A serendipity-biased Deepwalk for collaborators recommendation

Scientific collaborators recommender systems

Methods for recommending scientific collaborators have been studied for decades. The recommendation methods can be divided into content-based, collaborative filtering-based, and random walk-based algorithms on the whole.

Serendipity in recommender systems

Increasing researchers are interested in investigating serendipity in recommender systems, Kotkov, Wang & Veijalainen (2016) wrote a survey to summarize the serendipity problem in recommender systems, including the related concepts, the serendipitous recommendation technologies and metrics for evaluating the recommendation results. They also analyzed the challenges of serendipity in recommender systems (Kotkov, Veijalainen & Wang, 2016). Herlocker et al. (2004) considered that serendipitous recommendations aim to help users finding interesting and surprising items that they would not discover by themselves. While Shani and Gunawardana (Shani & Gunawardana, 2011) described that serendipity associates with users’ positive emotions on the novel items. The serendipitous items usually are unexpected and useful simultaneously for a user (Manca, Boratto & Carta, 2015; Iaquinta et al., 2010). From these perspectives, serendipity emphasizes the unexpectedness and value components.

Relevance score

Relevance between target scholar and his/her collaborators may be quantified with their proximity in co-author network. Therefore, we perform Random Walk with Restart (RWR) (Vargas & Castells, 2011; Tong, Faloutsos & Pan, 2008) in the co-author network for computing the relevance score of all collaborator nodes for their target scholars. Finally, we get the relevance score between each pair of collaborators.

Unexpectedness score

Unexpected scientific collaborators have connectivity to different research areas of their target scholars. Such unexpected collaborators may expand target scholars’ horizons, since they have diverse research topics compared with their target scholars. We get each scholar’s research areas by LDA (Blei, Ng & Jordan, 2003), and a collaborator who has connectivity to other areas different from that of his/her target scholar is regarded as a unexpected collaborator. LDA computes the cosine similarity between the topic probability distribution of each scholar and area, where the topic probability distribution of a scholar is parsed from his/her publication contents, and the topic probability distribution of an area is extracted from the proportion of each topic contained in this area. The areas with similarity higher than 0.6 are regarded as the research areas of a scholar. Finally we add the betweenness centrality (Leydesdorff, 2007) of a collaborator node with the number of communities it crosses as its unexpectedness score for its target scholar, since betweenness centrality represents the ability of a node to transfer information among separate communities in a network, which stresses the strong position of unexpected node.

Value score

Value of a scholar is defined as the influence of this scholar node, and more influential nodes are more valuable for his/her collaborators in co-author network. We compute the value scores of all collaborator nodes with the Eigenvector Centrality (Bonacich, 2007), where the centralized value of a node is determined by the nodes linked by it. If the high-degree node connects with the target node, it usually are more valuable than those low-degree nodes for the target node. Besides, the influence of a node not only depends on its degree, but also depends on its neighbor nodes’ influences according to the peculiarity of Eigenvector Centrality.

The relevance, unexpectedness, and value scores are computed between each pair of collaborators according to above quantification methods. A serendipitous collaborator has high unexpectedness score, high value score, and low relevance score for his/her target scholar relatively.

Integrate serendipity into co-author network

We first integrate serendipity into co-author network G = (V, E) for vector representation learning of author nodes. The node v ∈ V in network represents the author, and edge e ∈ E reflects the collaboration relationship between two connected nodes. We attach the serendipity of a collaborator for his/her target scholar to their edge weight. From Fig. 1, our co-author network is directed, because the edge weight of node A to B is different from that of B to A. In other words, the serendipity brought by A for B is different from that of B for A, since A’s relevance, unexpectedness and value scores for B are different from that of B for A.

Serendipitous collaborators are unexpected and valuable, but less relevant for their target scholars; therefore, we combine three indices as the edge weight in a linear way. The expression of edge weight is as follows: (1)${\displaystyle w=\alpha \times RS+\beta \times US+\gamma \times VS,}$ where RS, US and VS represent the relevance score, unexpectedness score, and value score, respectively. While α is smaller than β and γ, as α determines the proportion of relevance score, and α + β + γ = 1. We aim to adjust these parameters and find the optimal collocation of them by analyzing the experimental results.

Seren2vec

We improve the traditional DeepWalk model to learn vector representations of author nodes in co-author network for our recommendation task. In terms of DeepWalk, the walker during random walk jumps to the next node with the equal probability, $\frac{1}{N}$, where N represents the number of last node’s collaborators. DeepWalk excludes the importance or corresponding attributes of nodes. Take the random walk process in Fig. 1 as an example, the walker arrives at node A, and continues to walk to the next node. It will walk to B with the probability of $\frac{1}{3}$ according to DeepWalk. In this work, we distinguish the importance of all collaborator nodes based on their serendipity extent for their target nodes. The extent of serendipity brought by collaborator B for target scholar A corresponds to their edge weight w1. If w1 is higher than w2 and w3, the walker will jump to B from A with higher probability.

We attach serendipity to the edge weight in co-author network, and finally guide to a serendipity-biased DeepWalk. As a consequence, the representation of the author vector will carry the attribute of serendipity. If a collaborator is serendipitous for a target scholar, his/her vector representation is similar with that of target scholar. The complete algorithm is described in Algorithm 1, where b represents the set of betweenness centralities with respect to each author node, and b_i denotes the betweenness centrality of node i.RS(i, j), US(i, j), VS(i, j) correspond with the relevance score, unexpectedness score, and value score of collaborator j for his/her target scholar i, respectively. The flow chart of Seren2vec is shown in Fig. 2.

 
____________________________________________________________________________________________ 
 Algorithm 1: Seren2vec 
_____________________________________________________________________________________________ 
  Input: Graph G = (V,E), transfer matrix T, betweenness centrality set b, community 
         degree set c, eigenvector centrality set e, parameter α, parameter β, parameter 
         γ, context size w, dimension of vertex vector d, walks per vertex r, walk length 
         l, length of recommendation list N 
   Output: Recommendation List Rec 
 1 for edge(i,j) ∈ E do 
 2     RS(i,j) = RWR(j,T); 
 3 for edge(i,j) ∈ E do 
 4     US(i,j) = bj + cj; 
 5 for edge(i,j) ∈ E do 
 6     VS(i,j) = ej; 
 7 Build the weighted co-author network; 
 8 for edge(i,j) ∈ E do 
 9     Weight(i,j) = α × RS(i,j) + β × US(i,j) + γ × V S(i,j); 
10 for k = 0;k < r;k + + do 
11     for u ∈ V do 
12         walk[u] =Biased Random Walk(G,u,l); 
13 P = SkipGram(walk,w); 
14 for t = 0;t < row(P);t + + do 
15     Rec[t] =Top-N similar collaborators; 
16 return Rec; 
______________________________________________________________________________________________    

Vector representation of Graph

The random walker walks on the co-author network with the probability of p(i, j) from the scholar node i to its collaborator node j: (2)${\displaystyle p\left(i,j\right)=\frac{Weight\left(i,j\right)}{\sum _{q\in M\left(i\right),q\ne i}Weight\left(i,q\right)},}$ where M(i) is the set of scholar i’s collaborators. We can find from Perozzi, Al-Rfou & Skiena (2014) that if the random walk algorithm is performed on the network with power law distribution, the nodes being visited also follow the power law distribution. This is the same distribution with the term frequency in natural language. Therefore, it is reasonable to regard a node in network as a word, and consider all the previous vertices being visited in the random walk as the sentence. Moreover, we utilize the Word2vec (Mikolov et al., 2013) model to input the sentence sequences generated during random walk into the Skip-Gram model, and take advantages of the stochastic gradient descent and the back propagation algorithm to optimize the vector representations. Finally, we obtain the optimal vector representation of each vertex in our co-author network.

Specifically, in order to learn the vector representations of vertices, Seren2vec makes use of the local information from the truncated random walks by maximizing the probability of a vertex v_i in terms of the previous vertices being visited in the random walk: (3)${\displaystyle P\left(\left\{v_{i-w},\dots ,v_{i+w}\right\}\setminus v_i|\varphi \left(v_i\right)\right)=\sum _{j=i-w,j\ne i}^{i+w}P\left(v_j|\varphi \left(v_i\right)\right),}$ where ϕ denotes the latent topological representation associated with each vertex v_i in the graph, and ϕ is a matrix with |V| × d. For speeding the training time, Hierarchical Softmax is used to approximate the probability distribution by allocating the vertices to the leaves of the binary tree, and we compute P(v_j|ϕ(v_i)) as follows: (4)${\displaystyle P\left(v_j|\varphi \left(v_i\right)\right)=\sum _{l=1}^{\lceil log\left|N\right|\rceil }\frac{1}{1+e^{-\varphi \left(v_i\right)\cdot \psi \left(s_l\right)}},}$ where ψ(s_l) represents the parent of the tree node s_l. In addition, (s₀, s₁, …, s_log|V|) is the sequence to detect the vertex v_j, and s₀ is the tree root.

The output of Seren2vec is the latent vector representations of all scholar nodes with d-dimension in our co-author network. We calculate the cosine similarity between other vectors with the target scholar vector v_i: (5)${\displaystyle sim\left(x_{v_i},x_{v_j}\right)=\frac{x_{v_i}\cdot x_{v_j}}{\sqrt{\left|x_{v_i}\right|\cdot \left|x_{v_j}\right|}},v_j\in Vand{v}_j\ne v_i.}$ Finally, Top-N similar scholars, who are serendipitous to the target scholar, are contained in the collaborator list for recommendation.

Data set

We extract collaboration data from five areas including Artificial Intelligence, Computer graphics and multimedia, Computer Networks, Data Mining and Software Engineering in DBLP data set. The co-author network is built by utilizing the collaboration data from year 2010 to 2012, and there are 49,317 nodes and 242,728 edges in the network. We randomly choose 100 authors who have one collaborator at least as the target scholars, and the final goal of our work is to recommend the serendipitous collaborators for them via Seren2vec.

Baseline methods

Evaluation metrics

We refer to the metrics in Ge, Delgado-Battenfeld & Jannach (2010), Zheng, Chan & Ip (2015) and Kotkov, Wang & Veijalainen (2016) for evaluating our serendipitous collaborators recommendation, which are the serendipity-based metrics including unexpectedness, value and serendipity. We compute the average RS and US of each target scholars’s collaborators. If RS of one collaborator is higher than the average RS, and on the contrary, his/her US is lower than the average US, we regard this collaborator as the expected one of target scholar. Expected collaborators are more relevant and less unexpected than other collaborators for their target scholars. According to Ge, Delgado-Battenfeld & Jannach (2010) and Zheng, Chan & Ip (2015), a recommended collaborator not in the set of target scholar’s expected collaborators is considered as unexpected. Therefore, we extract the expected collaborators of each target scholar first, and a recommended collaborator not in the expected set is evaluated as unexpected. The unexpectedness is measured as the rate of unexpected collaborators in the recommendation list.

In terms of the metric of value, Zheng, Chan & Ip (2015) measured the usefulness of a recommended item through its rating given by the target user. While in our recommendation scenario, we analyze the collaboration times between the recommended collaborator and target scholar in the next 5 years. If their collaboration times is over or equal to 3 times from 2013 to 2017, the recommended collaborator is evaluated as valuable. Besides, the value is measured as the rate of valuable collaborators in the recommendation list.

Ge, Delgado-Battenfeld & Jannach (2010) combined the unexpectedness and value metric to evaluate serendipity. Similarly, we measure serendipity through the rate of collaborators who are both unexpected and valuable for the target scholar in the recommendation list.

Recommendation results analysis

We take the widely used serendipity-based metrics to evaluate our recommendation results, including unexpectedness, value and serendipity. Therefore, the evaluations are no longer limited by the accuracy-based metrics. In this section, we examine the effects of different experimental parameter sets on the recommendation performance, including the range of d, r, l, w, different combinations of α, β and γ, and the length of recommendation list N.

Effects of the recommendation list

We measured the recommendation results with different length of recommendation list N and different combinations of α, β and γ via Seren2vec. The results shown in Fig. 3 indicate that when α = 0.25, β = 0.375 and γ = 0.375, the recommendation performance is better than others with respect to the precision Fig. 3A), value (Fig. 3D) and serendipity (Fig. 3E) evaluations. We also find that the optimal N is 5. The precision, value and serendipity decrease with the increases of N, which are contrary to the recall (Fig. 3B) and unexpectedness (Fig. 3C). Furthermore, the unexpectedness of different combinations keeps close distributions with the variation of N.

Furthermore, we show the effects of the recommendation list length with α = 0.25, β = 0.375, and γ = 0.375 via different baseline methods. From Fig. 4, Node2vec obtains the highest precision (Fig. 4A) and recall (Fig. 4B), but it shows the worst performance from the serendipity-based metrics (Figs. 4C–4E) evaluation. Our Seren2vec outperforms others in terms of the serendipity-based metrics, and keeps adequate accuracy simultaneously. RWRW has lower precision than Seren2vec because it lacks the vector representation process, but it has the second highest serendipity finally because of the serendipity-biased random walk. Meanwhile, the collaborators recommended by Seren2vec show higher unexpectedness than others when the length of recommendation list is lower than 60. Node2vec and Deepwalk share close serendipity with low value, because they have not integrated other serendipity-related elements into the vector representation learning.

Parameter sensitivity

We tested the recommendation performance with different parameters, and the length of recommendation list is optimally five according to the last subsection. When testing one parameter of l (Fig. 5A), r (Fig. 5B), d (Fig. 5C), w (Fig. 5D) with different values on the recommendation performance, we fix other three parameters with corresponding initial values. We can get from Fig. 5 that the measurements from both accuracy-based and serendipity-based metrics almost have the steady distributions under different parameter sets. We take the set where r = 80, d = 208, l = 80 and w = 6 as our final parameter set, since each of them contributes to the highest serendipity and maintains adequate accuracy simultaneously.

Performance comparison

Next, we compare our Seren2vec which are assigned to the optimal parameters with other two baseline methods. We set the length of recommendation list of TANGENT and KFN as 5, which is the same with Seren2vec. From the comparison results in Fig. 6, Seren2vec obtains better performance for recommending the serendipitous collaborators via the evaluations from serendipity-based metrics, since it adopts the serendipity-biased representation learning strategy. Its highest value contributes to the highest serendipity. TANGENT and KFN stress the unexpectedness of recommendations, but they ignore the value component of serendipity. Therefore, they are inferior to Seren2vec in terms of the serendipity evaluation. Seren2vec outperforms other two methods except for the unexpectedness evaluation, which is 0.014 lower than the unexpectedness of TANGENT, but 0.048 higher than that of KFN. Furthermore, we find that the recall of three methods are very low, and Seren2vec has higher recall than TANGENT and KFN slightly.

In summary, our proposed Seren2vec is superior to other baseline methods for recommending more serendipitous collaborators. It learns the serendipity-biased vector representation of each author node in co-author network successfully, which integrates the serendipity between two connected nodes.