1 Introduction

Academic social networks include various network service support systems and platforms that provide specific academic and social functions for learners, such as Google Scholar, Academia.edu, Semantic Scholar, ResearchGate, Academia.edu, and Scholat.com [1]. Academic social networks can help realize the organic integration of academic resources and the social connections of learners, facilitate scientific and educational cooperation, and maintain the academic circles of scholars. A friend recommendation system can accurately and efficiently recommend a list of potential friends by mining the historical behavior preferences of learners and providing personalized recommendation services.

However, the association data of learners, especially the data of lazy learners and cold-start learners, are sparse, which makes it difficult to recommend valuable suggestions with nearly zero experience. Therefore, mining implicit friends to provide targeted academic services considering the spatial distribution of learners is a significant research direction. Discovering similar learners using multiple evaluation factors, including the learners’ attribute characteristics, disciplinary backgrounds, and academic levels in academic social networks, has become an important task in learner social networks [2]. Due to the development of learner social networks, some researchers have used the explicit social relationships of learners to address the problem of data sparseness and explore the implicit relationships between friends through inferences of friend preferences [3,4,5]. The methods of mining implicit friends continue to gain more attention in the field of academic social network studies. With a recommendation system, learners can obtain friends who have similar learning interests, majors or geographical locations to create new learning communities and build academic circles. Doing so helps us standardize and guide learners' learning behavior, timely identify learning partners who can provide them with learning-oriented services, and make personalized recommendations, so as to promote the achievement of learners' learning goals and achieve better academic progress. In this paper, implicit friends are learners who share learning interests with other learners in academic social networks.

There are still problems to solve for academic social network recommendation systems. First, the recommendation fit is low, and there is a lack of personalized recommendations for learners, resulting in too much useless information. Second, the explicability is insufficient, and the recommendation reasons are either insufficiently persuasive or provided inappropriately. Third, for cold-start learners, it is impossible to obtain enough topological relationships and attribute feature information to mine potential friends. Several empirical studies have reported that scholar recommendation methods based on location-based social network (LBSN) information [6,7,8,9,10] can recommend a wider range of strangers according to the users’ frequently used check-in information. These studies aim to solve the problems of sparse data and increase the possibility of acceptance by users.

Similarity-based recommendation algorithms [11,12,13,14] have explored the use of explicit social relationships among learners to mine implicit friends. However, these approaches still cannot solve the aforementioned problems.

In this paper, a personalized explainable learner implicit friend recommendation method (PELIRM) is proposed, which provides a solution for potential friend mining of cold-start learners by utilizing the combined information of the learners' three-degree influences and IP check-in information in the learner's social network. Our proposal is built on the trust model proposed in [15]; the similarity of academic interests is screened, the Top-N recommendation targets are identified, and the recommendation reason is provided. This method can better describe the implicit associations between learners, especially for cold-start learners, effectively alleviating the problem of data sparseness in the learners' social networks and enabling learners to obtain more accurate and efficient services and management.

The main contributions of this paper are as follows.

  1. (1)

    PELIRM is proposed. It integrates learners’ check-in information, trust, and academic interest similarity to provide recommendation reasons and enhance the learners' confidence in the recommendation effect. To the best of our knowledge, this is the first study to employ learners’ check-in information as an influencing factor of recommendations.

  2. (2)

    The learners' implicit topological friend relationships are defined to address the data sparseness and cold-start problems. We can obtain the nodes of implicit friends to construct the learner's learning topology relationship network with the built model by using the learner's three-degree influences in the academic social network and IP check-in information.

  3. (3)

    A large number of experimental analyses are conducted on a real Scholat.com dataset, and the experimental results demonstrate that our proposed PELIRM is superior to other traditional algorithms.

2 Related Work

Potential friend recommendation for learner social networks has become a research hotspot. In this section, we review some of the latest literature on recommendation methodologies that take advantage of explainability.

2.1 Recommendation Methods Related to Learner Social Networks

In recent years, the rise of social networks for learners has received widespread attention. The results of existing research have laid a solid foundation for learners to understand the value of their social networks, such as promoting academic cooperation and knowledge exchange and influencing the future direction of development. Currently, the recommendation approaches for academic social networks are mainly divided into three categories: (1) collaborative filter recommendation, (2) content-based recommendation, and (3) hybrid recommendation. In brief, collaborative filter recommendation is based on an information matrix constructed between users and products. Content-based recommendation matches the user's interests with the degree to which the system recommends items. Hybrid recommendation is mainly for fusion recommendation by the first two algorithms.

Hannon et al. [24] analyzed the similarity of interests among learners to cluster learners according to degrees of similarity for personalized recommendation. In [20], He et al. proposed a two-label LDA model, using the social relationship between well-known users and ordinary users in the Twitter network, as well as the potential relationship between well-known users, extracting the interest tags of ordinary users, and using a random walk model to generate rankings for ordinary users' interest tags. The authors of [16] developed an approach that combines personalized user preferences, social relationships, and geographic locations for recommendation. In [17], Shi et al. employed a collaborative filtering method to construct a similarity matrix of user learning records on an education platform to make personalized recommendations. Liu et al. [18] designed a model for measuring the implied similarities between friends to improve the accuracy of their algorithm with the help of implicit feedback. Li et al. [23] put forward a model for assigning tasks based on work preference, using bipartite embedding and attention mechanisms, as well as tree decomposition techniques, to model social impact preferences and group task assignments, respectively. Farid et al. [22] classified the potential friends of learners in large-scale social networks into two categories of "possibly known" and "possibly interested" to provide personalized recommendations based on the user's common friend relationship topology and a user profile text similarity calculation model. Xiong et al. [21] proposed a scholar recommendation model for a virtual community that uses the latent Dirichlet allocation (LDA) model to calculate text similarity and the ratio of common friends between scholars that incorporates the weights of the similarities of friends recommended by scholars. In [19], Qiu et al. made use of the term frequency-inverse document frequency (TF-IDF) model and LDA model, respectively, to calculate the similarities of learners' interests and academic achievements with mixed weightings to obtain the comprehensive academic interest similarity. Combined with the trust between learners, the comprehensive similarity between learners is used to recommend learners. Although the above algorithms have achieved good results, none of them explain the recommendation results.

2.2 Explanatory Research on Personalized Recommendation Methods

Explainability is becoming a new hot topic in the field of recommendation systems. When users are faced with a list of recommendations without explanations, it will be difficult for them to judge the usefulness of the recommendation results [25]. Having meaningful reasons for recommendations can increase the user’s acceptance and trust in the recommendation result. Making the recommendation system transparent is important for the development of recommendation systems [26]. In [27], the author summarized five aspects of interpretable recommendations: when, where who, what, and why. That is, explainable recommendations should include time-aware recommendation (When), geographical location point of interest recommendation (Where), social network friend recommendation (Who), e-commerce website product recommendation (What), and reasoned recommendation results (Why). Zhang et al. [28] put forward interpretable suggestions for the issues that users care about regarding a product by extracting the user's preferences for the product from the comments. Zhao et al. [29] took advantage of probability models to obtain users' characteristic preferences and geographical location preferences for points of interest and combined the theme model to determine a user's preferences for a certain aspect of the point of interest (geographical location, theme model) and provide explanations for user recommendations. In [30], Wang et al. developed a model of the intent to use an AI recommendation system by looking for users’ behavior intent factors in AI recommendation, considering the fairness of the program and the interpretability of the system. Custode et al. [32] proposed a method of enhancing interpretability learning through decision trees, complementing the advantages of evolutionary algorithms and Q-learning. In [31], since interpretability is inherently subjective, Marco et al. proposed a way to control the process of model synthesis through user preferences (ML-PIE), using a biobjective evolutionary algorithm to make trade-offs between accuracy and interpretability and using neural networks to train on user feedback. In [33], Xie devised a recommendation method for disseminating knowledge across disciplines and considered the intrinsic factors of the recommendation results in an interpretable manner. In [34], Chen proposed an unsupervised learning model (HAI) that combines attention mechanisms and mutual information, explores potential relationships through the metapaths of learner concern, and provides interpretable suggestions.

In summary, although the current personalized recommendation and interpretability research on academic social networks has made great efforts, there are still many problems in practical applications. (1) The principle of solvability is widely used in recommendations of items such as commodities and has not yet been widely used in academic social networks. Interpretable recommendations can be more easily accepted by learners. (2) For cold-start learners, their preference information cannot be obtained, causing difficulty in recommendation problems. This paper uses the method of IP check-in information to push nearby learners because nearby learners are most likely to belong to the same college or the same major. In this paper, the PELIRM algorithm integrates the trust degree of learners' friends and the similarity of academic interests and includes nearby scholars through IP check-in information to deliver an explainable recommendation method.

3 Research Methods

In the development of academic social networks, learners can enhance mutual trust through interactive information, such as the number of homepage visits and the number of likes within a circle of friends. The similarity of preferences among learners can be judged by the learners' research interests and academic achievements. Two learners who are close together are more likely to become friends. Combining these three pieces of information yields personalized, interpretable potential friend recommendations based on learners' trust, similarity, and distance. The flowchart of the PELIRM algorithm proposed in this paper is shown in Fig. 1.

Fig. 1
figure 1

Algorithm flowchart

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3.1 Calculation of Learner Trust Based on Three Degrees of Influence

3.1.1 Three Degrees of Influence

A learner's social network is modeled as an undirected complex network graph \(G(V, E)\), where V represents a set of learners in the social network and E represents the set of friendships between learners; if there is a friendly relationship between two learners, an undirected edge is drawn between the two learners in the graph. Figure 2 shows a graph with 6 nodes. Each node represents a learner from \({\rm learner}_{1}\) to \({\rm learner}_{6}\), each solid link between two nodes indicates a direct friendship between the two learners, and each dotted line indicates that two learners may become friends.

Fig. 2
figure 2

Diagram of an undirected social network

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This research uses three degrees of influence to find second- and third-degree friends. The specific method is described as follows:

Step 1 is to obtain a set of direct friend relationship pairs for each node in the complex network graph \(G(V, E)\). A pair of nodes is called a buddy node pair if there is a direct link between the two nodes in G. That is, we generate a buddy set \(\{ < {\rm learner}_{i}, {\rm learner}_{j}> in E, i\ne j, {\rm learner}_{j} in V\}\) for every node \({\rm learner}_{i}\).

Step 2 is to find a set of second-degree friendships of each node \({\rm learner}_{i}\) through the known buddy node pairs by traversing the public nodes in G. That is, if a node \({\rm learner}_{i}\) has two buddy node pairs \(<{\rm learner}_{i},\,{\rm learner}_{j} >\) and \(<{\rm learner}_{i}, {\rm learner}_{k} >\), we can obtain a second-degree friend relationship of \({\rm learner}_{i}\), recorded as \(<{\rm learner}_{j}, {\rm learner}_{i}, {\rm learner}_{k} >\). Similarly, we can obtain a set of second-degree friends of any arbitrary node \({\rm learner}_{x}\) in the learner social network.

Step 3 is to pair the acquired second-degree friend relationship with the existing one-degree buddy pairs to generate third-degree friendships. Specifically, we choose an arbitrary node \({\rm learner}_{i}{s}^{\prime}\) one-degree friend pair \(<{\rm learner}_{i},\,{\rm learner}_{j} >\) to match to a second-degree friend relationship triplet \(<{\rm learner}_{i}, {\rm learner}_{x},{\rm learner}_{y}>\), where \({\rm learner}_{i}\) is a common head node appearing in both friendships. Third-degree friendship quadruple is obtained as \(<{\rm learner}_{j},{\rm learner}_{i},{\rm learner}_{x},{\rm learner}_{y}>\) for node \({\rm learner}_{i}\).

Let's consider a real-life example: the idea that teachers are seen as friends is becoming more and more accepted. As shown in Fig. 2, the relationship between teacher and learner can be seen as friendship. Student \({\rm learner}_{2}\) and \({\rm learner}_{4}\) are students of teacher \({\rm learner}_{1}\) and \({\rm learner}_{3}\), respectively, and teacher \({\rm learner}_{1}\) and \({\rm learner}_{3}\) are friends, and their research content and topics are similar. Applying the algorithm of three-degree friendship, we can get two triplets of second-degree friendship, as shown in Fig. 2. Therefore, a potential suggestion is based on ({\({\rm learner}_{3}\)|\({\rm learner}_{1}\)}, \({\rm learner}_{2}\)) and ({\({\rm learner}_{1}\)|\({\rm learner}_{3}\)},\({\rm learner}_{4}\)). \({\rm learner}_{1}\) teachers recommend \({\rm learner}_{4}\) to students and instruct students \({\rm learner}_{4}\) to conduct more in-depth research in the major. Since teacher learner1 and teacher \({\rm learner}_{3}\) are friends and have the same research interests, you can try to recommend student \({\rm learner}_{4}\) to student \({\rm learner}_{2}\) to promote academic exchanges between students and make progress together.

3.1.2 Calculating the Degree of Learners' Interactive Trust

In complex social networks, each learner may have many friends, but the intimacy between them varies. Reference [16] proposed two kinds of trust relationships between friends: cognitive trust and interactive trust. Cognitive trust is calculated as follows: two learners have established a friendship relationship, which is defined as knowing trust. Interactive trust is calculated as follows: a pair of friends usually communicate frequently in social networks, such as by visiting each other's homepages and liking a post by someone in their friend circle. In this paper, the degree of friend trust is calculated by mixing cognitive trust and interactive trust. The calculation formula is shown in Eq. (1).

$$\begin{array}{c}Fr\left(u,v\right)=Kr\left(u,v\right)+Ir\left(u,v\right)\end{array}$$
(1)

where \(Fr(u,v)\) indicates the degree of trust of learner \(u\) with respect to learner \(v\). \(Kr(u,v)\) is cognitive trust, indicating whether learner \(u\) and learner \(v\) are already friends. In the literature [15], it is proposed that cognitive trust has less influence on users than interactive trust, if a friendship relationship exists, \(Kr(u,v)\) is set to a fixed value of 0.1; otherwise, it is 0. \(Ir(u,v)\) is interactive trust, indicating the interactive behavior of learner \(u\) with respect to learner \(v\). We use home page visits and dynamic likes in interactive behaviors to calculate learner trust. The calculation methods of each interactive trust level are shown in Eqs. (2) and (3).

$$\begin{array}{c}Ar\left(u,v\right)=\frac{Ia\left(u,v\right)}{\mathrm{Sum}\left(Ia\left(u,i\right)\right)}\end{array}$$
(2)
$$\begin{array}{c}Zr\left(u,v\right)=\frac{Iz\left(u,v\right)}{\mathrm{Sum}\left(Iz\left(u,i\right)\right)}\end{array}$$
(3)

where \(Ar (u, v)\) and \(Zr (u, v)\) represent learner \(u\)'s access-based interactive trust and like-based interactive trust toward learner \(v\), respectively, and \(Ia (u, v)\) and \(Iz (u, v)\) represent the number of visits and dynamic likes of learner \(v\)’s home page, respectively. \({\rm Sum} (Ia (u, v))\) and \({\rm Sum} (Iz (u, v))\) represent the total number of visits and total likes of learners for all learners, respectively. Equations (2) and (3) above can be synthesized to obtain the interactive trust degree \(Ir (u, v)\) calculation method as shown in Eq. (4).

$$\begin{array}{c}Ir\left(u,v\right)=\partial Ar\left(u,v\right)+\left(1-\partial \right)Zr\left(u,v\right)\end{array}$$
(4)

where ∂ is a parameter. According to the actual situation, the weights of the interaction behaviors of different learners' social networks are adjusted, and the trust value between learners is obtained by substituting it into Eq. (1).

The level of trust between learners' friends within the third degree is calculated from the second-degree friendship and the third-degree friendship based on the third degree of influence in Sect. 3.1.1, as shown in Eqs. (5) and (6).

$$\begin{array}{c}{T}_{2}\left(u,\,v\right)=\frac{{\sum }_{\left(u,\,i,\,v\right)\in S}\left(Fr\left(u,\,i\right)\times Fr\left(i,\,v\right)\right)}{2}\end{array}$$
(5)

where \({T}_{2}\left(u,v\right)\) represents the second-degree friend trust value between learner \(u\) and learner \(v\); \(S\) represents the set of second-degree friends of learner \(u\),\(Fr(u, i)\) represents the trust value between learner \(u\) and learner \(i\), and the denominator 2 represents the number of edges between learners u and \(v\).

$$\begin{array}{c}{T}_{3}\left(u,\,v\right)=\frac{{\sum }_{\left(u,\,j,\,k,\,v\right)\in T}\left(Fr\left(u,\,j\right)\times Fr\left(j\,,k\right)\times Fr\left(k,\,v\right)\right)}{3}\end{array}$$
(6)

where \({T}_{3}\left(u,v\right)\) represents the third-degree friend trust value between learner u and learner \(v\); \(T\) represents the set of third-degree friends of learner \(u\), and the denominator 3 represents the number of edges between learner \(u\) and learner \(v\).

Mix-weighting the degrees of trust of friends within three degrees yields the final degree of trust of learner \(u\) in learner \(v\), \(T(u, v)\), as shown in Eq. (7).

$$\begin{array}{c}T\left(u,v\right)=\alpha {T}_{2}\left(u,v\right)+\left(1-\alpha \right){T}_{3}\left(u,v\right)\end{array}$$
(7)

where \(\alpha \) adjusts the second- and third-degree friend trust parameters, and \(\alpha > 0.5\). In real life, second-degree friends are often easier to contact than third-degree friends. However, in learner social networks, sometimes a friend is both the learner's second-degree friend and third-degree friend. As shown in Fig. 2, \({\rm learner}_{2}\) and \({\rm learner}_{4}\) have a second-degree friendship, as shown by the triplet \(< {\rm learner}_{2}, {\rm learner}_{5}, {\rm learner}_{4} >\), and the quadruple \(< {\rm learner}_{2},\,{\rm learner}_{1},\, {\rm learner}_{3},\,{\rm learner}_{4}>\) shows a third-degree friendship between \({\rm learner}_{2}\) & \({\rm learner}_{4}\). We only consider the situation in which \({\rm learner}_{2}\) and \({\rm learner}_{4}\) are second-degree friends.

3.2 Similarity of Academic Interests

In this section, the interest data of each learner are selected from the academic interest dataset T of the Scholar Network, the cosine similarity method is used to calculate the text similarity between learners, and the TF-IDF model is used to calculate the similarity of the learner's recently published academic achievements (papers). Finally, the two methods are weighted and mixed to calculate the degree of academic interest similarity between learners.

To obtain the similarity for text calculation, first, the learner's interests and hobbies are segmented into words, all words are listed (stop words can be processed), the word segmentation is encoded, the word frequency is vectorized, and finally the two text similarities are calculated by the cosine function. The calculation method is shown in Eq. (8):

$$\begin{array}{c}{S}_{COS}\left(u,v\right)=\frac{\sum_{i=1}^{n}\left({u}_{i}\,\times \,{v}_{i}\right)}{\sqrt{\sum_{i=1}^{n}{\left({u}_{i}\right)}^{2}\times \sum_{i=1}^{n}{\left({v}_{i}\right)}^{2}}}\end{array}$$
(8)

where \({S}_{cos}(u,v)\) represents the similarity value of \(learner u{^{\prime}}s\) and \(learner v{^{\prime}}s\) interests and hobbies, and \({u}_{i}\) and \({v}_{i}\) indicate the learners' interests and hobbies.

The TF-IDF model calculates the similarity of each learner's recent academic achievements (published papers). The TF-IDF model focuses on how often a word appears in one paper more frequently than in other papers. First, it iterates through all learners to obtain the corresponding academic achievement data, calculates the learner's academic outcome vector, and finally calculates the similarity between the two learners. The calculation method is shown in Eq. (9):

$$\begin{array}{c}{S}_{TF-IDF}\left(u,v\right)=\frac{\sum_{i=1}^{n}\left({p}_{ui}\,\times \,{p}_{vi}\right)}{\sqrt{\sum_{i=1}^{n}{\left({p}_{ui}\right)}^{2}\,\times \,\sum_{i=1}^{n}{\left({p}_{vi}\right)}^{2}}}\end{array}$$
(9)

where \({S}_{TF-IDF}(u,v)\) represents the similarity value of the academic outcomes of learner \(u\) and learner \(v\), and \({p}_{ui}\) and \({p}_{vi}\) represent the values of the ith learner \(u\) and learner \(v\) characteristic vectors.

The results of the interest similarity \({S}_{cos}(u,v)\) and the academic achievement similarity \({S}_{TF-IDF}(u,v)\) are weighted and mixed to obtain the final similarity \(S\left(u,v\right).\) The calculation formula is shown in Eq. (10).

$$\begin{array}{c}S\left(u,v\right)=\beta {S}_{cos}\left(u,v\right)+\left(1-\beta \right){S}_{TF-IDF}\left(u,v\right)\end{array}$$
(10)

where \(\beta \) is the adjusted weight parameter.

3.3 Geographical Distance Based on IP Check-In

We determine the common unit where the learners are located, such as a school, company, or community, through the check-in information of each learner logging on to the scholar network. The method obtains the corresponding IP information, finds the latitude and longitude corresponding to this information, calculates the geographical distance between the two learners through the latitude and longitude, recommends nearby learners, and facilitates offline communication and cooperation. Particularly for newly registered users, there is not much information available, and it is difficult to accurately make these cold-start user recommendations. We can obtain learner information near new users through IP check-in information and give them recommendations, effectively solving the recommendation problem of cold-start users. The difference between the latitude and longitude of any two points on Earth is calculated using Eq. (11).

$$\begin{array}{c}C\left(u,v\right)=\mathrm{sin}\left(MLat\left(u\right)\right)\times \mathrm{sin}\left(MLat\left(v\right)\right)\times \mathrm{cos}\left(MLon\left(u\right)-MLon\left(u\right)\right)\\ +\mathrm{cos}\left(MLat\left(u\right)\right)\times \mathrm{cos}\left(MLat\left(v\right)\right)\end{array}$$
(11)

where \(C(u, v)\) represents the difference between the latitudes and longitudes of learners \(u\) and \(v\), \(MLat(u)\) represents the latitude of learner \(u\), \(MLat(v)\) represents the latitude of learner \(v\), \(MLon(u)\) represents the longitude of learner \(u\), and \(MLon(v)\) represents the longitude of learner \(v\).

The distance between learners u and v is shown in Eq. (12).

$$\begin{array}{c}D\left(u,v\right)=\frac{R\times Arccos\left(C\left(u,v\right)\right)\,\,\,\,\times\,\,\,\,\pi }{180}\end{array}$$
(12)

where \(D(u,v)\) represents the distance (km) between learners \(u\) and \(v\) and \(R\) represents the average radius of the Earth.

3.4 Recommendation Based on Trust, Similarity, and IP Check-in Information

After obtaining the degree of trust and similarity of friends within three degrees through Eqs. (7) and (10), the two are weighted, mixed, and combined with the geographical distance between the two learners as an additional consideration. The result is calculated to obtain the combined similarity \(Sim(u, v)\) of learners within three degrees to generate the recommendation rationale. Finally, the Top-N implicit friends are recommended to learners according to the comprehensive similarity. The formula for calculating the comprehensive similarity is shown in Eq. (13):

$$\begin{array}{c}Sim\left(u,v\right)=\frac{\theta T\left(u,v\right)+\left(1-\theta \right)S\left(u,v\right)}{\mathrm{exp}\left(D\left(u,v\right)\right)}\end{array}$$
(13)

where \(\theta\) is a mixture of fusion trust and similarity.

3.5 Generating Explanations for Recommendations

The Top-N learners with the highest similarity as implicit friends will be recommended. The recommendation statements will be based on trust, academic interest similarity, and geographic distance to explain the reasons for the recommendation to the learners. The recommended sentences are constructed in a complete semantically coherent sentence template. For example, in Fig. 2, the explanatory recommendation "\({\rm learner}_{2}\) and \({\rm learner}_{4}\) have a common friend, \({\rm learner}_{5}\) , and both of them are interested in the courses taught by \({\rm learner}_{5}\); 1 km apart." could be given to achieve the goal of constructing explanatory statements based on individualized algorithm selection features to enhance the acceptability of the recommendation system. The pseudocode of PELIRM is shown in Alg. 1.

figure a

3.6 Time Complexity Analysis

In Alg. 1, the cost of calculating both the access matrix and the like matrix between learners is \(\mathrm{O}(n)\), where n represents the number of learners, and the cost of obtaining the intimacy matrix within three degrees between learners is \(\mathrm{O}(\frac{1}{2}{n}^{2})\). The cost of calculating the similarity of academic interests among learners is \(\mathrm{O}({n}^{2})\), The cost of performing the recommendation in the end is \(\mathrm{O}(n)\), Therefore, we can conclude that the time complexity of algorithm 1 is \(\mathrm{O}(2\mathrm{n}+\frac{3}{2}{n}^{2})\).

4 Experiments

4.1 Dataset

The experiments were based on an academic social networking site for a learner community, using a real dataset from http://www.scholat.com to personalize recommendations for each learner. After the data were preprocessed, 28,689 one-way friendships were deduplicated, and finally, 1,514 learners were selected for the experiments, including a total of 30,349 papers published by each learner in the past three years. The dataset includes the basic information of learners, such as academic interests, paper results, home page visits, dynamic links and IP check-ins.

4.2 Evaluation Measures

In this paper, offline experiments are used to test the recommendation algorithm, and Top-N is the most common evaluation criterion among the recommendation algorithms. Validation of the recommendation results uses the F1-measure. The calculation method is as shown in Eqs. (14), (15) and (16):

$$\begin{array}{c}Precision=\frac{\left|R\left(u\right)\;\cap\;T\left(u\right)\right|}{\left|R\left(u\right)\right|}\end{array}$$
(14)
$$\begin{array}{c}Recall=\frac{\left|R\left(u\right)\;\cap\;T\left(u\right)\right|}{\left|T\left(u\right)\right|}\end{array}$$
(15)
$$\begin{array}{c}F1-measure=\frac{2\;\times\;Precision\times Recall}{Precision\;+\;Recall}\end{array}$$
(16)

where \(R(u)\) represents the recommended learner in the experiment, \(T(u)\) is the learner in the verification set, and \(R(u) \cap T(u)\) is the set of recommended learners who have become friends; the accuracy and recall rate are between 0 and 1, and the closer the value is to 1, the better the effect.

We set N to Top-5, Top-10, Top-15 to study the recommended effect. This paper calculates the average similarity of all learners and pairs them with a sample t test p-value.

4.3 Experimental Analysis

4.3.1 Parameter Analysis

According to Eqs. (4), (7), (10), and (13), the corresponding weights of 4 sets of parameters \(\partial , \alpha , \beta ,\) and \(\theta\) are adjusted to home page visits, mixed weighted friend trust within three degrees, mixed weighted academic interest similarity and the comprehensive recommendation scores of learners; they are experimentally compared according to the recommendation effect, and we obtain the optimal parameters by changing the F1-measure value. The experimental effect is shown in Fig. 3 Here, a, b, c, and d represent the F1-measure corresponding to the parameters ∂, α, β, and θ, respectively.

Fig. 3
figure 3

F1-measure change of parameter

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It can be seen from Fig. 3 that when the weight ratio of access information to like information is 3:7, the recommendation effect is the best, and as the number of recommended second-degree friends decreases, the recommendation effect will be worse, the hobbies and interests are better than the academic achievement research recommendation effect, and the trust score has a more obvious impact on the recommendation effect.

Through the analysis of the experimental results in Fig. 3, the four sets of parameters were verified in a combination experiment, and the recommended effect was best when the parameters a = 0.3, b = 0.9, c = 0.1, and d = 0.9. In this paper, 10 sets of parameters are combined by the trend of optimal values obtained by the four parameters in Fig. 3, and F1-measure is verified when the recommended number is Top-5, Top-10, and Top-15. The experimental effect is shown in Fig. 4.

Fig. 4
figure 4

F1 under different parameters of personally recommended

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From Fig. 4, we can see that trust has a greater influence relative to similarity, while other hyperparameters remain constant, which also reflects the tendency of learners to become friends with people they communicate with more.

4.3.2 Comparative Experiment

In this paper, we use ablation experiments to study the influence of the number of recommendations on F1-measure, precision, as well as recall when only learner trust is used, only academic interest similarity is used, and IP check-in is not considered. At the same time, ** showed that the improvement of p < 0.01 was statistically significant through paired t test. The experimental results are shown in Tables 1, 2 and 3.

Table 1 F1-measure for only one model is considered
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Table 2 Precision for only one model is considered
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Table 3 Recall for only one model is considered
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Through this experiment, we can see that the algorithm is still very impressive in precision, but in the recall, there is not much difference compared to other methods. Only similarity is considered to have the worst impact on recommendation performance. The PELIRM used in this paper combines three factors to obtain better recommendation results.

In order to enhance the comparison, we try to combine two modules to form a new ablation experiment and compare and verify with the PELIRM algorithm. Experimental effects are shown in Tables 4, 5 and 6.

Table 4 Consider the F1-measure of the combination of two models
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Table 5 Consider the Precision of the combination of two models
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Table 6 Consider the recall of the combination of two models
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In the experimental comparison after combining the two models, we can see that trust still has a greater impact on the recommendation algorithm, which also reflects that people are more interested in potential friends who are close and communicate a lot. Compared with these models, the recommendation effect of the PELIRM algorithm is still the best.

In addition, the algorithm also compares the effect of F1-measure with three other learner recommendation algorithms under the recommended numbers of 5, 10, and 15. They are the collaborative filtering algorithm, a scholar recommendation method based on trust and research interest (SsmAlg) [15] and a personalized recommendation method based on scholar similarity and trust (LqAlg) [19]. The experimental effect is shown in Fig. 5.

Fig. 5
figure 5

F1-measures of different methods

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It can be seen from Fig. 5 that the recommendation methods in this paper are better than those of the other algorithms in terms of precision, recall and F1-measure performance for different numbers of recommendations. In particular, there is a significant improvement compared to the classic traditional algorithm CF, and the effect is also improved by 3% compared to the recent new algorithm. When the PELIRM algorithm recommends 5 learners, the recommendation accuracy and F1 value are much higher than the number of other recommendations.

5 Conclusion

Academic social networks have become the main gateway for learners to communicate and cooperate. The social relations of learners are an important factor of the effectiveness of recommendations, and they are reflected in academic social networks as interactive behavior. In this paper, we determine the degree of trust between friends through the interactive behavior of learners and use three degrees of influence to explore the implicit friend sets of learners, which solves the problem of data sparseness in academic social networks to a certain extent. Taking into account each learner's research interests and academic achievements, calculating the mixed similarity ensures the feasibility of learner friendships. IP check-in information is used to mine users near learners, which solves the problem of cold-start nodes to a certain extent.

Future work will investigate the effect of the time decay factor on recommendation effectiveness. The current dataset can also be used for offline experiments. Because new users cannot be recommended in real-time updates for learners, in the future, we will make real-time recommendations the main research goal.