1 Introduction

Big data has become one of the significant topics in various research areas, including social networks and online shopping. A large volume of digital data is often produced by users when they purchase/ rate items. Such information, along with users/items contextual data can be used to obtain user-items interactions, model user’s preferences, and make proper item recommendations for them. Recommendation Systems (RSs) have been developed to perform such tasks [1]. RSs have significant applications in many industrial systems in recent years, which work on the availability of large-scale social network data. RSs have been successfully used in many fields such as videos [2, 3], webpages [4], friends [5], mobile applications [6], OLAP sessions [7], travel packages [8,9,10], tourisms[11, 12], e-commerce [13], Business-to-Consumer (B2C) controls [14], business process models [15], jobs [16], routs [17], learning objects [18], and, etc. in industry and academia applications. Some of the papers have worked on optimizing the performance of their proposed recommender systems using evolutionary algorithms [19], and others used additional information such as time, location, etc.

Because recommendations are usually personalized in RS(s), different users or user groups receive a variety of recommendations. For personalized recommendations, the system provides a list of ranked items. In performing this ranking, the system attempts to predict the most appropriate and the best products and services for users based on preferences and limitations, and in order to complete such operations, it collects the users’ past transactions [20]. RS(s) use different data sources such as rating matrix and user and item features to extract correlations between users and items. Based on the recommendation technique and method, recommender systems can be divided [1] into Content-Based (CB), Collaborative Filtering (CF), Knowledge-Based (KB), Demographic-Based (DB), and Hybrid System (HR) as shown in Fig. 1. The system uses only the item rating given by active user and items features are called CBRS. In contrast, the system recommends the items to active users based on users-items interaction data called CFRS. There are also HRSs that use both data types. In KBRS users define explicitly her/his requirements and according to them system recommends the items. The CFRS is divided into model-based and memory-based. Model-based CF uses machine learning algorithms such as matrix factorization and Singular Value Decomposition (SVD), to train the data and construct the model. Memory-based methods, such as user/item-based approach, identifies the nearest neighbors of active user or items which observed by an active user based on similarity measures. This approach works on the assumption that similar users have similar tastes and preferences, and a target user gives positive ratings to the items that have already been positively rated by his/her neighbors. Item-based approach assumes that the target user gives the same rating to similar items. Although CFRS has been successfully applied to many applications and are indeed the most widely used RSs in the industry, they suffer from several issues, including rating sparsity, cold-start, scalability, and attack. When users rate a small number of items, the sparsity issue occurred. The cold-start problem happens when a few item ratings exist in the rating matrix for new users or new items, and similar users or items cannot be found easily. Several techniques have been used in the literature to handle these issues [21]. CFRS are easy to understand; that is why the fake users attacked these systems. Recently, methods have been introduced to detect and remove these attacks. Contextual data, friendship, membership, and social trust relationships are approaches to solving the cold start problem in social networks and community structure. Purchase/rating time is another important factor that, if available, can be used to improve the efficiency of recommendation lists. Traditional RSs ignore this factor and consider all the ratings as the same value for prediction, regardless of their transaction time. However, users might change their preferences over time, and also the popularity of items change over time.

Fig. 1
figure 1

The models of recommender systems

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Shilling attacks are one of the new challenges of recommender systems where the user attempts to increase /decrease the popularity of a particular item by using one or more fake profiles and add/remove item to/from the Top@K items recommendations. Shilling attacks are divided into push or nuke categories in terms of the attack target item. In push attacks, the attacker tries to add a specific item to the recommendation list with the fake items ratings. Nuke attacks try to remove a specific item from the recommendations list of recommender systems. In recent studies, researchers are trying to reduce the destructive effects of shilling attacks on recommender systems. Each attack profile has different dimensions such as: attack model, attack content, profile size, and attack size [22]. The attack content describes the attacker’s target, which includes both push and nuke target item. Profile size is the number of ratings that an attacker has assigned to an attack profile. If the attack profile contains a large number of ratings, it will be detected sooner. For this reason, the attacker does not increase the profile size. The number of profiles that an attacker adds to the system is the size of the attack. The attack model describes the properties of the items used in the attack [23].

Lam and Reidl in [24] classify attacks into two main categories of random and average, based on the attackers' behavior patterns and ratings. Attack profiles contain; selected items (Is), filler items (IF), unrated items (Iθ) and target item (It). In the random and average attack, the value of IF is normal distribution around the system mean items rating and normal distribution around the mean rating value for the specific item; i ∈ IF, respectively. In both attacks, It = rmin/rmax, Is =φ and the value of Iθ determines by filler size.

Numerous methods have been presented for attack detection to improve the robustness of collaborative filtering recommender systems. The purpose of these methods is to reduce the impact of shilling attacks by identifying and eliminating attack profiles. Fake accounts and fake followers are also dangerous on social platforms because they may change concepts such as popularity and influence, which may have a great impact on the economy, politics, and society. Caruccio et al. in [25] presented a new technique for detecting fake accounts. Their technique extracted knowledge automatically from big data to identify the patterns of fake accounts. This article discusses topics related to fake account discrimination. Today, one of the user’s worries is privacy in social media. Cerruto et al. in [26] used an image-recognition technique to recognize users from their pictures, aiming to collect their personal data accessible through social networks. They analyzed the amount of extrapolated data for evaluating privacy threats when users share information on different social networks. Also, Cirillo et al. in [27] proposed an intuitive framework that improves users' awareness of their data privacy on social network platforms. The article discusses topics related to user privacy awareness in the social network domain.

In this paper, we proposed a collaborative filtering recommender System, called T&TRS which is robust against the Random and Average attacks for nuke and push strategy attack. T&TRS system considered time of item ratings and user trust in its recommendation process.

The contributions of our proposed system are as follows:

  • New method of community detection has been introduced, that has increased the precision of clustering for finding fake users. The most important problem to identify communities is the initial number of clusters and also the centers of the clusters which are selected randomly. In T&TRS, the nodes with maximum links in the generated user-user network are selected as the center of the clusters. In overlapping community detection of the proposed method, a user may belong to more than one community. So, systems can consider more users in the prediction process.

  • The proposed system removed the fake users and items from the rating matrix and predicted the rating of unobserved items based on the new rating matrix to improve the accuracy of collaborative filtering recommender systems and being resistant to the attacks.

  • The proposed system employed an imputation method integrating with a reliability measure for estimating the missing ratings. This approach is used to solve the sparsity problem in recommender systems.

  • We extracted the implicit trust between users and present a new formula to calculate the similarity between users based on the implicit and explicit trust for constructing the weighted user-user networks.

  • The new fitness function, which is used to assign a node to the best possible detected communities has been applied in our proposed system.

The structure of the paper is as follows: Section 2 reviewed the related works. In Section 3, T&TRS is explained in detail and also the novel community detection algorithm is described. Section 4 presents the evaluation of our proposed system, and finally, Section 5 describes the conclusions and future works.

2 Related work

Recently, some methods have been introduced to detect and remove the attacks in recommender systems by researches. Rezaeimehr and Dadkhah in [28] studied the methods to identify the attacks and classified them into four categories; 1) clustering, 2) classification, 3) probabilistic methods and 4) features extraction.

Recently, Narayanan et al in [29] extracted dynamic features by Convolutional Neural Networks (CNN) and Recurrent Neural Network (RNN) techniques for detecting shilling attacks. Ran et al in [30] proposed a schema to address the difficulty of analyzing sensitivity by exploiting the polynomial representation of the objective function in a large-scale recommender system. Ovaisi et al in [31] presented a software library for comprehensive robustness as Robustness Gym for Recommender System (RGRecSys) that evaluates the robustness of different recommender systems.

According to the topic of our proposed system, we focused our studied papers on the area of time and trust recommender system, the community detection algorithms, prediction, and the approaches for detecting the fake user or review as follows:

2.1 Trust based recommender systems

Trust among users can be explicitly collected from users or can be implicitly inferred from users’ behaviors such as items rating information. Ahmadian et al in [32] used a probabilistic model to determine how many ratings are required for each user to produce an accurate prediction. Moreover, they used the implicit ratings based on a reliability measure, for enhancing the rating profiles of users with insufficient ratings. In implicit methods, a trust network is constructed for each user based on her/his ratings in the system. Implicit relationships in the recommendation process can be effective to improve the performance of social recommender systems, especially for the users whose explicit relationships are insufficient to make accurate recommendations. Ahmadian et al. in [33] proposed a social recommender system based on reliable implicit relationships. Dempster–Shafer theory is used as a powerful mathematical tool to calculate the implicit relationships. Moreover, a new measure is introduced to evaluate the reliability of predictions, where unreliable predictions are recalculated using a neighborhood improvement mechanism. This mechanism used a confidence measure between the users to identify ineffective users in the neighborhood of the target user. Finally, new reliable ratings are calculated by removing the identified ineffective neighbors. The standard content-based or collaborative-filtering recommendation approaches may address this problem by asking users to share their data. Wahab et al in [34], solved the cold-start problem for new items using a federated learning-based approach. The originality of their solution compared to existing federated learning-based solutions comes from applying federated learning specifically to the cold-start problem and proposing a mechanism to calculate trust rating and then a double deep Q learning scheduling approach.

2.2 Time based recommender systems

The main motivation for a time-aware recommender system is that in realistic scenarios users’ tastes might change over time (user drift). Most traditional recommender algorithms exploit the data as static and do not consider this issue into account. Both memory-based and model-based CF approaches have been recently adopted to take into account users’ drifts in their recommendation processes. In time window algorithms only a number of the most recent ratings are considered in the recommendation process. In time decay-based methods, the temporal effect of the data is handled by boosting recent ratings and penalizing older ratings. Rezaimehr et al. in [35] introduced a novel time-aware recommendation algorithm that is based on identifying overlapping community structures among users. As mentioned earlier, user interests may change over time. Accurately dynamic user preferences modeling is a challenge in designing efficient personalized recommendation systems. System popularity is constantly changing as new selection emerges. Thus, modeling temporal dynamics should be important. Classical time-window or instance-decay approaches have a lot of challenges, as they lose too many data instances. Rendle et al. in [36] proposed a matrix factorization method that includes temporal effects in RSs. Their behavior model change with the time throughout the life span of the data. They exploit the relevant components of all data instances, while discarding only what is modeled as being irrelevant. Daneshmand et al. in [37] proposed a time-aware recommender system that models dependencies between items using statistical diffusion. They indicated that future ratings of a user can be detected from his/her rating history. There is a hidden network structure among the items and each user tracks a sequence of items in this network. Moradi et al. in [38] introduced a novel trust-aware recommendation algorithm based on overlapping community structures between users. Users’ interests might change over time, and thus dynamic modeling of users’ tastes accurately is a challenging issue to design the efficient personalized recommendation systems.

2.3 Community detection

Community detection algorithms are used to cluster users and find neighbors of active users and it is very crucial in social network analysis. Many methods used topological features and node attributes, including community size, modularity, clustering, dynamic, and overlapped clusters [39]. These algorithms concentrated on the undirected/directed graph that used real and artificial datasets. Most existing community detection algorithms, ignore the structural information of the posts and the semantic information of users’ interests and only use network topology. Jiang et al. in [40] Used an Interest Community Detection model to address these challenges. Their model is based on modified Hypertext. Recently, Al-Gorabi et al in [41] proposed a Node Influence k-Nearest Neighbor (NI-KNN) algorithm for detecting the community using an undirected graph. In addition, there are various applications that benefit community detection methods, including healthcare, economics, social media, e-commerce, communication networks, etc. In Table 1, we compared the mentioned algorithms from the following dimensions.

Table 1 The characteristics of different algorithms
Full size table

2.4 Sentiment analysis

Shubham and Krishan Kumar used the concept of lexicon-based approach to give star rating to the reviews. Instead of classifying reviews as positive, negative or neutral, they have categorized them into five subcategories, i.e., Excellent, Good, Neutral, Bad and Worst using the star-scale method. They got the results in a reasonable time by using the concept of Virtual Machines [42].

Negi et al. in 2021 used the residual learning-based framework, “ResNet-50”, with transfer learning to propose an intelligent human action recognition system that can automatically recognize daily human activities. They present extensive empirical evidence demonstrating that residual networks are simpler to optimize and can gain accuracy from significantly higher depths [43].

Kumar et al. in 2017 employed a lightweight Docker container over the cloud as a utility for sentiment analysis using the four classification approaches. They analyzed the reviewer's comment on a product across multiple websites. The analyzed information can be used as a product recommendation to a customer [44].

Negi et al. in 2021 proposed an advanced CNN technique to care for farming by classifying a recognizing citrus disease that helps grow healthy plants. Their proposed model uses different training epochs, batch sizes, and dropouts. The dataset includes images of unhealthy and healthy citrus leaves and fruits used in Deep learning technique [45].

Negi et al. in 2021 proposed an advanced Deep Learning model for face mask detection in real-time video streams. They analyzed a series of video streams/images to recognize individuals who comply with the regulation of wearing medical masks by the government. This could allow the government to take sufficient action against non-compliant persons [46].

Sharma et al. in 2017 presented an advanced model for a dictionary-based sentiment analysis algorithm for human sentiment analysis. They believed that public sentiment in future and past events, such as public gatherings, and government policies, reflects public beliefs and can be used to analyze measures of support, disorder, or disruption in such situations [47].

Sharma et al. in 2017 used a new approach, D-FES, to recognize emotions based on lip structure over time. Using a recurrent neural network to analyze the pattern over time provided a classification of emotions into 6 different classes. They believed that their proposed system can work in a real-time environment to accurately track and classify emotions [48].

Kumar et al. in 2017 proposed a local-alignment-based FASTA approach for summarizing the events in multi view videos as a solution to the aforementioned problems. A deep learning framework is used to extract features to solve the problem of changes in illumination and to remove fine texture details and identify objects in a frame. Interview dependencies are then captured across multiple views of the video through local alignment via the FASTA algorithm. Finally, object tracking is applied to extract frames with low activity [49].

Vijayvergia et al. in 2018 proposed the STAR model and highlighted two Phases of the model based on novel approach using a transfer learning framework to analyze the reviews by exploiting the variation in human emotions [50]. Their experimental results have shown that the star model outperforms the state-of-the-art models.

2.5 Prediction approach

Kumar et al. in 2021 proposed a price model predicted in the stock market. Their model predicted the price of Google Stock using two deep learning models with the least possible error. They applied the Recurrent Neural Network for predicting the price on a short-term basis [51].

Negi et al. in 2021 described a deep convolutional neural network model to care for farming by identifying leaf disease. They believed that leaf disease detection helps in growing up the healthy plants. They used CNN techniques on large datasets of agricultural plants to accurately diagnose plant leaf diseases [52].

Alok et al. in 2021 investigated whether artificial intelligence can use low-cost, reliable and accurate deep learning solutions to predict lethal malaria. They reported some findings on the accurate classification of malaria infected cells using deep convolutional neural networks. They also discussed strategies for assembling a pathologist-treated visual dataset for training deep neural networks, as well as some data augmentation approaches used to significantly increase the dimensionality of the data, given the over fitting problem, especially in deep CNN training [53].

Kumar et al. in 2021 proposed a classification algorithm in the therapeutic dataset. Their approach used the dataset of Indian Liver Patient and their experimental result clearly showed that grouping classification algorithms efficiently improve the rate of illness prediction [54].

Negi et al. in 2020 trained a customized deep learning model to recognize whether or not a person uses a mask. They studied the concept of model pruning with Keras-Surgeon. Model pruning can be efficient in reducing model size so that it can be easily implemented and inferred in embedded systems [55].

Kumar et al. in 2018 proposed an accurate and efficient technique for event detection and summarization in multi-view surveillance videos using boosting as machine learning technique. Interview dependencies are captured across multiple views of the video are captured through weakly learning classifiers in boosting algorithm. The light changes and still frames are controlled by the deep learning framework with moving an object in the frame. It helps to make the correct decision for active frame and inactive frame without any prior information about the number of issues in a video [56].

Table 1 shows the characteristics of different methods which have discussed in this section.

3 Proposed method

The proposed T&TRS system consists of seven steps as shown in Fig. 2. The step 3 contains the novel similarity measure for constructing the user-user-network based on implicit and explicit trust between users. The step 4 contains the new community detection algorithm for clustering the users based on the time of rated items and trust between users. According to the detected communities, the proposed system detects and removes the items ratings of fake’s users and suspect items to improve the efficiency of the system.

Fig. 2
figure 2

The structure of proposed method; T&TRS

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We explain the detail of proposed system, T&TRS, based on the Fig. 2 as follows:

  1. Step 1:

    Inject attack

First, we injected many Average and Random attacks using the tools has been introduced by Rezaimehr and Dadkhah in [57] on the Epinion datasets and the details of the attacks such as type, strategy and other parameters has explained in the evaluation section. They designed a new user-friendly tool to inject any type of attack into the selected data set for collaborative filtering recommender systems based on Attack strategies.

  1. Step 2:

    Tag suspect ratings

Each item rating recorded in the dataset must be validated; for this purpose, a reliability value [58] is calculated using Eq. (1) based on positive and negative factors for each entry in the initial rating matrix. T&TRS labeled the item rating with a reliability value less than the threshold as a suspicious rating and the others are considered as the correct and reliable ratings.

$${R}_{a,i}={\left( fp\left({r}_{a,i}\right).{f}_n{\left({r}_{a,i}\right)}^{fp\left({r}_{a,i}\right)}\right)}^{\frac{1}{1+ fn\left({r}_{a,i}\right)}}$$
(1)

Where, fp(ra, i) and fn(ra, i) are the positive and negative factors for rating of item; i that is given by the user; a, which are calculated from Eq. (2) to Eq. )6).

$$fp\left({r}_{a,i}\right)=1-\frac{\overline{s}}{\overline{s}+\sum\limits_{\textrm{u}\in {\textrm{N}}_{\textrm{a},\textrm{i}}}{\textrm{sim}}_{\textrm{a},\textrm{u}}}$$
(2)
$${f}_n\left({r}_{a,i}\right)={\left(\frac{\mathit{\max}-\mathit{\min}-{V}_{a,i}}{\mathit{\max}-\mathit{\min}}\right)}^{\gamma }$$
(3)

Where, \(\overline{\ \textrm{s}}\kern0.5em\)is the mean value of similarity between users (Na, i) that rated item i.

$$sim_{\boldsymbol a,\boldsymbol u}=\frac{\sum_{i=\text{1}}^m\left(r_{a,i}-\overline{r_a}\right)\left(r_{u,i}-\overline{r_u}\right)}{\sqrt{\sum_{i=\text{1}}^m\left(r_{a,i}-\overline{r_a}\right)^\text{2}\sum_{i=\text{1}}^m\left(r_{u,i}-\overline{r_u}\right)^\text{2}}}$$
(4)
$$\upgamma =\frac{\mathit{\ln}\,0.5}{\mathit{\ln}\frac{\mathit{\max}-\mathit{\min}-\overline{V}}{\mathit{\max}-\mathit{\min}}}$$
(5)

\(\overline{r}\) u is the mean item ratings that is given by user u, max and min are the maximum and minimum item ratings in the initial rating matrix and ru,i is the rating that is given by user u for item i.

$${V}_{a,i}=\frac{\sum_{u\in {N}_{a,i}}{sim}_{a,u}.{\left({r}_{u,i}-{\overline{r}}_u-{r}_{a,i}+{\overline{r}}_a\right)}^2}{\sum_{u\in {N}_{a,i}}{sim}_{a,u}}$$
(6)

If the reliability value of item rating is more than a threshold that was tuned by systems, then that rating item is a suspect rating.

  1. Step 3:

    Construct network

A weighted user-user network is created using the rating matrix and Trust relationships among users. The weight for each item rating in the initial rating matrix with time t is calculated as Eq. (7).

$${W}_{a,i}^t=\left\{\begin{array}{c}{e}^{-\left(T-t\right)/\theta }\ if\ t>0\\ {}0\kern3.5em otherwise\end{array}\right.$$
(7)

Where, T indicates the last time that item; i was rated by users.

θ is a parameter specified by the user and the value is between 0.25 and 1.25. It should be noted that the higher value of this parameter indicates less effectiveness of time. Accordingly, the new rating matrix (Rt) is ​​generated and its entries are calculated as Eq. (8).

$${tr}_{a,i}=\left\{\begin{array}{c}{r}_{a,i}\times {W}_{a,i}^t\kern1em if\ {r}_{a,i}>0\kern1.25em \\ {}0\kern4.75em otherwise\ \end{array}\right.$$
(8)

T&TRS calculated the implicit trust between users u and a as Eqs. (9) and (10).

$$Trust-{imp}_{a,u}=\frac{d_{max}-{d}_{a,u}+1}{d_{max}}$$
(9)

Where da, u is the distance between users u and a according to the explicit trust in the network.

$${d}_{max}=\frac{\ln (n)}{\ln (k)}$$
(10)

Where, n and k indicate the size and average degree of users in the explicit trust network, respectively.

T&TRS calculated the final similarity between users a and u, f − sima, u, as Eq. 11. This similarity has calculated based on trust between user and time of item ratings using Eq. (12).

$$f\_{sim}_{a,u}=\left\{\begin{array}{ll}{\quad}\frac{2\times t\_{sim}_{a,u}\times Trust-{ im p}_{a,u}}{t\_{sim}_{a,u}+ Trust-{ im p}_{a,u}} & {t}\_sim_{a,u}>0\ and\ Trust-{ im p}_{a,u}>0 \\ {\qquad} t\_{sim}_{a,u} & {\quad} t\_{sim}_{a,u}>0\ and\ Trust-{ im p}_{a,u}\le 0\\ Trust-{ im p}_{a,u} & {\qquad}{t_{sim}}_{a,u}\le 0\ and\ Trust-{ im p}_{a,u}>0 \\ {\quad}0 & {\quad}{t_{sim}}_{a,u}\le 0\ and\ Trust-{ im p}_{a,u}\le 0 \end{array}\right.$$
(11)
$$t\_{sim}_{a,u}=\frac{\sum_{i\in {I}_{a,u}}\left(t{r}_{a,i}-{\overline{tr}}_a\right)\left({tr}_{u,i}-{\overline{tr}}_u\right)}{\sqrt{\sum_{i\in {I}_{a,u}}{\left({tr}_{a,i}-{\overline{tr}}_a\right)}^2}\sqrt{\sum_{i\in {I}_{a,u}}{\left({tr}_{u,i}-{\overline{tr}}_u\right)}^2}}$$
(12)

Where \({\overline{tr}}_a\) is the average ratings that given by user a and Ia, u indicates the items which are rated by both users u and a.

  1. Step 4:

    Detect Clusters

In this phase, we proposed a novel community detection method that consists of three phases and find the sparsest sub graph of weighted user-user network. The pseudo-code of our proposed graph-based community detection as algorithm 1 is shown in Fig. 3. In the first phase, the initial centers of communities are obtained using a sparsest sub graph of weighted user-user network. After selecting the initial center of communities, our proposed community detection algorithm calculates the fitness function using Eq. 15 for each node. The nodes add to the community with the maximum value of fitness function and the algorithm identifies the new initial centers. These steps will continue until all nodes have been attached to the communities. In the next step, our proposed algorithm merges the overlapped communities.

Fig. 3
figure 3

Our proposed community detection algorithm

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Figure 4 shows the pseud-code of algorithm 2 for selecting the initial centers of communities. It should be noted that the initial centers must have the maximum dissimilarities with each other based on the general concept of clustering and community detection algorithms. Consider the graph G = (V, E, H) as a weighted user-user network, V, E and H indicate users, the relationship between users, and the weights of the relationship (f _ sima, u), respectively. The density of a sub-graph S⊆V is defined as Eq. 13.

$$\rho (S)=\frac{\sum_{e\epsilon E(S)}{H}_e}{\left|S\right|}$$
(13)
Fig. 4
figure 4

Finding initial centers algorithm

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Where He ∈ H is the weight of the edge e and E(S) denotes the edges set of the sub-graph S.

The weighted degree of each node a (user a) ∈ S is calculated as Eq. 14.

$${wd}_s(a)=\sum_{e_{au}\in E(S)}{H}_{e_{au}}$$
(14)

The candidate nodes set, \(\overset{\sim }{A}(S)\) consists of the nodes which weighted degrees are higher than the threshold value ((2 + 2ε) ∗ ρ(S)). The algorithm sorts the members of this set based on their weighted degrees and removes a portion of them with the highest weighted degree. The algorithm will be continued on the remaining nodes in an iterative process until the resulted sub-graph is non-empty. It should be noted that the output of the algorithm is a sub-graph with k nodes. These nodes can be considered as the initial centers of the graph.

After selecting the initial centers of communities, the users can be assigned to their nearest communities. For each user, T&TRS calculated the fitness function as Eq. 15. User has associated to the community, Cj which has a high value of fitness function. Then the centers of communities were updated in order to maximize a fitness function.

$${f}_{v_a}=\frac{\sum_{v_t\in {C}_j,{v}_u\ne {v}_a}f\_{sim}_{a,u}}{\sum_{v_u\in {C}_j,{v}_u\ne {v}_a}f\_{sim}_{a,u}+\sum_{C_k\in C,{C}_k\ne {C}_j}\sum_{v_u\in {C}_k,{v}_u\ne {v}_a}f\_{sim}_{a,u}}$$
(15)

Where C indicates the set of communities, f _ sima, u is the weight between the nodes va and vu which is calculated as Eq. 11. This process is iteratively repeated until members of communities do not change and a steady state is achieved. A set of communities are identified where the users are assigned to their corresponding communities. Some of the communities may have overlap and they can be merged. The pseudo-code of the overlapping community algorithm [59] is shown in Fig. 5. If two communities have too many overlapping nodes, they should be merged into a single community according to the different sizes of communities. First, our propose system calculated the overlap ratio and the combined parameter as Eqs. 16 and 17 respectively. Then according to these values, our proposed system decides how to combine the communities based on the two rules as follow:

$$r_{pq}=\frac{\max\left(\left|C_p\right|,\left|C_q\right|\right)}{\min\left(\left|C_p\right|,\left|C_q\right|\right)}$$
(16)
Fig. 5
figure 5

Overlapping community algorithm

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Where Cp and Cq are the pth and qth overlapping communities.

$$\zeta =\frac{\rho_2+{\rho}_1\times {\rho}_2-{\rho}_1}{\rho_1}$$
(17)

ρ 1, ρ2 ∈ [0, 1] are pre-designed thresholds.

If rpq < ζ It means that the size of the two communities is different.

  1. Rule 1:

    If the size of two communities is equal, then we calculated the overlapping proportion using Eq. (18) and if this value is greater than ρ1, our propose system will combine the two communities.

$${\delta}_{pq}=\beta \times \frac{\left|{C}_p\cap {C}_q\right|}{\left|{C}_p\cup {C}_q\right|}+\left(1-\beta \right)\times \frac{\left|{NC}_p\cap {NC}_q\right|}{\left|{NC}_p\cup {NC}_q\right|}$$
(18)

Where NCp and NCq are the set of neighbor nodes that directly connected to the nodes in Cp and Cq, respectivly. βϵ[0, 1] is a parameter to determine the influence of internal nodes of the neighbors list.

  1. Rule 2:

    If the size of two communities is different, then we calculated the overlapping proportion using Eq. 19 and if this value is greater than ρ2, our propose system will combine the two communities

$$\delta_{pq}=\frac{\left|C_p\cap C_q\right|}{\min\left(\left|C_p\right|,\left|C_q\right|\right)}$$
(19)

The final communities were used as the nearest neighbors set of the active user in the same community for items recommendation.

Figure 6 shows an example of our proposed graph-based community detection method. The weighted user-user network is shown in Fig. 6a. The initial centers of communities are identified in Fig. 6b where four nodes are considered as the centers set. Based on the general concept of clustering and community detection algorithms, the obtained centers should be dissimilar to each other as much as possible. Finally, the final communities are shown in Fig. 6c.

Fig. 6
figure 6

a Example of trusted user-user network, b community centers, and c final communities

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The most important problem to identify communities is the initial number of clusters and also the centers of the clusters which are selected randomly. In this method, the center of the clusters should be the nodes that have the maximum links with other nodes in the network.

  1. Step 5:

    Identify the suspicious users

The similarity of these users with the center of the cluster is calculated Using Eq. (11) described in step 3 of proposed system. If this value was less than the threshold, that user is considered as a fake user and if all item rates given by this user are not labeled as fake, the user will not be removed from the collection, otherwise the user will not be considered in the prediction process.

  1. Step 6:

    Predict the rating of unobserved items

In this step, our propose system recommends the items that relevant to the active user. The users that belongs to the same cluster which contains the active user have considered as the neighbors of active user. We proposed the novel formula as Eq. (20) to predict the rating of unobserved items for active user.

$${P}_{a,i}=\overline{r_a}+\frac{\sum_{u\in {N}_{a,i}}f\_{sim}_{a,u}\ \left({r}_{u,i}-\overline{r_u}\right)}{\sum_{u\in {N}_{a,i}}f\_{sim}_{a,u}}$$
(20)

Where, ̅𝑟̅𝑎̅ is the average rating given by user a, and 𝑁𝑎,𝑖 is the set of neighbors of user 𝑎 who rated item 𝑖, and 𝑓_𝑠𝑖𝑚𝑎,𝑢 is the similarity between user 𝑎 and user 𝑢, that was calculated as Eq. 11 described in the step 3 of proposed system. After ranking the unobserved items based on the prediction values, the Top@N recommendation generated for active user.

  1. Step 7:

    Remove the suspect items

In this step, the propose system check the Top@N recommendation for active users. Any item of the list which has been rated for more than 80% of fake users will delete and the remained items recommend to the active user.

4 Evaluation of T&TRS

We evaluated the proposed T&TRS system on the Epinions dataset contains 943 users, 1682 items, 3212 ratings, 3325 trust and 99.97% sparcity in two phases: Recommendation list and Attack detection. The Epinions dataset has been collected over several years. We grouped items into different months to better assess the impact of time on user tastes. Item ratings are 1 to 5, that 5 represent the highest rate. This dataset also contains the rating time and trust between users

We evaluated T&TRS based on Precision, Recall, F-measure, MAE, RMSE and RC measures, which can be calculated using Eqs. 21 to 26, respectively. In this paper, in addition to evaluate the Top@N items recommendations to the target user, the accuracy of detecting and deleting attack profiles was also calculated.

$${Precision}=\frac{1}{n}\sum\limits_{i=1}^n\frac{TP}{TP+ FP}$$
(21)
$${Recall}=\frac{1}{n}\sum\limits_{i=1}^n\frac{TP}{TP+ FN}$$
(22)
$$F1=\frac{2\times {precision}\times {recall}}{{precision}+{recall}}$$
(23)

In the above equations, True Positive (TP) represents the items that are attractive to users and are recommended to users, False Positive (FP) represents the items that are not attractive to users but are recommended to them, False Negative (FN) represents the items that are not recommended but users are interested in them and (TN) presents real negative.

$$MAE=\frac{\sum_{i=1}^N\left|{r}_i-{p}_i\right|}{N}$$
(24)
$${RMSE}=\sqrt{\frac{1}{N}\sum\limits_{i=1}^N\left({\textrm{r}}_i-{p}_i\right)}$$
(25)

Where, pi and ri are the predicted and actual rates of item i, respectively and N is the number of all predicted rates.

$$RC=\frac{\#{number}\ {of}\ {predicted}\ {ratings}}{\#{number}\ {of}\, all\,{ratings}}$$
(26)

4.1 Community detection

We evaluated our proposed algorithm on the Epinions data set and compared the results with a time-based recommender system. Tables 2, 3 and 4, show precision, recall, and F1 measures of different algorithms for N = 5, 10, 15, 20, 25 and 30 for Top@N recommendation respectively. As shown in Table 3, TRACCF [60] method has the best performance for all values of N except the value 30 and the precision decreases when the value of N increases. As shown in Tables 3 and 4, our proposed method, T&TRS, outperforms the two K-means methods for User-based CF (KMCF-U) and Item-Based CF(KMCF-I), TOTAR [59] algorithms and TRACCF algorithm for N=30. The performance of T&TRS is better than TRACCF according to the recall and F1-measure.

Table 2 The precision of different algorithms
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Table 3 The Recall of different algorithms
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Table 4 The F1-measure of different algorithms
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Figure 7 illustrates the performance of different recommender systems in terms of MAE, RMSE, and RC measures. Our proposed method has the lowest MAE and RMSE values in comparison to the other methods.

Fig. 7
figure 7

The comparison of methods based on RMSE, MAE and RC measures

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Our proposed community detection algorithm includes two adjustable parameters (φ and θ), and its performance depends on assigning proper values for these parameters. Tables 5 and 6 show the experimental results considering the different values of these parameters. According to these results, it can be seen the best value for θ = 0.25 and φ = 1 for MAE, RMSE and RC measures. So, we considered these values for evaluating our proposed method.

Table 5 Impact of θ parameter of proposed community detection algorithm
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Table 6 Impact of φ parameter of proposed community detection algorithm
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Table 7 shows the time complexity of the proposed system compared to the other systems. n is a number of users and m is a number of items. In cluster-based methods, the number of clusters must be predefined. For example, in TRACCF [60], KMCF-U and KMCF-I, C denotes the number of clusters and k denotes the maximum number of iterations. In real-world cases, k and c are often small (k, c <  < n), and thus can be ignored in the time complexity analysis. Also in the clustering method, the number of iterations is considered as a fixed number, so the time complexity of TRACCF [60] can be reduced to O(nm). On the other hand, graph-based methods such as T&TRS and TOTAR [59] need to create a graph of users and items in their processes and their time complexity is O(n2m). Moreover, the graph-based methods require O(n2m + nm) memory, while the memory complexity of the other methods is O(nm).

Table 7 Time complexity of the different algorithms
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However, the time and memory complexities of the proposed method, T&TRS, are the same as graph-based methods such as TOTAR [59]. On the other side, the time complexity of TRACCF [60] is better than T&TRS, but it does not consider the Time concept in the recommendation process, and their MAE, and RMSE values are more than T&TRS.

4.2 Attack detection

To evaluate the proposed system, a number of fake profiles as attack were first added to Epinion dataset, including 20 fake profile sizes, each of which had 20 random and average attacks in a compressive and declining manner through tools introduced in [57] by adding the ratings between 1 to 5. The results obtained after applying the proposed method to the dataset with and without attack for TOP@N recommendation can be seen in Table 8. These results show the negative impact of attacks on the performance of the recommender system.

Table 8 Experimental results of the T&TRS
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Figures 8, 9 and 10 show the results of Precision، Recall and F1 measures for random and average attack in deference filler and attack size conditions.

Fig. 8
figure 8

Precision for Top@N item recommendation

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Fig. 9
figure 9

Recall for Top@N item recommendation

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Fig. 10
figure 10

F1 measure for Top@N item recommendation

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Table 9 shows the evaluation results of proposed method after detecting fake users and items and removing them from the data set.

Table 9 Evaluation of T&TRS after removing attacks
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In order to set the optimal value of the parameter θ and threshold different values ​​of 0.25,0.5,0.75 and values of 0.25,0.8 ​​were examined, respectively. For the final evaluation of the proposed system according to Tables 10 and 11, the values ​​of 0.5 and 0.1 are considered the best values ​​for the parameters of θ and threshold, respectively.

Table 10 Parameter values of θ to evaluate T&TRS
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Table 11 Parameter values of thereshold to evaluate T&TRS
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5 Conclusion and future work

Attack detection is one of the major challenges of collaborative filtering recommender systems. If recommender systems able to detect attacks, then they can increase the precision of Top@K items recommendations. Our proposed collaborative filtering recommender system, T&TRS, reduced the impact of Average and Random attacks by identifying and eliminating attack profiles. In our proposed system, a new method of community detection has been introduced, that has increased the precision of clustering for finding fake users. The most important problem to identify communities is the initial number of clusters and also the centers of the clusters which are selected randomly. In T&TRS, the nodes with high links in the generated user-user network are selected as the center of the clusters. We evaluated our proposed community detection algorithm on the Epinions data set and compared the results with the similar methods. The experiential results showed that the precision of our community detection method was superior to theirs. The precision of the algorithm for Top-30 items recommendation was 0.8543 that shows a 0.03 improvement by comparison with the other algorithm. The F1-measure value of our proposed community detection algorithm was also better than the other algorithms. However, the time and memory complexities of the proposed community detection method are the same as graph-based methods such as TOTAR. The overall performance of T&TRS with this community detection algorithm is better than TRACCF according to F1-measure and has the lowest MAE and RMSE values in comparison to the other models

The experimental results of T&TRS evaluation on the Epinion data set by injecting the attacks have shown that the precision of recommendations has been increased after the attacks have been detected and the rating of fake users in the rating matrix has been removed.

Unfortunately, the strategies of attack often mix together to carry out the actual attacks. In future work, the proposed system will be evaluated on these attacks called group attacks and we will introduce a framework to design a robust collaborative filtering Recommender system against all types of attacks.