. We used a power-law distribution that is commonly in social networks for computing degree distribution among the trustors and trustees for both trust networks of Ciao and Epinions as shown in Fig. 6 and 7, respectively.

E. DATA SAMPLING: TRAINING SET AND TEST SET
We trained TrustCTR model by selecting the data on time range t 1 , after training, we predict the ratings for test set data that was available on time t 2 . The new trust relationship is established among users of the source domain and target domain at time t 2 . Besides, the user-item interactions are also   improved in terms of their preferences, such as drift at their interests over time. The train set and test set sampling that we performed in our experiments for the cross-domain scenario of 'No Overlap', are described below:

1) TRAINING AND TEST SET FOR ALL USERS, COLD START USERS, HEAVY RATERS AND OPINION USERS
For our experiments, we constructed a trainset and testset for All Users, as described in Table 4. The training set is built by including user-item interactions at time t 1 and trust relations available at time t 1 . In the testset, we have found less user-item interactions as compared to the training set since at time t 2 the range of time-slice that we assumed, is just one year. We also constructed a trainset and testset for Cold Start Users, Heavy Raters, and Opinion Users as described in Table 5, Table 6, and Table 7, respectively. The training set is constructed by including user-item interactions and trust    relations available at time t 1 . The test set contains user-item interactions and trust relations at time t 2 .

2) DOMAIN PARTITIONING
We evaluated proposed model on different aspects and split each domain into different views of users including: All Users: A set of users that assigned ratings to the items in the range [1][2][3][4][5].
Cold Start Users: Some users express a lot of ratings, whereas some express a few ratings. We considered cold-start users are those who have assigned ratings for less than 3 items in each domain of our experimental study. From Table 8, it is observed that there are more than 14% of users who are cold start related to five domains of each dataset. Heavy Raters: A set of users who rated higher than 10 items. The ratio of Heavy Raters is less than the ratio of Cold Start Users and Opinion Users related to each domain as given in Table 8.
Opinion Users: These are the set of users that assigned more than 3 ratings to the items and the standard deviation of these ratings is higher than 0.48. Table 8, shows the ratio of Opinion Users to each domain.

VI. EVALUATION AND EXPERIMENTAL RESULTS
This section describes the results obtained by using TrustCTR model, and also discusses the evaluation obtained by comparing the results of TrustCTR model with state-of-the-art methods.

A. EVALUATION METRICS
For evaluation, we used Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and F-measure. The RMSE metric shows the closeness of predictions to outcomes [71], as described in equation (35). RMSE can be computed as r ui is the actual rating andr ui is predicted rating of an item i about user u. N is the total number of items under evaluation. The MAE measure is defined in the work [64] and can be computed as Some recommendation systems may not predict all ratings available in test data, this occurs due to the high ratio of sparsity in the dataset. Therefore, we used a coverage metric VOLUME 8, 2020 to compute < user, item > prediction for this pair. coverage = n predict n actual × 100% (37) Here n predict is the number of observed ratings and n actual is the number of actual ratings. We also computed the F-measure by combining RMSE and coverage into a single measure. So, to define F-measure, first, we converted RMSE into precision within range [0,1].
In equation (38), we set the maximum possible error i.e. 4 because rating values lie in between the range [1,5]. Therefore, F-measure [11] is defined as

B. EVALUATION USING STATE OF THE ART METHODS
Since TrustCTR is a hybrid model, so we evaluated the performance of the proposed model with state-of-the-art methods, and we divide the state-of-the-art methods into three categories: Rating based methods, Trust based models and Cross domain model. These state-of-the-art methods are implemented using Python 3.6 and MATLAB, and the proposed model is implemented using Python 3.6.
ItemCF: It estimates the prediction about an item for a user based on the item's similarity [55].
BasicMF: It is based on user and item characteristics and predicts the ratings of an item about a user [25].
PMF: PMF is based on probabilistic matrix factorization and is discussed in [44].
SVD: This method integrates neighborhood model and matrix factorization, which improves the prediction accuracy [26].
SVD ++: SVD ++ combines the basis of the neighborhood model and factorization model [27].
SocialMF: The SocialMF incorporates trust propagation technique into matrix factorization for solving a cold start problem in social recommender systems [21].
SoRec: It solves the data sparsity problem that occurs in trust-based social recommendation [38].
SocialFD: SocialFD maps a user's trust and items in low dimensional latent factor space by combining the distance metric and matrix factorization model [74].

RSTE:
Ma et al. proposed a trust aware recommendation model called RSTE that is a hybrid model of matrix factorization and social network-based approach [39].
SoReg: This model performs matrix factorization with social regularization by improving prediction accuracy using the social trust information of trusted friends and solves the trust-aware recommendation problem [40].
LOCABAL: This method integrates the local and global context related to social media for generating recommendations [63].

3) CROSS DOMAIN MODEL
We compared proposed model with one of the recently used cross-domain model called TRACER as it overcomes the limitations of codebook transfer [33].
TRACER: Zhuang et al. proposed a model called TRACER that predicted ratings for target users by adopting the concept of transfer learning from multiple source domains into a target domain [82].

C. PARAMETER ANALYSIS FOR STATE-OF-THE-ART METHODS AND TrustCTR MODEL
In our experiments, Table 9 described the parameter settings as we used these parameters for state-of-the-art methods with 100 iterations and 10 reduced dimensions. Parameters settings for TrustCTR model are determined after performing some experiments based on parameters α, regU, and reduced dimensions. We performed experiments to study the impact of parameters in two aspects of users that is for All Users and Cold Start Users, as our focus is on solving a new user coldstart problem.

1) IMPACT OF DIMENSIONALITY
The purpose of the training phase for TrustCTR model is to reduce the dimensions of the user-item rating matrix for extracting the features and models the user-item characteristics. Therefore, we studied the impact of dimensionality using TrustCTR to find the best parameters for All users as shown in Fig. 8 and for Cold Start users as shown in Fig. 9. For All users, we set α = 0.3, λ = 0.03 to 1, regU = 0.050, regI = 0.050, regB = 0.10 with k =40 reduced dimensions for Electronics, k =30 for Education, k =40 for House and Garden, k =10 for Musical Instruments and k =20 for Sports and Education domain. For Cold Start Users, we considered same parameter settings for α, λ, regU, regI, regB with k =10 as the best parametric value over all domains.  The prediction accuracy in terms of MAE for cold-start users, is not improved in most of the domains when the dimensionality is increased as shown in Fig. 9. Moreover, for All users when the dimensions are increased then prediction accuracy is improved in most of the domains as shown in Fig. 8.
It means that the larger dimension may lead to model overfitting that turns out in degrading the accuracy. Another intuition is that when the dimensionality is small then the prediction accuracy is improved [12].

2) IMPACT OF α
The α is the learning parameter that controls the influence of users' trust on their friends and employs the user's characteristics. It means that by fusing the user's preferences information with favors of their trusted friends improves the prediction accuracy. The impact of incrementing the value of α from 0.1 to 1.0 for cold start users is same when we increment the value except House and Garden Domain. For All Users, the prediction accuracy remained same on the domain of Sports and Outdoors and Musical Instruments, and for Electronics domain the MAE value is not improved and for other domains the prediction accuracy is improved. We performed a sensitivity analysis of α using TrustCTR model by adjusting the value of α from 0.1 to 1.0 and find the best values of α on various domains that help improve the prediction accuracy. We set λ = 0.03 to 1, regU = 0.050, regI = 0.050, regB = 0.10 with k =10 reduced dimensions. From Fig. 10, it is observed that for All users, we obtained better MAE value when α = 0.1 for Electronics domain, α = 0.4 for Education, α = 0.4 for House and Garden, α = 0.1 for Musical Instruments and α = 0.4 for Sports and Outdoors. Fig. 11 shows the impact of α on Cold Start Users on various domains. The value of α = 0.9 shows the best result on House and Garden domain whereas for all other domains α is set to 0.3.

3) IMPACT OF REGULARIZATION PARAMETER
For observing the impact of the regularization parameter 'regU' that controls the effect of social network on a user's behavior, we set the value of regU from 0.06 to 0. 10. Larger values of regU shows the more influence of social networks on users' behavior whereas the smaller values of regU lead to a model close to the baselines. An extremely small value of regU have a weak impact on social regularization terms. We observed that in most of the domains, the regU = 0.06 has given the best MAE prediction accuracy for both views of All Users and Cold Start Users as shown in Fig. 12 and Fig. 13, respectively. With the increase in the value of regU, there is slight improvement in MAE results. Along with the VOLUME 8, 2020   parameter settings of regU, we also set α = 0.3, λ = 0.03 to 1, regI = 0.050, regB = 0.10 with k =10 reduced dimensions.

D. EXPERIMENTAL RESULTS
We computed the performance of TrustCTR model using MAE, RMSE, and F-measure and discussed the evaluation on different domains for all users, cold start users, heavy raters, and opinion users. We chose the best parameters based on the analysis of parameters as performed in section VI-C. The performance of TrustCTR model is evaluated for the view of All Users, Heavy Raters and Opinion Users, by setting the value of λ = 0.03 to 1,regU = 0.05, regI = 0.050, regB = 0.10, k = 10 and α = 0.1 for Electronics domain, α = 0.4 for Education, α = 0.4 for House and Garden, α = 0.1 for Musical Instruments and α = 0.4 for Sports and Outdoors.
For Cold Start Users, the performance of proposed model is evaluated using the same parameters except for the value of α that is 0.9 for House and Garden domain, and for all other domains, α is set to 0.3.

1) EVALUATION OF TRUSTCTR MODEL OVER DOMAIN OF ELECTRONICS
In Table 10, it is observed that our TrustCTR model gives better results on the domain of Electronics as compared to other state-of-the-art methods in terms of MAE and RMSE. F-measure also outperforms other methods such as UserCF, BasicMF, PMF,RSTE,SoRec, SoReg,SocialMF, CUNEMF, LOCABAL, and TRACER, and have some of the results equivalent to ItemCF, SVD, SVD ++, and SocialFD. The experiments conducted for All Users, proposed model converged after 63 iterations out of 100 iterations, whereas other state-of-the-art methods are converged after 90 iterations. Since TrustCTR model solves the new user cold-start problem that is if a new user comes in the source domain and has no profile history then proposed model can estimate predictions and generate recommendations for a new user from trusted friends available in the target domain. In Table 10, TrustCTR model given improved results on Electronics domain as compared to baselines in terms of MAE and RMSE. Accuracy through F-measure for TrustCTR found better than UserCF, BasicMF, PMF, SVD ++, RSTE, SoReg, SoRec, SocialMF, LOCABAL, CUNEMF and TRACER but found equivalent to SocialFD, SVD and ItemCF. In this experiment, TrustCTR model is converged after 57 iterations for Cold Start Users. Similarly, for Heavy Raters and Opinion users, we got improved results as compared to other baselines methods, as described in Table 10.
The performance of proposed model is also evaluated by computing the mean improvement value of MAE with respect to different views of users. It is revealing that improvement rate is 12.62%, 9.31%,7.59%, and 15.22% for All Users, Cold Start Users, Heavy Raters, and Opinion Users, respectively, as reported in Table 10. It is observed that the improvement rate varies with different views of users and the main improvement found is 15.22% in Opinion Users.

2) EVALUATION OF TRUSTCTR MODEL OVER DOMAIN OF EDUCATION
In Table 11, we can see that TrustCTR has out class results as compared to all baselines on Education domain. All of the three metrics presented better results. In the Education domain, our model is converged after 62 iterations for All Users. For Cold Start Users, TrustCTR model has given improved results and model is converged after 59 iterations. Similarly, for Heavy Raters and Opinion users, we obtained the improved results as compared to other baselines methods, as described in Table 11.
The performance of proposed model is also evaluated by computing the mean improvement value to different views of users. It is revealing that improvement rate is 111.67%, 4.45%,33.82%, and 12.45% for All Users, Cold Start Users, Heavy Raters, and Opinion Users, respectively, as reported in Table 11. The higher improvement rate is found in the view of All Users.

3) EVALUATION OF TRUSTCTR MODEL OVER DOMAIN OF HOUSE AND GARDEN
In   We also computed the mean improvement value for different views of users. It is revealing that improvement rate is 17.61%, 7.03%,34.14%, and 9.65% for All Users, Cold Start Users, Heavy Raters, and Opinion Users, respectively, as reported in Table 13. It is observed that the improvement rate varies with different views of users and the major improvement found is 34.14% for Heavy Raters.

5) EVALUATION OF TRUSTCTR MODEL OVER DOMAIN OF SPORTS AND OUTDOORS
In Sports and Outdoors domain, MAE and RMSE metrics performance are better than all state-of-the-art methods. F-measure metric is shown improved accuracy than UserCF, ItemCF, BasicMF, SVD, PMF, SVD ++, RSTE, SocialMF, LOCABAL, CUNEMF and TRACER; and for remaining baseline methods, TrustCTR model shows equivalent results  Table 14. We have found a higher rate of improvement for All Users that is 13.07%.

E. CONVERGENCE ANALYSIS
In this section, we compared the convergence property of proposed model to the most recently used rating based methods such as PMF [44], and SVD ++ [27], trust aware models such as Social FD [74], and CUNEMF [78], and cross-domain recommender systems such as TRACER [82].    We performed the convergence analysis for All Users. Figure 14 shows the convergence analysis graph of the TrustCTR to other baselines in the domain of Electronics.  It is observed that all methods are converged to lower values of MAE in later iterations, but the proposed model is converged early as compared to other methods. Since the proposed model utilizes the ACO search property and across domain information, so the convergence time and accuracy results of TrustCTR are better than other methods. Similarly, the convergence comparison of proposed model with other methods for the domains of Education, House and Garden, Musical Instruments, and Sports and Outdoors are shown in figure 15, 16, 17, and 18, respectively, which clearly shows that the proposed model converged early with lower MAE values as compared to state-of-the-art methods. Using the explicit and implicit trust relations as trust relevancy and importance of features learning across domains which help find neighbors, results in significant improvement of rating prediction process.

F. COMPARISON OF RESULTS
We compared proposed model with average MAE of ratingbased methods, trust-based models and cross domain model concerning all view of users. From Table 15, 16, 17 and 18,    it is obvious that TrustCTR has given improved results as compared with all three types of models in each domain. In comparing with rating-based methods, we observed that this significant improvement in proposed model is due to incorporating the rating of target domain based on user-item interactions with respect to time. In comparing with trust-based recommendations, the results are quite improved due to the use of explicit and implicit trust relationships across domains in the form of trust metric and the use of metaheuristics of ACO for filtering trusted neighbors, in prediction process. Moreover, in comparing with cross domain model, the prediction process of proposed model is improved as we related the time with user preferences and learned the latent features for users and items with trust relations across two domains.
Cross-domain model and rating based models performed well on large and sparse datasets as compared to trust-based methods for All Users and Cold Start Users, as given in Table 15 and XVI, respectively. From Table 17, it is also noticeable that for Heavy Raters, rating based methods and trust-based models provided improved results in different domains as compared to cross-domain models. For Opinion Users, rating-based methods provided better results in all domains except Musical Instruments.

VII. CONCLUSION
Nowadays, recommender systems are facing cold start and data sparsity problems. Collaborative filtering techniques have been failed and are unable to generate quality recommendations; however, hybrid models provide better recommendations as compared to traditional collaborative filtering models. Recently, recommender systems based on trust are beneficial in the improvement of quality recommendations and solve the problem of data sparsity and cold start. In a cross-domain scenario, trust-based recommendations recommended the items to the source users from the target domain. One of the challenges in trust-based recommender systems is that the trust relationship among users can change with time. Another challenge is that the user-item ratings vary with time and may become out of date. In our work, we also found data sparsity in cross domains about more than 99%. This was another challenged for proposed model that we did not find any dense rating system in both datasets. We addressed all these mentioned challenges of recommender systems. Notably, we proposed a model that solves a user cold-start problem in a cross-domain scenario of 'No Overlap' at category or item level domain by incorporating preferences. Our model predicts rating by integrating the neighborhood and latent factor models with baseline estimates and distance metrics to understand the dynamics of user preferences in cross-domain social networks. We also introduced the concept of trust relevancy that represents the trust degree among the trustors and trustees. For the quality of recommendations, we exploited the Ant colony system to find close neighbors of an active user. We have performed experiments on two public datasets and considered five cross domains. The evaluation gives satisfactory results. There are some interesting findings, our model overcomes the problem of data sparsity in the rating system and solves a user cold-start problem by generating recommendations from target domains to an active user by incorporating trust and preferences drift with temporal aspects. If there exists sparsity in source domain rating system and target domain rating system then TrustCTR model still has the capability to generate better recommendations than other baseline algorithms. We also investigated the applications of our model and found that it improves the rating prediction and trust prediction. In the future, for generating quality recommendations and enhancing the efficiency of recommendation systems, we will employ user-item ratings and distrust relations from multiple domains with time sensitive information.
UMER RASHID received the B.S. (CS) degree from the University of Lahore, Pakistan, in 2005, and the M.Phil. and Ph.D. degrees from Quaid-i-Azam University, Islamabad, Pakistan, in 2008 and 2017, respectively, all in computer science. He has teaching and research experience in international organizations. He is currently serving as an Assistant Professor with Quaid-i-Azam University. His research interests include user-centered computing, multimedia information retrieval, and multimedia technology. His work is published in international journals and conferences.
ABDULLAH BAZ (Senior Member, IEEE) received the B.Sc. degree in electrical and computer engineering from Umm Al-Qura University (UQU), in 2002, the M.Sc. degree in electrical and computer engineering from KAU, in 2007, and the M.Sc. degree in communication and signal processing and the Ph.D. degree in computer system design from Newcastle University, in 2009 and 2014, respectively. He was the Vice-Dean and then the Dean of the Deanship of Scientific Research with UQU, from 2014 to 2020. He is currently an Assistant Professor with the Computer Engineering Department, the Vice-Dean of DFMEA, the General Director of the Decision Support Center, and the Consultant of the University Vice Chancellor with UQU. His research interests include data science, ML, AI, VLSI design, EDA/CAD tools, intelligent transportation, computer systems and architecture, smart systems, and smart health. Since 2015, he has been serving as a Review Committee Member of the IEEE International Symposium on Circuits and Systems (ISCAS) and a member of the Technical Committee of the IEEE VLSI Systems and Applications. He served as a Reviewer for a number of journals, including the IEEE INTERNET OF THINGS, the IET Computer Vision, the Artificial Intelligence Review, and the IET Circuits, Devices and Systems. VOLUME 8, 2020