Deep Learning Based Link Prediction with Social ... - IEEE Xplore

2016 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData)

Deep Learning Based Link Prediction with Social Pattern and External Attribute Knowledge in Bibliographic Networks Chuanting Zhang, Haixia Zhang, Dongfeng Yuan and Minggao Zhang Shandong Provincial Key Laboratory of Wireless Communication Technologies Shandong University, Jinan, China 250100 Email: [email protected], {haixia.zhang, dfyuan}@sdu.edu.cn In feature extraction respect, the most commonly used features are those extracted from the network topology, for example, node degree, the number of common neighbors and shortest paths. Other kinds of features are also available, such as external attributes knowledge. Besides the aforementioned straightforward features, some social theory-based features [6] are also studied to uncover the micro-mechanisms of link formation. Considering the design of classification algorithms, conventional shallow layer models such as decision tree [5], support vector machines [7] and ensemble learning [8], are well studied. However, conventional shallow learning techniques are limited in their ability to effectively represent the features in nonlinear high-dimensional space. On the contrary, deep learning [9] or deep neural networks (DNNs) allow computational models to learn representations of data with multiple levels of abstraction. It has been successfully applied in many domains and improves state-of-the-art algorithms. Unfortunately it does not get much attention in link prediction domain. Only a few works [10], [11] has been carried out to explore the powerful feature representation of deep learning for link prediction. But these works mainly focus on Restricted Boltzmann Machines (RBM), other kinds of deep learning frameworks have not been fully studied yet. How to leverage the power of DNNs to boost the performance of link prediction still remains an open problem. In this paper, we focus on investigating the available and useful novel features besides network topology. We are also interested in integrating these features into a deep learning framework to enhance link prediction performance. Our main contributions can be summarized as follows: • We introduce two kinds of novel features, i.e., social pattern and external attribute knowledge (SPEAK), for improving link prediction. These two kinds of features are extracted based on microsociology and node-level attributes, respectively. • We propose a deep learning approach to solve the link prediction problem by incorporating both topological features and the SPEAK features. The impact of different parameter settings on link prediction performance, such as the number of hidden layers and the number of neural units, is also qualitatively analyzed. • The evaluation is performed in a large scale real-world

Abstract—The problem of predicting links for information entities is an important task in network analysis. In this regard, link prediction between authors in bibliographic networks has attracted much attention. However, most of these works only center around exploiting network topology features to do prediction, and other factors affecting link formation are rarely considered. In this paper, we introduce two kinds of novel features based on social pattern and external attribute knowledge (SPEAK), then integrate the SPEAK features and topological features into a deep learning framework using deep neural networks (DNNs). We present the performance based on a real world academic social network from AMiner. Experimental results demonstrate that the SPEAK features can significantly boost the link prediction performance especially when potential links span large geodesic distance. In addition, these features are helpful in understanding the mechanisms behind the link formation.

1. Introduction Social networks exist ubiquitously and are of vital importance in data generation and information sharing especially in the current era of big data. Bibliographic networks are typical social networks, which are highly dynamic as a great quantity of papers are published each year. The frequently upcoming publications are normally associated with new authors and/or new collaborations. Understanding the complex dynamics can benefit the comprehension of network evolution, and hence help to identify influential scientists. To this end, link prediction [1], [2], [3], [4] appears as a central problem of network science, as it calls for revealing the mechanisms that govern the dynamics of the network. In bibliographic networks, the link prediction problem concerns inferring whether two authors will establish coauthor relationship or not in the near future based on the observed information of the network. This can be formulated as a binary classification problem using learning features from machine learning perspective [5]. Two important parts lie at the core of feature-based link prediction, that is, finding informative features and designing a good classification algorithm. 978-1-5090-5880-8/16 $31.00 © 2016 IEEE DOI 10.1109/iThings-GreenCom-CPSCom-SmartData.2016.170

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bibliographic network to understand the effectiveness of the proposed method. Our findings show that the proposed SPEAK features can significantly boost the final performance of link prediction, especially when the geodesic distance between two authors in the network is greater than two. In addition, an interesting phenomenon is discovered that ordinary users (see Section 4.3) play more important role than elite ones in bridging two unconnected nodes. It is also showed that the capacity of DNNs has considerable influence on prediction performance. Too complex model will overfit the data and bring the performance down. The DNNs model needs to be carefully designed to obtain an encouraging result of link prediction. We have released all the source code along with part of the dataset to reproduce the work proposed in this paper. The resources can be accessed from https://github.com/zctzzy/speak lp. The remainder of the paper is organized as follows: Section ?? examines the related work. We formally define the link prediction problem and introduce the deep neural networks in Section 3. Feature set construction is elaborated in Section 4. Section 5 displays the experimental results and the corresponding analysis. Section 6 concludes the paper with future work.

learning both node-level and edge-level latent features without the need of manual work. Though these works shed new light on various ideas that using DNNs for link prediction task, the main difference between the above work on link prediction and our direction lies in that existing work focuses either on only topology-based features or on shallow layer classification models, while we try to explore novel features based on general social pattern and external attributes knowledge and incorporate them into a deep learning framework.

3. Problem formulation In this section, we first define the link prediction problem and then briefly introduce the prediction model used in our work.

3.1. Problem definition of link prediction Given an undirected bibliographic network graph G = (V, E), in which each edge e = u, v ∈ E represents a collaboration between u and v at a particular time t(e). Besides the authors and links in the network, author’s external attributes, such as research topics and location of workplace, can also be generated from the papers they published. Therefore, each user u has an attribute list A = a1u , a2u , · · ·, anu , where aiu denotes u’s i-th attribute, n is the number of attributes. The similarity between users can be calculated with these attributes in the list A. For time t ≤ t , G[t, t ] denotes the subgraph of G comprised of all the edges with a time-stamp between t and t . In a supervised learning framework for link prediction, two intervals, [t0 , t0 ] and [t1 , t1 ] on the condition that t0 < t1 , are selected to extract the data set D = {x 1 , x 2 , ···, x m } and its corresponding label set Y = {y1 , y2 , · · ·, ym }. x i is the feature vector of any author pair (u, v) who has no collaboration links in the current training interval [t0 , t0 ]. yi ∈ {0, 1} is the label of x i . If u and v form a collaboration link in the test interval [t1 , t1 ], the value of yi = 1, otherwise yi = 0. On the basis of the above descriptions, the link prediction is to learn a classification model using data set D, then the model outputs a list of edges not presented in G[t0 , t0 ] that are predicted to appear in the network G[t1 , t1 ].

2. Related work Link prediction is a basic computational problem underlying network evolution and attracts lots of interests. [2] reviewed several classical unsupervised methods for link prediction and gave performance comparisons among different predictors. [5] first proposed to model the link prediction problem as a binary classification. A set of features were generated from both network topology and node attributes, then a classification model was learned from these features and used to predict likely links. In order to understand the formation of social links driven by human behaviors, social theory-based features were proposed in [6] and showed that different kind of users have different influence on the formation of links. The class imbalance problem, which implies the fact that there are much more pairs of nodes than actual links in a sparse network, have also been studied in [8], in particular, by grouping pairs of nodes according to the geodesic distance. With the prevalence of deep learning, a few work related to using deep learning for link prediction has been carried out. [10] introduced a dynamic link inference model based on temporal RBM. It has a simple way to learn deeper layers of hidden variables and is guaranteed to improve the overall performance. Subsequently the authors in [11] proposed a link prediction model based on stacked RBMs (also name as deep belief networks) in signed social networks. They utilized features extracted from network topology to train a supervised model, then used this model to finish link sign prediction. Beside the features from hand engineering, [15] proposed an algorithmic framework for learning continuous feature representations automatically for nodes in networks. It is a task-independent framework and can be used for

3.2. Deep neural networks A DNN is a feed-forward network that has more than one layer of hidden units between its inputs and its outputs [12]. Fig.1 shows a diagram of DNN with two hidden layers. In the diagram, x i = [x1 , x2 , · · ·, xd ] represents the input of the model. w is the weight connecting specific units from two connected layers. For example, wjk is the weight between the j -th unit of layer H1 and the k -th unit of layer H2. And yˆ denotes the output of the model. In each hidden unit j , an activation function f (·) will be used to map its

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× 10 5

The # of papers published each year

1 0 1990

1995

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2005

2010

Year Node out degree distribution

Count

10 5

10 0 10 0

10 1

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Node Degree

Figure 1: A diagram of DNNs with two hidden layers.

Figure 2: General description of the data set. total input from former layer aj to the scalar state hj that is sent to the next layer. aj = wij hi , (1)

4.1. Data description The bibliographic network data set used in this paper comes from the AMiner Open Science Platform [13]. It contains about 2.1 million papers and involves more than 1.7 million authors and 4.25 million collaboration links among authors. The content of the data includes the meta data of published papers such as title, abstract, author’s name and affiliation. A general description of the data set is shown in Fig. 2.

i

hj = f (aj ) + bj = max(0, aj ) + bj ,

(2)

where bj is the bias of unit j , i is an index over units in the previous layer. For binary classification, output unit, say o, converts its total input ao into a class probability po by using a logistic function. yˆ = po = logistic(ao ) =

1 , 1 + e−ao

4.2. Topology based features

(3)

The most natural features for link prediction are these that extracted from the network topology. This kind of feature measures the “proximity” of nodes in the network based on node neighborhoods or based on the ensemble of reachable paths between two nodes. A variety of topological features can be extracted from the network topology, including common neighbors, preferential attachment, shortest paths, and PropFlow, just to name a few. Since these features are widely studied and used in [2], [6], [8], we do not explain them verbosely in this paper and only put emphasize on the features introduced by this work.

To measure the errors between yˆ and the true value y , we use cross entropy as the cost function, C , which can be written as 1 C=− [y lnyˆ + (1 − y)ln(1 − yˆ)], (4) m D

where m is the number of samples in the dataset D. Then backpropagation algorithm can be utilized to train the DNN classifier. The parameters, such as wko , can be updated as wko = wko + η

∂C , ∂wko

∂C ∂C ∂ yˆ ∂ao = , ∂wko ∂ yˆ ∂ao ∂wko

(5)

4.3. Social pattern based feature (6)

Though the features obtained from network topology can help people understand why the link forms between authors, it may still be hard to predict the existence of links correctly only using this kind of features. Therefore it motivates us to explore other features outside the network topology. Microsociology, which concerns the nature of human social interactions on a small scale, can offer us a new perspective to realize the dynamics of social relationships at a microlevel. In this paper, the dyadic or triadic relationships between authors are modeled under different conditions. Specially,

where η ∈ (0, 1) is the learning rate determining the size of steps we take to reach a minimum.

4. Feature set construction In this section, a brief description of the data set used in this paper is given firstly. Then the social pattern feature is introduced by considering both dyadic and triadic relationships in bibliographic networks. Finally, the method that measures similarities between authors is explained.

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X

Z

Z

A ?

C ?

E ?

Y

X

X

Z

Z

Z

B ?

D ?

F ?

Y

X

G ?

Y

X

̡̡̡

̡̡̡

X

Y

Y

X

H ?

0.18 0.16 Link Formation Probability

X

Z

Y

Y

X

I ?

B

0.12

C D

0.1

E

0.08

F

0.06

G

0.04

H I

0.02

̡̡̡

Y

A

0.14

0

Y

(b) Probability distribution of nine kinds of relationships

(a) Enumeration of author relationships

Figure 3: Different kinds of social patterns and their impact on link formation probability. we categorize authors into two groups by calculating the PageRank values of authors and treating the top 50% as elite authors and others as ordinary authors. When two authors are 2 hops away from each other and exactly have one common neighbor (2-hops, CN=1), the triadic relations are analyzed. And in other instances (2-hops and CN 2, distance 3-hops), the dyadic relations are considered, because inconsistent triadic relations exist when two authors have more than one common neighbors. We try to examine the microscopic mechanism of link formation with different types of author relations. Fig. 3(a) enumerates the nine kinds of author relations with gray nodes denoting the elite authors. The link formation probability between X and Y is examined on the condition that whether X , Y and Z are elite authors or not. Fig. 3(b) shows the link formation probability of different kinds of social relationships in Fig. 3(a). Conditioned on whether X and Y are ordinary authors or not, the probability that X and Y will have a link in the cases of C/D/H is slightly higher than that in the cases of A/B/G, and much higher than that in the cases of E/F/I. That is, PC,D,H > PA,B,G > PE,F,I . Besides, in the triadic relationships, authors X and Y are more likely to form a link if Z is an ordinary author than Z is an elite one, PA,C,E > PB,D,F . In contrast to information share-based social networks in which elite users dominate new link formation, our finding indicates that in the bibliographic networks, ordinary users play a more important role in bridging two unconnected users than elite users. This also implies that networks from different domains have diverse characteristics, and they should not be always treated as the same.

Link formation probability

Link formation probability

4.4.1. Affiliation similarity. Regarding a paper, the most direct information that can be used to measure similarity is author’s affiliation information. However, it is much more difficult to let computer automatically extract the workplace of a author precisely. Thus, this feature is rarely studied in current research works. Here we measure the affiliation similarity between authors and explore it’s influence on future link formation. 4 hop 3 hop 2 hop

0.2

Affiliation similarity

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(a) Degree of similarity Research topic similarity

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Figure 4: Link formation probability by external attribute knowledge. The most popular way of measuring attribute similarity is binary similarity [7]. However, binary similarity will lead to the loss of potentially useful information such as department name and location. For example, author u’s affiliation IBM Thomas J. Watson Research Center and author v ’s affiliation IBM Austin Research Lab. will be treated as two completely different affiliations by binary similarity measure. In other words, the binary similarity between u and v equals to zero. However, this is not reasonable, since they do have some similarities as they both come from the IBM Corporation. In consideration of the above reason, the

4.4. External attribute based features In this section, two kinds of features based on author’s attributes are introduced, namely affiliation similarity and topic similarity.

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TABLE 2: Data Description.

TABLE 1: Full Feature Set. Category

Feature Name

Note

Degree(u), Degree(v) Common Neighbors(u,v) Jaccard Coef.(u,v) Admic/Adar(u,v) Pref. attachment(u,v) Maximum flow(u,v) Shortest paths(u,v) PropFlow(u,v) Katz(u,v)

– – – – – – l=5 l=5 l = 5, β = 0.005

Social Pattern

Social pattern(u,v)

–

5. Experimental results and analysis

Attributes

Topic similarity(u,v) Aff. similarity(u,v)

– –

In this section, the proposed approach is quantitatively evaluated on the AMiner bibliographic network data set. Firstly, the detailed experiment setup and baseline predictors are introduced. Then the experimental results are reported and a comparison with other methods is given.

Topology

Data

D1

D2

Distance

337,636

797,511

699,800

1,993,100

Samples

New Edges

99,008

2,520

3 hop

427,573

1,203

4 hop

1,481,272

974

2 hop

800,210

13,090

3 hop

5,869,830

6,985

4 hop

30,160,999

5,703

5.1. Experiment setup Two time intervals is considered for the network according to the publication year of the paper: T1 = [1999, 2004], T2 = [2005, 2010]. D1 contains all the authors and their corresponding collaborations in T1 and D2 denotes the data set in T2 . For both data set D1 and D2 , the first five years (training interval) of the data is used for extracting features and the sixth year (test interval) of the data is used to obtain the labels. Besides, we try to make predictions only for “active” authors [14], where an author u is defined to be active if u has more than K co-authors in the training interval. In this paper, K is set to be 5. To handle the class imbalance problem, the node pairs are separately considered in terms of their geodesic distance. To avoid the excessive computing between nodes that are unrelated, here we consider the cases of n = 2, 3, 4. Table 2 shows the detailed information of D1 and D2 .

T

u v . uv

Edges

2 hop

cosine similarity, which measures the semantic similarity at word level, is used to estimate the author similarity for the bibliographic network. After transforming two authors’ affiliation information to term frequency vectors u and v , the cosine similarity k between two authors is defined as ku,v =

Nodes

(7)

The cosine similarity between u and v in the above example is about 0.408 calculated by (7). This implies the subtle information hidden in affiliation can be captured by this measure effectively. Fig. 4(a) displays the impact of affiliation similarity on link formation probability and it verifies that authors with similar affiliation link to each other with high probability. Besides, this impact is sensitive to distance, namely, the users are more likely to form a link if they are “close” to each other when they have equal affiliation similarity. 4.4.2. Topic similarity. Each author can have a series of research topics such as social network, network evolution, network analysis. And the principle of homophily indicates that people with similar interests are more likely to link each other. Different from the simple keywords number count [5] and meta-path count, we still use cosine similarity to measure author’s topic closeness because of the reasons explained in section 4.4.1. Fig. 4(b) reveals that the link formation probability generally increases with the increase of topic similarity and decreases with increase of geodesic distance. The influence of this feature on link formation probability is especially distance dependent. When authors are two hops away from each other, the probability that they form a link is much higher than that they are three or four hops away. All the features described in this section are listed in Table 1. The feature set is categorized into three kinds: topological features (neighbor based and path based), social pattern feature and external attribute features (research topic similarity and affiliation similarity).

5.2. Baseline predictors PropFlow [8]. It is a localized unsupervised metric and is proportional to the probability that a restricted random walk starting at u and ending at v in no more than l steps. • HPLP [8]. A supervised learning framework with ensemble strategies (Random Forests) for link prediction. Most of the features used in HPLP are coming from network topology. • Stacked RBMs [11]. A deep learning approach using RBM for link sign prediction. • Node2vec [15]. It learns low-dimensional representations for nodes in graph by optimizing a neighborhood preserving objective. The edge features are obtained using a binary operator. To evaluate the performance of the proposed approach, two classical measures, receiver operating characteristic •

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0.8

0.8

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PropFlow Node2Vec HPLP with SPEAK RBM with SPEAK DNN

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0.2

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(a) D1


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1



1

0.4

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0.4

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(f) D2

n = 4

Figure 5: ROC curve for D1 and D2 . TABLE 3: AUC Performance. Dataset

D1

D2

PropFlow

HPLP

RBM

Node2vec

HPLP+SPEAK

RBM+SPEAK

DNN

2 hop

0.711

0.728(0.016)

0.718(0.018)

0.744(0.010)

0.768(0.015)

0.780(0.010)

0.799(0.008)

3 hop

0.669

0.683(0.013)

0.667(0.022)

0.740(0.018)

0.783(0.012)

0.780(0.016)

0.804(0.020)

4 hop

0.676

0.654(0.024)

0.625(0.018)

0.734(0.017)

0.792(0.024)

0.792(0.019)

0.812(0.015)

2 hop

0.747

0.769(0.006)

0.768(0.005)

0.742(0.005)

0.787(0.004)

0.789(0.005)

0.812(0.006)

3 hop

0.736

0.723(0.005)

0.702(0.008)

0.728(0.007)

0.749(0.007)

0.775(0.006)

0.797(0.007)

4 hop

0.739

0.737(0.007)

0.643(0.010)

0.719(0.010)

0.794(0.008)

0.836(0.007)

0.865(0.007)

(ROC) curve and the area under ROC curve (AUC), are used. ROC curve plots the true positive rate against the false positive rate and performs fairly well no matter what the class distribution is.

with baseline predictors. This shows that the introduced novel features, SPEAK, can indeed improve the link prediction performance, as they contain the information that network topology can not captured. We can also tell that with the increase of geodesic distance n, the performance of topology-based methods gradually decline due to the loss of available structure information. On the contrary, methods with SPEAK features perform consistently well especially when geodesic distance is greater than two. This implies the SPEAK features can be served as compensation when limited topology information can be used.

5.3. Evaluation results To obtain the following results, a DNN classifier is trained on the data set. We take 20% of the samples as testing set and the others as training set. The experiment is repeated 20 times and we report the averaged AUC value. Fig. 5 illustrates the ROC curve performances of baseline predictors and the proposed DNN method. In addition, their corresponding AUC values are displayed in Table 3, in which the best performance on each data set is highlighted in boldface. From Table 3 we can see that the proposed DNN method achieves the highest AUC values compared

5.4. Parameter sensitivity There are several parameters that have impact on the performance of a DNN classifier, i.e., the ratio of test data set r, the number of hidden layers h, and the number of units

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Figure 6: AUC values with different parameters

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In this work, the feature-based link prediction problem in bibliographic networks was studied. First, two kinds of novel features were introduced to capture node similarity based on social pattern and external attribute knowledge, respectively. Their influence on link formation probability was quantitatively analyzed. Besides, a deep learning approach using DNN was proposed to incorporate both topological features and the SPEAK features. Moreover, the impact of DNN’s capacity on classification results was also given in detail. Experiments on the AMiner bibliographic network have shown that by considering the introduced novel features, SPEAK, the AUC value of link prediction can be significantly improved. The SPEAK features can be served as complementary information of topological features, especially when little structure information is available. The source code and sample data set can be accessed from https://github.com/zctzzy/speak lp

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Acknowledgments The work presented in this paper was supported in part by the Special Project for Independent Innovation and Achievement Transformation of Shandong Province (2013ZHZX2C0102, 2014ZZCX03401).

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