MEgo2Vec: Embedding Matched Ego Networks for UserAlignment Across Social Networks∗

Jing Zhang, Bo Chen, Xianming WangInformation School, Renmin University of China

{zhang-jing,bochen,wxm}@ruc.edu.cn

Hong Chen*, Cuiping Li, Fengmei JinInformation School, Renmin University of China

{chong,licuiping,jinfm}@ruc.edu.cn

Guojie SongMOE Key Laboratory of Machine Perception, PKU

gjsong@pku.edu.cn

Yutao ZhangTsinghua University

yt-zhang13@mails.tsinghua.edu.cn

ABSTRACTAligning users across multiple heterogeneous social networks isa fundamental issue in many data mining applications. Methodsthat incorporate user attributes and network structure have re-ceived much attention. However, most of them suffer from errorpropagation or the noise from diverse neighbors in the network.To effectively model the influence from neighbors, we propose agraph neural network to directly represent the ego networks oftwo users to be aligned into an embedding, based on which wepredict the alignment label. Three major mechanisms in the modelare designed to unitedly represent different attributes, distinguishdifferent neighbors and capture the structure information of theego networks respectively.

Systematically, we evaluate the proposed model on a numberof academia and social networking datasets with collected align-ment labels. Experimental results show that the proposed modelachieves significantly better performance than the state-of-the-artcomparison methods (+3.12-30.57% in terms of F1 score).

CCS CONCEPTS• Information systems→ Entity resolution;

KEYWORDSSocial network; Network Integration; User LinkageACM Reference Format:Jing Zhang, Bo Chen, Xianming Wang, Hong Chen*, Cuiping Li, FengmeiJin, Guojie Song, and Yutao Zhang. 2018. MEgo2Vec: Embedding MatchedEgo Networks for User Alignment Across Social Networks. In The 27thACM International Conference on Information and Knowledge Management(CIKM ’18), October 22–26, 2018, Torino, Italy. ACM, New York, NY, USA,10 pages. https://doi.org/10.1145/3269206.3271705

1 INTRODUCTIONThe proliferation of heterogeneous social media platforms, such asFacebook, Twitter, LinkedIn, Instagram, etc., enables us to satisfy∗Produces the permission block, and copyright information

Permission to make digital or hard copies of part or all of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor profit or commercial advantage and that copies bear this notice and the full citationon the first page. Copyrights for third-party components of thisworkmust be honored.For all other uses, contact the owner/author(s).CIKM ’18, October 22–26, 2018, Torino, Italy© 2018 Copyright held by the owner/author(s).ACM ISBN 978-1-4503-6014-2/18/10. . . $15.00https://doi.org/10.1145/3269206.3271705

?W. Wang Wei Wang

Computer Science

J. Limachinelearning

J. Lideep learning Shi Yuan-Le

PKU

Shi YLPeking University

Peng YangPan Yang

Eric Zhang

v1 u1

u4v4 v3u3

v5

v2 u2

Gs Gt

Figure 1: Illustration of the user alignment task. Given twonetworks Gs and Gt , we aim at aligning user v1 from Gs and useru1 fromGt . The lines between users within each network representthe relationships between users. The lines between users across thetwo networks denote whether two users are aligned or not, wherethe black dashed lines mean they may be the same person, but theactual labels are unknown, and the red solid line represents thealignment between the target users to be predicted.

our different interests. A study conducted by IPGMedia Lab showsthat over 50% US adults use more than one social media platform1.Aligning the same users across different social networks has re-cently been attracting considerable attention, as it can provide acomprehensive view of users’ profile, and then benefit many appli-cations. For example, linking users of a E-Commerce system anda social media platform can enable product recommendation fromthe E-Commerce system to the social media platform, and linkingusers across different social networks can tell us how the informa-tion is diffused between them.

One intuitive way to align same users across social networks isto compare the profile attributes such as name, affiliation, descrip-tion, etc. However, the profile attributes usually cannot providesufficient evidence. For example, in Figure 1, it is difficult to deter-mine that v1 and u1 are the same person only according to theirnames “W. Wang" and “Wei Wang". Fortunately, the neighbors ofthe two users in their respective ego networks2 may provide ad-ditional clues. Among the neighbors of v1 and u1, “Shi YL" from“Peking University" and ‘Shi Yuan-Le" from “PKU" have a high pos-sibility to be a same person, similarly for “J. Li" being interested1https://www.ipglab.com/wp-content/uploads/2014/05/A-Network-for-Every-Interest-140-Proof_IPG-Whitepaper.pdf2An ego network consists of a focal node (“ego") and the nodes to whom ego is directlyconnected to plus the ties between them.

CIKM ’18, October 22–26, 2018, Torino, Italy Zhang et al.

in “machine learning" and “J. Li" being interested in “deep learn-ing". The clues would be more powerful if there are more potentialsame neighbor pairs. In the Figure, the neighbors ofv1 and u1 thathave a high possibility to be the same person are linked by blackdashed lines. In practice, most of the neighbor pairs are unlabeled,which prevents us from directly calculating the metrics like Jac-card’s coefficient or Adamic/Adar based on the shared neighborsas that proposed in [7, 8, 26, 30]. One way to leverage the unla-beled information is to estimate the possibility that a user pair canbe matched, based on which we can update the matching scores ofits neighbor pairs [9, 27, 28]. For example, SiGMa [9] proposed anunsupervised method to iteratively propagate the matching scoresfrom a confidential seed set of user pairs to their neighbor pairs.COSNET [28] proposed a supervised method to infer the marginalprobabilities that two users can be matched based on the attributesof the two users and the marginal probabilities of their neighborpairs. Essentially, to predict the label of a user pair, they both needto infer the labels of its neighbor pairs, and this may cause errorpropagations during the iterative process.

Despite existing studies on user alignment [7–9, 26–28, 30], theproblem still poses several unsolved challenges. First,how to unit-edlymodel profile similarity?Traditional methods usually com-pare different profile attributes by human defined metrics, such asJaro-Winkler similarity [25], TF-IDF based cosine similarity [7, 20],etc. However, they cannot capture the semantics of different literalstrings. Thus, a unified way with little effort of feature engineer-ing to better represent different profile attributes is worth study-ing. Second, How to deal with diverse neighbors in differentsocial networks? The neighbors of a user in different networkscan be very diverse due to the various purposes of different socialmedia platforms. For instance, people use Twitter to communicatewith friends and obtain information, while they use LinkedIn tofind a job. Leveraging all neighbors’ information without distinc-tionmay contrarily bring in additional noise. Third,How to incor-porate the influence of network topologies? Different topolo-gies of ego networks may exert different effects. For example, inFigure 1, neighbor pair (v3,u3) is linked to another neighbor pair(v4,u4), i.e., v3 is v4’s friend in Gs and u3 is u4’s friend in Gt . Thelinkage reduces the possibility that v3 is wrongly matched to u3,and v4 is wrongly matched to u4, and it further provides strongevidence that v1 and u1 are the same person, compared with thesituation that (v3,u3) and (v4,u4) are not linked.

To deal with the above challenges, we formalize the task of useralignment across social networks as a classification problem usingthe ego networks of two users as input. We propose a graph neuralnetwork model—MEgo2Vec to represent the matched ego networkbetween the two users into a low-dimensional real-valued repre-sentation, based on which we align the users. The representationincludes two parts, one is embedded from the attributes of the tar-get user pairs and their neighbor pairs, the other is embedded fromthe topologies of the matched ego network. Specifically, first, tounitedly model the profile attributes, we adopt a multi-viewembedding mechanism to represent the character-view and word-view features for an attribute together. Second, to tackle the issueof diverse neighbors in different networks, we adopt attentionmechanisms to convolve neighbors’ attributes, so as to distinguish

their influence. Three attentions are proposed to respectively con-sider the individual characteristics of each user in a pair, the simi-larity between two users in a pair, and the relationship of a neigh-bor pair with the user pair to be predicted. Third, to capture theinfluence of network topologies, we adopt a CNN network toconvolve the adjacency matrix of the matched ego network.

The main contributions can be summarized as:

• We propose MEgo2Vec (embed theMatched Ego network toa vector), a novel graph neural network model, to formalizeour problem as a unified optimization framework.• The multi-view node embedding can model the literal andsemantic characteristics of different attributes unitedly; theattention mechanism can distinguish the effects of differentneighbors to alleviate error propagations; structure embed-ding can capture the influence of different topologies.• Experiments on a number of academia and social network-ing datasets demonstrate that the proposedmodel comparesfavorably classification accuracy (+3.12-30.57% in terms ofF1 score) against the state-of-the-art models for user align-ment task.

2 RELATEDWORK

User Alignment. One intuitive way to align users across socialnetworks is to compare users’ attributes, among which name isthe most important one. Many attempts have been made to studyhow to leverage user names [11, 13, 17, 24, 25]. For example, Za-farani et al. dealt with user names by adding or removing theirprefix/postfix [24]. They further made a comprehensive study ofthe habits when users select names [25]. For other attributes likethe post contents of users, Kong et al. [7] calculated the cosine sim-ilarity of the bag-of-words vectors weighted by TF-IDF.

However, user attributes may be missed or not strong enough toindicate a user’s identity. Thus a lot of research utilizes the networkstructure to enhance the prediction performance. Some of them cal-culated the metrics like Jaccard’s coefficient or Adamic/Adar basedon the number of the shared neighbors [7, 30]. However, most ofthe neighbor pairs are unlabeled, preventing us from calculatingthe above metrics. Somemethods such as IONE [12] and PALE [15]learned user embeddings by encoding the structure information ofthe network but totally ignored user attributes, and it is not easyto add user attributes into their models.

Several research incorporates both user attributes and unlabeledneighbor pairs together. For example, Lacoste et al. solved the prob-lem by an unsupervised propagation method [9], where the sim-ilarities of the attributes in the method are defined empirically.Zhong et al. proposed an unsupervised co-training algorithm toincorporate attributes and relationships with the neighbor pairstogether [29]. Zhang et al. further formulated the propagation pro-cess based on attributes and network topologies from an optimiza-tion perspective [27], but only one attribute can be considered intheir model. Zhang et al. proposed a supervised model—COSNETto iteratively infer the labels of the unlabeled pairs and update themodel based on the inferred labels and the user attributes [28].However, error propagations may be introduced in above meth-ods. This paper aims at investigating a supervised method that

MEgo2Vec: Embedding Matched Ego Networks for User Alignment Across Social Networks CIKM ’18, October 22–26, 2018, Torino, Italy

avoids label propagation, but directly represents a pair of users bytheir attributes, their neighbors’ attributes and the network struc-ture among the neighbors, and then aligns the users based on thelearned representations.

NeuralNetworks onGraphs. Substantial research has been doneon modeling the graph-structured input by neural networks. Shal-low models such as DeepWalk [18], LINE [21] and node2vec [5]learn node embeddings via the prediction of the first-order or high-order neighbors. Graph neural networks (GNNs) were proposed asa generalization of the recursive neural networks, which assign astate to each node in a graph based on the states of neighboringnodes [4, 19]. Recently, Li et al. improved GNNs using gated recur-rent units and also extended the output to sequences [10].

Several works studied how to generalize convolutions to graphdata [1, 3, 6, 16, 23]. For example, Niepert et al. [16] generated arepresentation for a selected sequence of nodes that covers largeparts of a given graph, and then used CNN to predict the label ofthe graph. Duvenaud et al. defined convolutions directly on graphsand learned node degree-specific weight matrix. [3]. Thomas et al.considered a single weight matrix per layer and dealt with vary-ing node degrees by an appropriate normalization of the adjacencymatrix [6]. Veličković et al. [23] introduced the attention mech-anism into the graph convolutional networks to distinguish theinfluence of the neighbors. Inspired by these recent works, we pro-pose a graph neural network model to align users in two networks.Most of the recent work on graph convolutional networks feed thewhole graph as the input, which hinders the mini-batch trainingprocess. The proposed method in this paper, on the contrary, isperformed on ego networks of two nodes, which is able to adaptto mini-batch training and thus can be conducted efficiently.

3 PROBLEM DEFINITIONIn this section, we will provide necessary definitions and then for-mally formulate the problem. Let G = (V ,A, P) denote an undi-rected attribute augmented social network3, whereV is set of users.NotationA represents a |V |× |V | adjacencymatrix with an elementai j indicating there is a relationship between vi and vj . NotationP represents a |V | × d property (attribute) matrix with an elementpik indicating the k-th attribute of the i-th user in G.

Definition 3.1. Ego Network. Given a user vi ∈ V , we useGi = (Vi ,Ai , Pi ) ⊆ G to denote vi ’s ego network, where Vi ⊆ Vcontains the focal node vi (i.e., the node in the center) and vi ’sfirst-order neighbors in G. Notation Ai ⊆ A is the adjacency ma-trix representing the relationships between the users in Vi and Pirepresents an |Vi | × d attribute matrix of the users in Vi .

We only consider first-order neighbors, out of the considerationof the computational efficiency and the assumption that high-orderneighbors usually provide weak evidence on identifying a user. Weassume that two users are more likely to be the same person, ifthere are more neighbors in their respective ego networks thathave a high possibility to be matched as the same person. Basedon the intuition, we define matched ego network as:

3We simply ignore the direction of a directed relationship as it is found to be not veryuseful in the task.

Definition 3.2. MatchedEgoNetwork. Supposewe have a sourcenetwork Gs and a target network Gt . Given two users vi ∈ Gs

and ui ∈ Gt , we denote vi ’s ego network as Gsi and ui ’s ego net-

work as Gti . Then we construct a matched ego network GM

i =

(VMi ,A

Mi , P

Mi ) with each node in it as a pair of users from the two

ego networks by the following steps:(1) Add the pair of users (vi ,ui ) into VM

i as the focal pair.(2) Find all the potential matched neighbors of vi and ui , and

add them intoVMi as the neighbor pairs (More explanations

are as follows).(3) Add an edge between (vi ,ui ) and each neighbor pair. Ad-

ditionally, add an edge between two neighbor pairs (vj ,uj )and (vk ,uk ) if there is an edge betweenvj andvk inGs , andalso an edge between uj and uk in Gt . Notation AM

i is theadjacency matrix of GM

i .(4) Notation PMi represents an |VM

i | × 2d attribute matrix witheach row pj as a concatenation of vj ’s attributes p(vj ) anduj ’s attributes p(uj ), i.e., pj = (p(vj ), p(uj )).

We will explain what are the potential matched neighbors, andwhy and how they are constructed. The potential matched neigh-bors are the neighbor pairs that have some possibility to bematched,and they are filtered from all possible pairs of the neighbors. Dueto the various purposes of different social media platforms, theneighbors in two ego networks may be very diverse. Directly us-ing all pairs of neighbors as evidence to align users may introducemuch noise. Thus we propose an attention basedmechanism to dis-tinguish different neighbor pairs in our model (See details in Sec-tion 4). To improve the computational efficiency, before resortingto themodel, we can easily select the most useful neighbor pairs byheuristic rules [28]. This paper simply selects the neighbor pairs iftheir names are similar, i.e., the Jaro-Winkler similarity of the twonames is larger than a threshold, as the potential matched pairs.Wealso restrict the neighbor pairs to satisfy the one-to-one mappingconstraint as Kong et al. did in [7], based on the same assumptionthat a user usually maintains one major account in each social me-dia platform. Thus the constructed matched ego network has nomore thanmin{|V s

i |, |Vti |} user pairs. We useNM

i to represent theset of the neighbor pairs of (vi ,ui ) including (vi ,ui ) itself.

Problem 1. User Alignment across Social Networks: Given aset of matched ego networks {GM

i = (VMi ,E

Mi )} constructed from

a pair of a source network Gs and a target network Gt , we aim atlearning a predictive function

f : GMi = (VM

i ,EMi ) → yi (1)

to predict whether vi and ui belong to the same person in the realworld, where yi is a binary value, with 1 indicatingvi and ui are thesame person, and 0 otherwise.

4 METHODOLOGY4.1 OverviewWe argue that the above defined classification performance can beimproved if the node attributes and the structure of the matchedego network are elaborately represented. The overview process ofthe proposed method is shown in Figure 2.

CIKM ’18, October 22–26, 2018, Torino, Italy Zhang et al.

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Gs1

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Gt1

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GM1

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+

+--

(a) Two ego networks (c) Model input(b) Matched ego network

Adjacency matrix

Node attributes

(d) Model: MEgo2Vec

Graph normalization Structure convolution

Node embedding Social convolution

4

(e) Model output

Ground truth

Stru

ctur

e E

mbe

ddin

gA

ttri

bute

E

mbe

ddin

g

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Figure 2: The Overall process of the proposed method. (a) Extract the ego networks of the two users to be predicted; (b) construct amatched ego network for the two users; (c) input the attributes of all the nodes and the adjacency matrix of the matched ego network to themodel; (d) embed the attributes and the structure information by MEgo2Vec; (e) output an embedding for the matched ego network.

Candidate Generation. In practice, the number of all the userpairs across two networks is very large. Thus, we need to generatecandidate user pairs from all the pairs. Following [17, 28], we onlykeep the user pairs if their names are similar to each other (Cf.Section 5 for the details).

Matched Ego Network Construction. For each candidate pair(v1,u1), we extract their ego networksGs

1 andGt1 from their respec-

tive networks (Figure 2(a)), and construct a matched ego networkGM1 according to definition 3.2 (Figure 2(b)). Figure 2 is correspond-

ing to the case in Figure 1, where v2, v3 and v4 are matched to u2,u3 and u4 respectively. User v5 inGs is not matched to any user inGt , so it is removed from GM

1 . Note that a matching between twousers only indicates that they have the potential possibility to be asame person, but the true label is usually unknown.

Matched Ego Network Embedding. We take the attributes ofall the node pairs inGM

1 and the adjacency matrix ofGM1 as the in-

put of the proposed model—MEgo2Vec whose output is an embed-ding. The model consists of two components: attribute embeddingand structure embedding. The component of attribute embeddingadopts the attributes as input, and generates two embeddings v1and u1 for v1 and u1. Specifically, we first generate an embeddingvector for each user in GM

1 based on his/her attributes by the pro-posed multi-view node embedding mechanism (Figure 3), and thenupdate the embeddings of the focal pair (v1,u1) through convolv-ing their neighbors’ embeddings by the proposed attention mecha-nism (Figure 4). The component of the structure embedding adoptsthe adjacency matrix AM

1 as input, normalizes and convolves AM1

into another embedding t1 (Section 4.3).Finally, we predict the label of (v1,u1) based on the combination

of the attribute embeddings and the structure embedding, and cal-culate the loss according to the ground truth. We will explain thedetails of different components as follows.

4.2 Attribute Embedding

Node Embedding. Many works demonstrate the effectiveness ofCNN in representing texts [14]. However, in our task, there are

multiple attributes for each user, and different attributes presentdifferent characteristics when they are used to determine whethertwo users are the same person or not. For example, in our datasets,more than 70% users change a few characters in their nicknames ondifferent social media platforms. In this case, although the wholewords of their names are totally different, the characters in thosenames are highly correlated. But for other attributes of long textssuch as research interests, words maymakemore effects than char-acters. Tomodel both the literal and semantic characteristics of theattributes unitedly, we propose amulti-view node embedding strat-egy. We will introduce the details as below.

We divide each attribute into a list of words. For each word inan attribute, we firstly represent it as an embedding vector, namedas word-view embedding. Then we divide the word into a list ofcharacters, represent each character as an embedding vector, con-volve all the character embeddings by a CNN network and outputan embedding as the word’s character-view embedding. The word-view and character-view embeddings are concatenated as the finalembedding for a word. Then the sequence of the word embeddingsin an attribute are convolved by another CNN network to outputthe final embedding for the attribute. Finally, we use an attributepooling strategy to aggregate the embeddings of all the attributesof a node together as the node embedding:

vi =d∑k=1

aikγk , (2)

where aik represents the embedding of the k-th attribute of uservi , γk ∈ R is the corresponding weighting parameter to be learned,d is the number of attributes of a user and vi is the K-dimensionembedding learned for uservi . Figure 3 illustrates the above multi-viewnode embeddingmechanism,where all the attributes are dealtwith in the same way as name.

Social Convolution. To determine whether two users can bealigned or not, the missing attributes or the attributes that are notdistinguishable enough usually cannot provide sufficient evidence.But additional evidence may be obtained from the attributes ofthe neighbors. Thus after we obtain the embedding for each node

MEgo2Vec: Embedding Matched Ego Networks for User Alignment Across Social Networks CIKM ’18, October 22–26, 2018, Torino, Italy

W e i Wei

CNN

Word-levelCharacter-level

Attribute pooling

Name

……

W a n Wang

CNN

Word-levelCharacter-level

CNN

Other attributes

g

Figure 3: Multi-view node embedding.

based on their own attributes, we further smooth each node’s em-bedding by their neighbors’ embeddings.

The general idea of social convolution is that, for the focal pair(vi ,ui ) to be predicted, we convolve the above obtained embed-dings of all its neighbor pairs {(vj , uj ) : j ∈ NM

i } (including theembeddings of the focal pair itself, i.e., (vi , ui )) into new embed-dings of the focal pair:

(vi , ui ) = c ({(vj , uj ) : j ∈ NMi }), (3)

where vi , ui ∈ RK . The convolution operation c (·) can be definedin various ways. A straightforward way to define c (·) is to averagethe embeddings of all the neighbors together, i.e.,

vi =1|NM

i |

∑j ∈NM

i

vj , ui =1|NM

i |

∑j ∈NM

i

uj . (4)

However, different neighbor pairs may exert different effects.For aligning two users, some neighbor pairs may provide strongevidence, while others may bring in additional noise. Although wehave already filtered out most of the neighbors pairs if their namesare totally different when constructing the matched ego networkfor a focal pair, the rule to filter neighbor pairs is heuristic andis very likely to keep the wrongly matched neighbor pairs in thematched ego network. Thus, it is necessary to distinguish the ef-fects from different neighbor pairs. Recently, the attention mecha-nism used in neural networks is a well-adopted way to achieve thegoal [2]. Inspired by this, we propose using attention mechanismsto realize the social convolution operation c (·).

Essentially, attention mechanism is introduced to determine thecontribution of a neighbor pair to the focal pair. Formally, giventhe embeddings of a neighbor pair (vj , uj ) and the embeddings ofthe focal pair (vi , ui ), we perform a shared attentional mechanismд : RK ×RK ×RK ×RK → R on the four input embedding vectorsto calculate the attention coefficient:

eji = д(vj , uj , vi , ui ), (5)

ṽ1 ũ1

v1 u1

v3 u3v4 u4

v2 u2

𝛼11𝛼31𝛼41

𝛼21

Figure 4: Social convolution.We convolve the embeddings ofv1tov4 by attention coefficients α1 to α4 to obtain the final embeddingv1 for user v1. The same is for user u1.

?

feature

relation

difference|vj�uj |

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Figure 5: Illustration of different attentionmechanisms thatdetermine the contribution of a neighbor pair (vj ,uj ) on pre-dicting the label of a focal pair (vi ,ui ).

where eji indicates the contribution of (vj , uj ) on predictingwhethervi and ui are the same person or not. Then we apply the softmaxfunction to obtain the normalized coefficients across all the neigh-bor pairs of (vi ,ui ):

α ji = softmaxj (eji ) =exp(eji )∑

j′∈NMi

exp(ej′i ). (6)

The normalized coefficients are used to compute a linear combi-nation of the embedding vectors corresponding to them. Then weapply a non-linear function σ (·) on the linear combination, whichis regarded as a final embedding vector for a user:

vi = σ (∑

j ∈NMi

α jivj ), ui = σ (∑

j ∈NMi

α jiuj ). (7)

Figure 4 illustrates the social convolution process.We design theattention mechanisms based on the knowledge in vj , uj , vi and ui .Three specific attention mechanisms are proposed progressivelyby considering individual features of each user in a neighbor pair(feature attention), the similarity between two users in a neighborpair (difference attention) and the relationship of a neighbor pairwith the focal pair (relation attention).• Feature Attention. The assumption of feature attention isthat a neighbor pair (vj ,uj ) makes more contribution on in-ferring the label of the focal pair (vi ,ui ) if the features ofvjand uj are more discriminative. For example, the neighborpair with the same name "Jaspher Wang" benefits more onpredicting the label of (vi ,ui ) than the neighbor pair withthe same name "Wei Wang", as the name "Jaspher Wang" is

CIKM ’18, October 22–26, 2018, Torino, Italy Zhang et al.

more unique than "Wei Wang". According to this assump-tion, we calculate the attention coefficient based on the con-catenation of the embeddings of the neighbors in a pair:

eji =WT [vj ; uj ] + b, (8)

where notationsW andb in this and the following equationsare the model parameters to be learned. The concatenationof the embeddings reserves the features of the two users.• Difference Attention. The assumption of difference attentionis that a neighbor pair (vj ,uj ) takes a more important roleon predicting the label of (vi ,ui ) if the two neighbors vjand uj are more similar to each other. Under this assump-tion, we calculate the attention coefficient solely based onthe difference between the embeddings of the neighbors:

eji =WT |vj − uj | + b, (9)

where we use the difference between two embeddings torepresent whether two neighbors are similar or not.• Relation Attention. The assumption of relation attention isthat a neighbor pair (vj ,uj ) takes more effects on determin-ing the label of (vi ,ui ) if the relationship between user vjandvi inGs share the same semantics with the relationshipbetween user uj and ui in Gt . For example, if we alreadyknow user x in Twitter is aligned to user a in MySpace, anduser y in Twitter is aligned to user b in MySpace, suppose xshares the same interest with y in Twitter, then most proba-bly a also shares the same interest withb inMySpace. Underthis assumption, we calculate the attention coefficient bycomparing the difference between the embeddings of twousers in two networks:

eji =WT | |vj − vi | − |uj − ui | | + b, (10)

wherewe use the difference between two users, e.g., |vj−vi |,to represent the semantics of the relationship between theusers vj and vi , and then use the difference between the re-lationship semantics to represent whether the two relation-ships are similar or not.

Figure 5 illustrates the knowledge that is used to infer the at-tention coefficient of (vj ,uj ) on (vi ,ui ). We can also consider theknowledge used in all the three attention mechanisms and unifythem in one equation:

eji =WT [vj ; uj ; |vj − uj |; | |vj − vi | − |uj − ui | |] + b . (11)

The unified attention mechanism is used in our final model.

4.3 Structure EmbeddingDifferent from attribute embedding, the component of structureembedding aims at embedding the structure information of thematched ego network to predict the label of the focal pair. Theintuition is two users are more likely to be the same person if theyhave more potential matched neighbor pairs, and furthermore, if

there are more neighbors know each other. For example, in Fig-ure 2(b), the focal pair (v1,u1) has three potentially matched neigh-bor pairs, which provides significant evidence on predicting the la-bel of (v1,u1). In addition, neighbor pair (v4,u4) is linked to neigh-bor pair (v3,u3), i.e, v4 knows v3 and u4 knows u3, which furtherimproves the probability that v1 and u1 are the same person. Thelinks between neighbor pairs reflect the structural characteristicsof the matched ego network, which can benefit the predicting task.From the example, we can see that the structural roles of differentneighbor pairs are different when they are used to infer the label ofa focal pair. The core problem of leveraging the structure informa-tion is to map the network structure to an embedding vector suchthat the neighbor pairs with similar structural roles in differentmatched ego networks are positioned similarly in the correspond-ing embedding vectors. Inspired by [16], we address the problemby firstly normalizing the adjacency matrix of the input matchedego network and then applying a convolutional neural network onthe normalized graph to learn an embedding vector for the graph.

Normalization. Normalization aims at finding an order of theneighbor pairs in each matched ego network to reserve the rela-tive position of the neighbor pairs. The basic idea is two neighborpairs in different matched ego networks can be located at the sim-ilar position of the respective adjacency matrix if their structuralroles within the matched ego networks are similar. Intuitively, aneighbor pair can be ranked higher if it is more closer to the focalpair. Multiple similarity metrics defined on graphs can be used tomeasure the distance between two nodes such as common neigh-bors, Jaccard Coefficient, SimRank, etc.

Structure Convolution. After we obtain a ranked list of nodepairs inGM

i , we get a new adjacency matrix AMi with the indexingof the node pairs correspond to the ranked pairs. Then we apply aconvolutional neural network on the normalized adjacency matrixAMi to learn an embedding vector for the adjacency matrix. Specif-ically, we firstly pad dummy node pairs to the adjacency matrixif the size of the pairs is smaller than a predefined number L, anddiscard the pairs with indexing larger than L; then we reshape theadjacency matrix to a L × L-dimension vector, and apply H differ-ent L×L-dimension convoluational kernels with 1 stride, to outputH -dimension embedding vector ti .

4.4 Objective FunctionFor each focal pair (vi ,ui ), we concatenate the difference betweentheir attribute embeddings vi and ui , i.e., |vi−ui | and the structureembedding ti . Then we apply a function f such as the full connec-tion operation on the concatenation to predict the matching scoreyi = f ( |vi − ui |; ti ). Finally we define the objective function as thecross entropy loss of the true label and the predicted score:

L = 1n

n∑i=1

CrossEntropy( f ( |vi − ui |; ti ),yi ), (12)

where n is the total number of labeled user pairs.

MEgo2Vec: Embedding Matched Ego Networks for User Alignment Across Social Networks CIKM ’18, October 22–26, 2018, Torino, Italy

Table 1: Statistics of the datasets.

Dataset Network #Users #Relationships Relation Type

AcademiaAminer 1,053,188 3,916,907 Co-authorLinkedIn 2,985,414 25,965,384 Co-view7

VideoLectures 11,178 786,353 Co-attendance8

SNS Twitter 40,171,624 1,468,365,182 followMySpace 854,498 6,489,736 friend

5 EXPERIMENTS5.1 Experimental Settings

Datasets. We collect threeAcademia networks and two SNS net-works4.Academia consists of networks collected fromAminer [22],an academic searching and mining service, LinkedIn, a business-and employment-oriented professional social network, and Vide-oLectures, the world’s biggest academic online video repository.SNS consists of Twitter, a well-known microblogging social plat-form, and MySpace, a social networking website for users to shareblogs, photos and music. The details are summarized in Table 1.We treat all the relationships in the networks as undirected onesin our experiments. All data and codes are available online5.

Training Data. An instance is a pair of users from two differ-ent networks, where a positive instance means the two users be-long to a same person, while a negative instance indicates theyare different persons. For the training data constructed across SNSnetworks, the positive instances were collected by Perito el. al us-ing Google Profile Service (GPS) [17]. GPS6 allows users to pro-vide their accounts on different online social networks, and theaccounts from same users can be treated as positive instances. Forthose constructed across academia networks, the positive instanceswere provided by the users in Aminer.org, where users can inputthe links of their LinkedIn and ViedoLectures profile pages in theirAminer profile pages. Negative instances should be constructedas they cannot be directly collected by existing services. Follow-ing the assumption that a user usually maintains one major ac-count in each platform [7], we get that in most cases the usersappeared in positive instances cannot be aligned to others users.Thus we sample several negative instances for each positive in-stances. Specifically, for each positive instance (vi ,ui ) where viis from Gs and ui is from Gt , we randomly sample several nega-tive partners from Gt for vi , and several negative partners fromGs for ui . All the negative instances are sampled from the gen-erated candidate pairs (Cf. Section 4.1). Finally, we keep the ratiobetween positive and negative instances as about 1:10 and collect33,981, 34,060 and 35,080 training instances for Aminer-LinkedIn,Aminer-VideoLectures and Twitter-MySpace respectively.

For all the users in training data of Academia networks, we se-lect the profile attributes of name, affiliation, education and re-search interests/skills to compare. Although there are many at-tributes in SNS networks,most of the attributes are extremely sparse.Thus we only choose screen name, account name and locations tocompare for users in the training data of SNS networks.

4https://www.aminer.cn/cosnet5https://github.com/BoChen-Daniel/MEgo2Vec6http:www.google.comprofiles

Baseline Methods. The comparison methods include:ExactNameMatch(ENM): considers a user pair collected from

two networks as a positive instance if the name of a user is an exactmatch to that of the other user in the pair. A user in one networkmay match to multiple users with same names in the other net-work.

SVM: defines the features as the Jaro-Winkler similarity of twonames, the edit distance of two names, and the cosine similaritybetween the TF-IDF weighted word vectors of other attributes.

SVM+N: averages the values for each feature in SVM over allthe neighbor pairs in a matched ego network as additional features.

SiGMa [9]: begins from a seed set of user pairs (output byName-Match and then filtered out the most common names) and itera-tively augments the seed set by propagating the matching scores(predicted by SVM) through the two input networks.

COSNET [28]: is a factor graph model that incorporates the at-tributes of two users as local factors (the same as SVM), and therelationships between user pairs as correlation factors. The intu-ition is two linked user pairs tend to be have the same labels.

MEgo2Vec: is the proposed model that incorporates the multi-view node embedding, unified attention mechanism and the struc-ture embedding together.

Variants of Our Model. We try seven variants of MEgo2Vec toevaluate the effectiveness of different components one by one.

Multi-viewNode Embedding: Firstly, to evaluate the effect ofthe multi-view node embedding component, we ignore the compo-nents of attention based social convolution and structure embed-ding, and only embed the attributes of the focal pair itself. Themodel is denoted as MEgo2Veccw . Additionally, we try word-viewand character-view embeddings separately, and denote them asMEgo2Vecw and MEgo2Vecc respectively.

Social Convolution: Secondly, based on MEgo2Veccw , we addthe attribute embeddings of neighbor pairs to evaluate the effectof the attention based social convolution component. The modelutilizes the unified attention mechanism and ignores the structureembedding, and is denoted asMEgo2Vecu . Additionally, we try thefeature attention, difference attention and relation attention mech-anisms separately, and denote them as MEgo2Vecf , MEgo2Vecdand MEgo2Vecr respectively. We also simply average the attributeembeddings of neighbor pairs and denote it as MEgo2Veca , i.e., at-tention coefficient α ji is set as 1/NM

i .Structure Embedding: Finally, based on MEgo2Vecu , we add

the structure embedding result to evaluate the effect of the struc-ture embedding component. The model is denoted as MEgo2Vecand is also the final proposed model.

Evaluation Strategies. We evaluate all the comparison methodsin terms of Precision, Recall and F1-Measure.

Implementaion Details. We implement the model by Tensor-flow and run the code on an Enterprise Linux Server with 6 Intel(R)Xeon(R) CPU cores (E5-2699 and 56Gmemory) and 1NVIDIATeslaP40 GPU core (24G memory).

7Co-view means two user profiles were viewed by a same user.8Co-attendance means two users attended a same event.

CIKM ’18, October 22–26, 2018, Torino, Italy Zhang et al.

Table 2: Prediction performance on three datasets (%).

Method Aminer-LinkedIn Aminer-VideoLectures Twitter-MySpace

Pre. Rec. F1 Pre. Rec. F1 Pre. Rec. F1ENM 59.50 69.94 64.30 46.56 84.10 59.54 73.29 41.82 53.25SVM 95.97 76.17 84.93 86.96 72.80 79.25 98.40 56.05 71.42SVM+N 95.78 81.62 88.14 86.71 76.09 81.06 97.74 60.58 74.80SiGMa 88.50 47.39 61.72 87.56 58.10 69.85 88.29 35.82 50.96COSNET 84.84 83.15 83.98 69.19 87.10 77.10 78.48 69.56 73.75MEgo2Vec 95.58 89.21 92.29 89.29 79.62 84.18 88.47 72.95 79.97

Table 3: Prediction performance on the instances of Aminer-LinkedIn with or without neighbors by MEgo2Veccw andMEgo2Vecu (%).

Instances Method Precision Recall F1

With Neighbors MEgo2Veccw 99.35 85.56 91.94MEgo2Vecu 99.10 92.22 95.54

Without Neighbors MEgo2Veccw 86.03 84.16 85.09MEgo2Vecu 88.99 82.43 85.59

For the academia networks, we select the candidate pairs if theyshare the same firstname, and the same initials of the lastname.For the SNS networks, we select the candidate pairs if their screennames or account names share at least four 2-grams. When gen-erating a matched ego network, the threshold to filter neighborpairs is set as 0.8. In node embedding component, the dimensionof word, character and attribute embedding is set as 64, 32 and 192respectively. In social convolution component, the maximal num-ber of neighbor pairs in a matched ego network is restricted to14. Then we pad dummy neighbor pairs if the size of the pairs issmaller than 14, and discard additional pairs otherwise. In struc-ture embedding component, we use common neighbors as the sim-ilarity metric to conduct graph normalization. Notation L denotesthe maximal number of neighbor pairs, and is also set as 14. Thedimension H , i.e., the output channel of CNN network, is set as64. The learning rate of the model is set as 0.001. The size B of amini-batch is 100.

5.2 Performance Analysis

Overall Prediction Performance. Table 2 shows the overall per-formance on three pairs of networks. The proposed method per-forms clearly better than the comparison baselines on all datasets(+3.12-30.57% in terms of F1 score). Our method improves moreF1 on the two academia datasets than on the SNS dataset, as theattributes of the academia dataset are much richer than those ofthe SNS dataset, which indicates neural networks are more suit-able for the complex input dataset. ENM is essentially a rough ruleand performs poorly, as on one hand, it totally ignores the positiveinstances with different names, and on the other hand, differentusers with same names are wrongly identified as the same users.SVM ignores the network information and defines features by hu-man experience, which is not comprehensive enough to representthe attributes. SVM+N leverages the attributes of neighbors, but it

+2.6%

(a) Aminer-LinkedIn

+3%

(b) Twitter-MySpace

Figure 6: Prediction performance of model variants.

does not distinguish the effects of different neighbors. SiGMa re-sults in high precision but suffers from a low recall. Because theoverlap between the input two networks is low, leading it not easyto propagate the matching scores from the seeds to other pairs.COSNET essentially propagates the inferred labels in the wholematched network, thus it may suffer from error propagation. Be-sides, the features in COSNET is also human defined. MEgo2Vecuses a graph neural network to embed the neighbors’ attributesand the structure information, which can capture both the literaland semantic characteristics of the attributes, and meanwhile alle-viate error propagations through the network.

On the academia datasets, processing 100 mini-batches requires150 seconds, and best validation F1 is reached after 20-40 epoches(about 270 mini-batches per epoch) through the data, which re-quires 2-3 hours of training. On Twitter-MySpace, as the attributesare extremely sparse, i.e., features are not sufficient, processing 100mini-batches requires 25 seconds, but best validation F1 is reachedafter 100-120 epoches (281mini-batches per epoch), which requires2 hours of training. We show the prediction performance of the dif-ferent variants of our model on one academia dataset and one SNSdataset in Figure 6 and analyze the results as follows.

Multi-view Node Embedding Effect. We compare two singleview models—MEgo2Vecw and MEgo2Vecc with the multi-viewmodel MEgo2Veccw , and show the results in Figure 6. We see thatMEgo2Veccw performs better thanMEgo2Vecw (+1.69-2.48% in F1)andMEgo2Vecc (+1.03-2.03% in F1), which demonstrates the strengthof the multi-view embedding mechanism when representing the

MEgo2Vec: Embedding Matched Ego Networks for User Alignment Across Social Networks CIKM ’18, October 22–26, 2018, Torino, Italy

node attributes. MEgo2Vecc performs better than MEgo2Vecw , asthe similarity between the characters of names takes the most im-portant role among all the attributes. Compared with MEgo2Vecw ,MEgo2Vecc improvesmore F1 onTwitter-MySpace than onAminer-LinkedIn, as other attributes except name are extremely sparse onthe SNS dataset, thus characters in names dominate the effect.

Neighbor Pair Effect. To verify the effect of social convolutioncomponent, based onMEgo2Veccw , we add the neighbors’ attributeembeddings by the unified attention mechanism and find that themodelMEgo2Vecu performsmuch better thanMEgo2Veccw (+2.60-3.00% in F1). We further evaluate the instances with and withoutneighbors separately on Aminer-LinkedIn and show the results inTable 3. We can see that if predicted by MEgo2Vecu instead ofMEgo2Veccw , the performance is improved by 3.6% in F1 for theinstances with neighbors, but it is almost not improved for thosewithout neighbors. The results indicate that the neighbors’ infor-mation captured by our method can indeed benefit the task. Notethat in the instanceswith andwithout neighbors, the ratio betweenthe positive and negative parts is different, so the performance isdifferent by the same method.

Social ConvolutionEffect. Wecompare the three attentionmech-anisms MEgo2Vecd , MEgo2Vecf and MEgo2Vecr and show the re-sults in Figure 6. MEgo2Vecr and MEgo2Vecd perform better thanMEgo2Vecf on academic networks, as relation attention and dif-ference attention determine the contribution of a neighbor pair bycomparing two neighbors’ difference or two relations’ difference,while feature attention only considers the features of a user, butignores the difference between two users. But on Twiter-MySpace,since the attributes in the SNS networks are quite sparse exceptname, the relationships between users are not so easy to describe,makingMEgo2Vecf perform better than the other attentions.Whencombining the three attention mechanisms as MEgo2Vecu does,the performance is better than each individual attention mecha-nism. MEgo2Veca averages neighbors’ embeddings. It performs al-most the same as MEgo2Veccw that totally ignores neighbors’ in-formation. The results indicate that neighbor pairs may bring innoise and it is necessary to carefully utilize the neighbors’ infor-mation by attention mechanism.

Structure Embedding Effect. Based on MEgo2Vecu , we add thestructure embedding, and denote it as our final model MEgo2Vec.The results in Figure 6 show that the performance can be improvedby 0.48-1.36% in terms of F1, which indicates that the structure in-formation of the matched ego network is effectively modeled bythe structure embedding component, and can indeed benefit thealignment task. But the effect is not so significant, as the connec-tions between neighbor pairs in the collected datasets are sparse.

5.3 Case Study

Attention Coefficients. We analyze the attention coefficientslearned by the proposed attention mechanisms. Figure 7 shows acase for predicting whether two “Osmar R. Zaiane"s in two egonetworks are the same person or not. We present the learned atten-tion coefficients of each neighbor by MEgo2Vecr beside the edges.It shows that the neighbor pair named Russell Greiner makes the

Osmar R. ZaianeAff: Alberta UniversityEdu: Simon Fraser Computer Science 1999, Laval University 1992Interest: data mining, association rule mining…

Osmar R. ZaianeAff: Simon Fraser University Alumni ... Edu: Computer Science Simon Fraser 1999, Universita Laval 1992Interest: machine learning, computer science…

Russell GreinerAff: Alberta UniversityEdu: Stanford University Computing Science 1985, California Institute of Technology Mathematics and Computer ScienceInterest: machine learning ...

Russell GreinerAff: Caltech Alumni…Edu: Computer Science Stanford University PhD 1985, California Institute of Technology Interest: machine learning, artificial intelligence, computer science...

Joerg Sander Aff: Department of Computing Science, University of AlbertanEdu: -Interest: clustering structure data, hierarchical/semi supervised clustering...

Joerg SanderAff: The Official Association for Computing Machinery ACM GroupEdu: -Interest: -

ReihanehRabbanyKhorasganiAff: Alberta UniversityEdu: -Interest: RESTful web service, closeness measure, network associations...

Reihaneh RabbanyAff: University of Alberta AlumniEdu: Computing Science University of Alberta, University of Technology Tehran PolytechnicInterest: Java, J2ee, C++, MySQL, latex, data mining...

?

Ego network in Aminer Ego network in LinkedIn

0.62 0.620.270.270.055

0.055 0.055

0.055

Figure 7: Case study of learned attention coefficients.

Ratul Mahajan

Ratul Mahajan

Ratul MahajanRatul Mahajan

Tim J. P. Hubbard

Tim HubbardTim J. P. Hubbard

Tim Hubbard

J. L. Wilkes John Wilkes

J. L. WilkesJohn Wilkes

Hans A. HanssonHans Hansson

Hans A. HanssonHans Hansson

Yvonne RogersYvonne Rogers Yvonne Rogers

Yvonne Rogers

(a) Positive Instances

Li Yongming

Li YU

Jianyi Liu

Jia Liu Liang Tang

Liang Tang

June Wang

Jin Song Wang

Roland van Gog

Ron van Lammeren Jin Song Wang

June Wang

Liang Tang

Liang Tang

Jianyi Liu

Jia LiuLi Yongming

Li YURoland van Gog

Ron van Lammeren

(b) Negative Instances

Figure 8: Case study of learned embeddings. ("Tim J. P. Hub-bard", "TimHubbard"), ("J L.Wilkes", "JohnWilkes"), ("Hans Hansson", "HansA. Hansson"), ("Ratul Mahajan", "Ratul Mahajan"), ("Yvonne Rogers","YvonneRogers"), ("Jianyi Liu, "Jia Liu"), ("Liang Tang", "Liang Tang"), ("Ron van Lam-meren","Roland van Gog"), ("Jin Song Wang", "June Wang") and ("Li Yong-ming","Li YU") are the positive and negative instances.

biggest contribution (with attention as 0.27) among all the neigh-bor pairs except the focal pair itself. Because Russell shares thesame affiliation with Osmar, and also gets the same degree of com-puter science (inferred from their educations) with Osmar in thefirst ego network. And in the second ego network, Russell Greinergets the same degree of computer science with Osmar, and alsoshares the same interest like “machine learning" and “computer

CIKM ’18, October 22–26, 2018, Torino, Italy Zhang et al.

X. Shirley LiuAff: department of Biostatistics …, Harvard School of Public Health Edu: Harvard UniversityInterest:ChIP DNase

Qian WangAff: Dept. of Mechanical and Nuclear Eng., Pennsylvania State Univ.Edu: Interest: Image Registration

Qian WangAff:Edu: 2010 Tongji University 2013Interest:

Yong ZhangAff: Dept. of Computer Science and Info. Systems.Edu: University of DelawareInterest: Online data analysis

Yong ZhangAff: Edu: Interest:

Xiaole LiuAff: Edu: Interest:

?

Figure 9: Case study of structure embedding component.

science" with Osmar. The relationship between Russell and Osmarin the first network is quite similar to the relationship betweenthem in the second network. If calculated by MEgo2Vecd , Russellalso makes more contribution than other pairs, because the two“Russell Greiner"s share the similar educations and interests.

Node Embedding Visualization. Figure 8 visualizes the nodeembeddings before the social convolution operation, i.e., (vi , ui ),and the embeddings after the social convolution operation, i.e.,(vi , ui ), by MEgo2Vecu for 5 randomly selected positive and neg-ative instances with neighbors respectively. The circle points arethe users in Aminer, and the triangle points are their partners inLinkedIn. For the positive instances in Figure 8(a), the two usersin a pair become more similar to each other after the social convo-lution operation, but for the negative instances in Figure 8(b), thetwo users in a pair do not tend to be more similar after the socialconvolution operation, which indicates that the proposed modelcan effectively leverage the neighbor pairs to align users.

Sturcture Embedding. Figure 9 shows a user pair ("X. ShirleyLiu, "Xiaole Liu") that is correctly predicted as the same person byMEgo2Vec, but is wrongly predicted by MEgo2Vecu . The case isdifficult to be predicted, because firstly, the attributes of one net-work is totally missing, and even the name of the two users are notvery similar; secondly, although there are two potentially matchedneighbor pairs ("Yong Zhang", "Yong Zhang") and ("Qian Wang","QianWang"), their attributes are very sparse in one network, thuscan not provide enough evidence. Fortunately, two neighbors knoweach other in their respective networks, which is an important clueto indicate that "X. Shirley Liu and "Xiaole Liu" are the same person.The structure information can be well captured by the structureembedding component of our model.

6 CONCLUSIONWe present the first attempt to solve the problem of user align-ment by a graph neural network model, which predicts whethertwo users can be aligned or not by matching and embedding theirego networks. The model deals with the issue of diverse neighborsby distinguishing them using attention mechanisms. Meanwhile,it captures both the literal and semantic characteristics of the at-tributes by a multi-view embedding mechanism, and also capturesthe structure of thematched ego network through normalizing andconvolving the adjacency matrix. The experimental results on dif-ferent genres of datasets validate the effectiveness of the model.

Acknowledgments. This work is supported by National Key R&D Pro-gramof China (No.2018YFB1004401) andNSFC under the grant No. 61532021,

61772537, 61772536, 61702522 and the Research Funds of Renmin Univer-sity of China(15XNLQ06). *Hong Chen is the corresponding author.

REFERENCES[1] JamesAtwood andDon Towsley. 2016. Diffusion-convolutional neural networks.

In NIPS’16. 1993–2001.[2] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 2015. Neural machine

translation by jointly learning to align and translate. In ICLR’15.[3] David K Duvenaud, Dougal Maclaurin, Jorge Iparraguirre, Rafael Bombarell,

Timothy Hirzel, Alán Aspuru-Guzik, and Ryan P Adams. 2015. Convolutionalnetworks on graphs for learning molecular fingerprints. In NIPS’15. 2224–2232.

[4] Marco Gori, Gabriele Monfardini, and Franco Scarselli. 2005. A new model forlearning in graph domains. In IJCNN’05. 729–734.

[5] Aditya Grover and Jure Leskovec. 2016. node2vec: Scalable feature learning fornetworks. In SIGKDD’15. 855–864.

[6] Thomas N Kipf and Max Welling. 2017. Semi-supervised classification withgraph convolutional networks. In ICLR’17.

[7] Xiangnan Kong, Jiawei Zhang, and Philip S Yu. 2013. Inferring anchor linksacross multiple heterogeneous social networks. In CIKM’13. 179–188.

[8] Nitish Korula and Silvio Lattanzi. 2014. An efficient reconciliation algorithm forsocial networks. Proceedings of the VLDB Endowment 7, 5 (2014), 377–388.

[9] Simon Lacoste-Julien, Konstantina Palla, Alex Davies, Gjergji Kasneci, ThoreGraepel, and Zoubin Ghahramani. 2013. Sigma: Simple greedy matching foraligning large knowledge bases. In SIGKDD’13. 572–580.

[10] Yujia Li, Daniel Tarlow, Marc Brockschmidt, and Richard Zemel. 2016. Gatedgraph sequence neural networks. In ICLR’16.

[11] Jing Liu, Fan Zhang, Xinying Song, Young-In Song, Chin-Yew Lin, and Hsiao-Wuen Hon. 2013. What’s in a name?: an unsupervised approach to link usersacross communities. In WSDM’13. 495–504.

[12] Li Liu, William K Cheung, Xin Li, and Lejian Liao. 2016. Aligning Users acrossSocial Networks Using Network Embedding.. In IJCAI’16. 1774–1780.

[13] Siyuan Liu, ShuhuiWang, Feida Zhu, Jinbo Zhang, and Ramayya Krishnan. 2014.Hydra: Large-scale social identity linkage via heterogeneous behavior modeling.In SIGMOD’14. 51–62.

[14] Xuezhe Ma and Eduard Hovy. 2016. End-to-end Sequence Labeling via Bi-directional LSTM-CNNs-CRF. In ACL’16. 1064–1074.

[15] Tong Man, Huawei Shen, Shenghua Liu, Xiaolong Jin, and Xueqi Cheng. 2016.Predict Anchor Links across Social Networks via an Embedding Approach.. InIJCAI’16. 1823–1829.

[16] Mathias Niepert, Mohamed Ahmed, and Konstantin Kutzkov. 2016. Learningconvolutional neural networks for graphs. In International conference onmachinelearning. 2014–2023.

[17] Daniele Perito, Claude Castelluccia, Mohamed Ali Kaafar, and Pere Manils. 2011.How Unique and Traceable Are Usernames?. In ICPET’11. 1–17.

[18] Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. 2014. Deepwalk: Online learn-ing of social representations. In SIGKDD’14. 701–710.

[19] Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, andGabriele Monfardini. 2009. The graph neural network model. TNN 20, 1 (2009),61–80.

[20] Kai Shu, Suhang Wang, Jiliang Tang, Reza Zafarani, and Huan Liu. 2017. UserIdentity Linkage across Online Social Networks: A Review. ACM SIGKDD Ex-plorations Newsletter 18, 2 (2017), 5–17.

[21] Jian Tang, Meng Qu, Mingzhe Wang, Ming Zhang, Jun Yan, and Qiaozhu Mei.2015. Line: Large-scale information network embedding. In WWW’15. 1067–1077.

[22] Jie Tang, Jing Zhang, Limin Yao, Juanzi Li, Li Zhang, and Zhong Su. 2008. Ar-netminer: extraction and mining of academic social networks. In SIGKDD’08.990–998.

[23] Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, PietroLiò, and Yoshua Bengio. 2018. Graph Attention Networks. In ICLR’18.

[24] Reza Zafarani and Huan Liu. 2009. Connecting Corresponding Identities acrossCommunities. ICWSM’09 9 (2009), 354–357.

[25] Reza Zafarani and Huan Liu. 2013. Connecting users across social media sites:a behavioral-modeling approach. In SIGKDD’13. 41–49.

[26] Reza Zafarani, Lei Tang, and Huan Liu. 2015. User identification across socialmedia. TKDD 10, 2 (2015), 16.

[27] Si Zhang and Hanghang Tong. 2016. FINAL: Fast Attributed Network Align-ment.. In SIGKDD’16. 1345–1354.

[28] Yutao Zhang, Jie Tang, Zhilin Yang, Jian Pei, and Philip S Yu. 2015. COSNET:Connecting heterogeneous social networks with local and global consistency.In SIGKDD’15. 1485–1494.

[29] Zexuan Zhong, Yong Cao, Mu Guo, and Zaiqing Nie. 2018. CoLink: An Unsuper-vised Framework for User Identity Linkage. (2018).

[30] Xiaoping Zhou, Xun Liang, Haiyan Zhang, and Yuefeng Ma. 2016. Cross-platform identification of anonymous identical users in multiple social medianetworks. TKDE 28, 2 (2016), 411–424.