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Privacy Preserving Social Tie Discovery Based onCloaked Human Trajectories

Ye Tian, Member, IEEE, Wendong Wang, Member, IEEE, Jie Wu, Fellow, IEEEQinli Kou, Zheng Song and Edith C. -H. Ngai, Member, IEEE

Abstract—The discovery of peoples’ social connectionsbecomes a flourishing research topic, considering therich social information inferable from human trajectories.Existing social tie detection methods often require mobileusers to upload their accurate locations causing seriousprivacy concerns. On the other hand, cloaking methodsallow users upload their obscured locations instead, andcan efficiently protect their location privacy. However, noexisting social tie detection method can generate socialrelationships among users when only obscured trajectoriesare provided. To tackle the above mentioned problem, thispaper proposes a novel semantic-tree based algorithm.Specifically, we model the obscured regions from thecloaking algorithm as a semantic region tree and assignweight values for regions based on their popularity, furtherindicating the similarity between users based on theirtemporal and spatial relations. We evaluate our proposedapproach using a real trajectory dataset, and show thatour algorithm can identify social ties successfully with 20%higher accuracy than the existing approaches.

Index Terms—Social tie discovery, cloaked trajectory,privacy preserving, semantic similarity.

I. INTRODUCTION

SOCIAL link prediction has emerged as a hottopic in social network analysis, as knowing the

social ties among people would be beneficial to link

Copyright (c) 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposesmust be obtained from the IEEE by sending a request to pubs-permissions@ieee.org.

This work was supported in part by the National Natural ScienceFoundation of China under Grant 61370197 and 61402045, andthe Specialized Research Fund for the Doctoral Program of HigherEducation under Grant 20130005110011, and the National HighTechnology Research and Development Program of China underGrant 2013AA013301

Y.Tian, W.Wang, Q.Kou and Z.Song are with the State KeyLaboratory of Networking and Switching Technology, BeijingUniversity of Posts and Telecommunications, Beijing 100876,China (email:{yetian,wdwang}@bupt.edu.cn, shuxi kql@163.com,sonyyt@gmail.com).

J.Wu is with the Department of Computer and InformationSciences, Temple University, Philadelphia, PA 19122 USA (e-mail:jiewu@temple.edu)

Edith C. -H. Ngai is with Uppsala University, Uppsala, Sweden(email:edith.ngai@it.uu.se)

prediction [1], rating prediction [2], product recom-mendation [3] and community discovery [4]. Onecommonly-adopted method of inferring social tiesis measuring the similarity of individuals’ historicallocations in both spatial and temporal dimensions,because recent researches have proven that people’ssocial relationship may partly influence their mo-bility patterns. In particular, people’s trajectory isan important clue for inferring social ties, since weand our friends are likely to visit similar locations[5]. In recent years, location-based social networkapplications have become highly popular around theworld. Increasingly more people are using GPS-enabled devices to log their outdoor locations andactivities [6],[7], and to share information abouttheir current locations and activities with friendsthrough remote servers. This kind of informationsharing has a profound impact on social networks[8], and provides the basis of inferring social ties.

Location is sensitive for individuals, and it isprobably to be leaked out, by an untrusted serv-er, to malicious third parties [9]. Extensive workshave been conducted to guard against individual’slocation privacy leaking in location-based services[9],[10],[11],[12],[13].

Most of the existing approaches are based on lo-cation perturbation and obfuscation, which employwell-known privacy metrics calculated at the serverside to evaluate the level of personal data disclo-sure [14]. K-anonymity is a representative measureguaranteeing that a user is indistinguishable from atleast k-1 other users. Generally, in order to achievek-anonymity, a centralized location anonymizer [15]is responsible for enlarging the queried location ina location-based service (LBS) query to a largerregion which geographically covering at least k-1 other users. This process is defined as cloaking[10] and the spatial cloaked area around user’sactual location is defined as cloaking region, whilea trajectory which is composed of a sequence ofemphcloaking regions, is then called a cloakedtrajectory. As show in Fig. 1, k is 4 and 7 for the

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two users, respectively. We notice that the cloakingregions have different sizes according to the settingof k. Sometimes, the cloaking region of a user with alarge k might contain the cloaking region of anotheruser with a smaller k (see the red rectangular regionin Fig. 1).

Considering that cloaking-based approaches arewidely adopted in location privacy preserving, iden-tifying social ties from cloaked trajectories is prettymuch a necessity. Based on k-anonymity cloaked lo-cations, Tan et al. [16] proposed social tie predictionalgorithm, though it suffers from low accuracy. Inour previous paper [17], we have introduced howto reveal the social connections via blurry trajec-tories processed by cloaking algorithms. Differentfrom Tan’s work [16], we take the different privacyprotection levels into consideration, and realize thatthe semantic meanings and hierarchical relations ofcloaking regions would be very useful.

This paper tackles the problem of inferring socialties from obscured trajectories for privacy preserva-tion purposes. Compared with traditional methodsthat ignore the location privacy of users, the distancebetween two cloaking regions can no longer reflectthe actual distance between two users.In order tosolve such problems, we proposed a weighted hier-archical semantic tree model in this paper. Firstly,we transform the cloaking regions into semanticregions. Considering the different levels of privacyrequirements of users, which can be reflected bytheir choices of k in k-anonymity cloaking, thereexists containment relationship among the semanticregions. The concept of containment relationshipof semantic regions is illustrated in Fig. 2. In thisfigure, residential community contains the park andthe market, for some users with high k values, thesemantic region could be residential community, andfor users with lower k values, the semantic regioncould be the park or the market. Furthermore, thedifference of popularity of regions is taken into ac-count in our paper. Since people appearing in somerarely-visited regions are considered to have a largerchance of knowing each other, less popular regionsare more successful in inferring social ties. Next,we propose a novel algorithm to infer social tiesamong people using weighted hierarchical semantictree. The probability of the existence of social tiesbetween two users is then measured by a similarityscore.

On the basis of the previous work, we improvethe accuracy in social tie discovery. In particular,we improve the semantic tree model by further

considering the impact of the popularity of semanticregions to the calculation of similarity among users.In this case, we divide regions into popular regionsand unpopular regions. For example, bars and sta-diums could be regarded as the unpopular regions,while markets and restaurants could be regarded aspopular regions. In our paper, the popularity of aregion is mainly decided by its number of checkins,and a region is more representative of people’shobbies and characteristics if it is an unpopular re-gion. Thus, unpopular regions should be assigned ahigher weight than popular regions when measuringsimilarity.

The contributions of this paper can be summa-rized as follows:

• We introduce a weighted hierarchical semantictree model. In this model, different levels of us-er privacy preservation are taken into account.We also consider some important features ofsemantic regions to help construct our model,such as the containment relationship of regions,and popularity differences among regions.

• We propose a trajectory similarity measuringalgorithm to discover social ties of users fromthe cloaked trajectories based on weighted hi-erarchical semantic tree model.

• We use the Gowalla dataset [18],[19] thatrecords 196,591 users to evaluate the perfor-mance of the proposed scheme. The resultsshow that our proposed method can improvethe social tie inferring accuracy by almost 20%when compared with existing algorithms.

The rest of this paper is organized as follows.Section II reviews the related literatures. Section IIIintroduces the weighted hierarchical semantic treemodel. Section IV gives full details of our algorithmfor social ties detection. Section V evaluates ourapproach with a real-world dataset and reports theevaluation results. Section VI concludes our work.

II. RELATED WORK

The relation between social ties and human mo-bility has been widely explored in recent years[6],[20],[8],[5]. It is revealed that human trajectoriesand social ties are closely correlated [8]. Cho etal. [5] further studied the relation between socialties, human geographic and temporal dynamics, andidentified the strong indication between trajectorysimilarity and social tie.

Semantic trajectory data mining has emerged asan important tendency in recent studies [21],[22].For example, Baratchi et al. constructed semantic

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Raw GPS Trajectories

!!

Mobile Users Trusted Third Party Cloaked Trajectories

Raw GPS Location Anonymous User Target User Cloaking Region

Application Server

Fig. 1: Cloaked Trajectories.

Residential Community

SchoolPark Market

Bank Hospital

Trajectory 1 Trajectory 2

Geographic PointTrajectory 3

Fig. 2: Containment relationship of coverage areas.

location histories (SLH), with which they proposeda novel mechanism to estimate the probability ifsocial tie exists between users by measuring theirtrajectory similarity [6],[23]. Liu et al. [24] cap-tured landmarks on trajectory, which was composedof a sequence of locations labelled with semantictags (called semantic locations). These semanticlocations contain a wealth of information aboutindividual’s daily activities. For example, Alvareset al. [21] have found semantic trajectory patternsfrom users’ mobility histories. They first mappedeach stop in trajectory to semantic landmark andthen applied sequential pattern mining to find user’sfrequent behaviors. The study of Ying et al. [22]goes further to predict user’s next location on theirtrajectory by analyzing the geographic and semanticfeatures.

Location information is important but sensitive,a mass of location privacy protection mechanismshave been proposed in social networking services.Zhang et al. proposed a suit of novel fine-grainedprivate matching protocols to enable two usersperform profile matching without disclosing priva-cy information for proximity-based mobile socialnetworking [25], [26]. Sun et al. studied social

tie discovery problem in mobile social network,and adopted geographic cell index to record mo-bile user’s location and further proposed a pri-vate set Intersection Cardinality (PSI-CA) protocoland a Bloom filter based protocol for privacy-preserving spatiotemporal matching [27].Locationperturbation and obfuscation are the most studiedapproaches [9],[28]. As a representative technology,k-anonymity, introduced by Gruteser and Grunwald[29], could reduce the probability that the targetobject being identified from a k-objects group toonly 1/k [30]. Gruteser et al. proposed an adap-tive interval cloaking algorithm to construct spatial-temporal cloaking areas containing at least kmin

users. After that, they sent only the cloaking areas toapplication servers for different kinds of services. Ink-anonymity cloaking, the level of user anonymity,indicated by k, could be maintained by changingthe size of the cloaking area [31]. A larger kcorresponds to higher privacy protection level, andvice versa.

A number of researches also discussed the metricsof location privacy evaluation [32],[33],[34],[35].Intuitively, the degree of location privacy is definedas the accuracy with which an untrusted party canlocate an individual. Since privacy is intrinsicallyrelated to uncertainty, entropy-based metrics aremostly adopted to evaluate the the privacy protec-tion level in anonymous communication [32],[33].Typically, the privacy metric is defined as Eq. 1:

H(k) = −I∑

i=1

pi lg pi, (1)

where, pi denotes the adversaries probabilities fordifferent assignments of user identities to the ob-served position and I indicates the the total numberof such assignment hypothesis. Hoh et al. [32] alsoproposed an alternative metric with the expectationof distance error to capture how accurate an adver-

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sary can estimate individual’s location. They gavethe formulation as Eq. 2:

E[d] =1

NK

K∑k=1

I∑i=1

pi(k)di(k), (2)

Where, di describes the total distance error betweencorrect assignment hypothesis and the hypothesis i,while N is the number of users and K denotes thetotal observation time.

In this paper, we try to identify social tiesbased on users’ cloaked trajectory resulted fromk-anonymity processing. Compared with previousworks, this approach extends the concept of seman-tic trajectory and explores hierarchical relationshipof semantic regions for social tie identification,meanwhile it preserves location privacy to userswith different privacy protection requirements level.

III. THE PROPOSED MODEL

In this section, we would elaborate the detail ofour proposed model. Intuitively, it is difficult todeduce social ties via obscured trajectories, sincethey are unable to reveal accurate location distanceat the same time. In our approach, we first transformthe cloaking regions to semantic regions in a prepro-cessing stage, to say, make cloaking regions carrysemantic information. Next, since users have differ-ent requirements in privacy protection, reflected inthe different values of k, the granularity of cloakingregions varies. In this case, there exists hierarchicalrelationship among semantic regions. Users in tworegions having a hierarchical relationship are likelyto know each other. Third, the weight of semanticregions is allocated based on the popularity ofregions. Two users have a higher probability ofknowing each other if they appear in a less visitedregion. In this way, we can improve the accuracy ofsocial tie discovery.

A. System OverviewA trusted anonymization server is deployed to

transform raw trajectories to cloaked trajectories.Only the cloaking regions will be forwarded to theapplication server to support various kinds of ser-vices. Fig. 1 shows the procedure in detail. First, thetrusted server collects raw GPS trajectories from themobile devices. Then, the trusted server anonymizesthe trajectories with k-anonymity to make usersindistinguishable from k-1 other users. Actually,different users may have different privacy protection

requirements which are determined by the value ofk. A larger k brings a higher privacy protectionlevel, and vice versa. In practice, a number of koptions are presented to user. Users select suitablek empirically according to their privacy protectiondemand. When all trajectories are processed by thetrusted server, cloaked trajectories could be sharedwith the application servers.

For convenience, cloaking region is representedwith rectangle indicated by the x,y-coordinates of itstop-left and bottom-right corners. Considering thatusers may have different privacy protection levels,the size of cloaking regions is varying accordingly.Let U = {Ui : i = 1, 2, ..., U} denote the set ofusers, and Tu denote the corresponding trajectories.Each trajectory is composed of a set of triples{Rp, Ep, Lp}. Where, Ep and Lp denote the timestamp when user u arrived and left region Rp

respectively, R = {Ri : i = 1, 2, ..., R} is the set ofcloaking regions.

B. Semantic RegionsIn this section, we will elaborate the procedure

of labeling cloaking regions with semantic tags.Actually the semantic meaning is represented byits detailed address rather than its GPS location.The procedure of transforming cloaking region tosemantic cloaking region is illustrated in the firstgrey box in Fig. 3. Services like Google Maps

Cloaked

trajectories

Semantic Region POI

Database

Cloaked

semantic

trajectories

Semantic Hierarchical Tree

Cloaking RegionSequences

Sequences

Social Tie Discovery

Algorithm

Fig. 3: The procedure of our model.

API, provide basic functions to geographic locationsto its corresponding toponym with accurate GPSinformation. However, a cloaked region cannot beprocessed with this service, since it lacks exactlatitude and longitude information.

It is worth noting that a semantic region trans-formed from a cloaking region should carry oneand only one semantic meaning. If a semanticregion could not meet this requirement, it needs tobe expanded in order to carry only one semanticmeaning. The operation is to include more regions.

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To implement the process of transforming acloaking region to a semantic region, we select sev-eral locations in the cloaking region as a sample set.This is conducted by dividing the cloaking regioninto disjoint rectangles with equal size, and selectingthe center point of each rectangle as a sample loca-tion. We denote all the sample locations in a cloak-ing region with L = {Li : i = 1, 2, ..., L}. For eachlocation Li ∈ L, the semantic meaning associatedto it could be derived by reverse geocoding usingGoogle Maps API 1. Let S = {Si : i = 1, 2, ..., S}be the set of semantic meanings associated to thelocations in L, such that Si represents the semanticinformation of location Li.

If all the sub-regions in L carry a same semanticmeaning, denoted as A, it could be deduced thatthe semantic meaning of the cloaking region is A.Otherwise, none of the semantic meanings in Scould satisfy the user’s anonymity level. Thus, aregion with bigger size, covering all of the semanticmeaning as the semantic region of this cloakingregion should be selected as the representative re-gion. As the structure of each semantic meaningobtained by reverse geocoding using Google MapsAPI is hierarchical, we search them along withthe hierarchical structure to the upper levels untilthe semantic meaning is the same. For example,the semantic meanings in a cloaking region aredifferent, including Library of BUPT, Canteen ofBUPT, and Basketball Court of BUPT, thus weshould select a larger region covering all of thesesemantic meanings as the semantic region. In thisexample, the semantic region is BUPT campus,which is a common upper level semantic meaning.In this way, we could transform all the cloakingregions into semantic regions. For each cloakingregion, Ap represents the semantic meaning of thespatial-temporal portion {Rp, Ep, Lp}.

C. Hierarchical Semantic TreeIn the previous discussion, we have transformed

cloaking regions into semantic regions. As theanonymity levels of individuals are different, thevarying sizes of semantic regions may result ininternal containment relationship. Take Fig. 2 asan example, we assume that Jack and John appearat a park, and the anonymity level of John ishigher than that of Jack. Moreover, the number ofusers in the park within a given timeslot is toofew to satisfy John’s needs in privacy preservation.

1https://developers.google.com/maps/documentation/geocoding

ROOT

…

… … … …

Semantic Region

1

Haidian

District

Beijing

The Third

teaching building

… …BUPT Campus

Tsinghua

University

2

…

…

…

BUPT library

Chaoyang

District

Shanghai

Fig. 4: Hierarchical Semantic Tree.

Thus, the semantic region should be expanded toa residential community, as in Fig. 2. Intuitively,person with larger k is more likely to be allocateda semantic region with larger size, and this regionwould probably contain the region which is allocat-ed to a person holding smaller k.

Based on the containment relationship, a hierar-chical semantic tree is constructed. Each node inthe tree is associated with a semantic region. Asillustrated in Fig. 4, nodes located in higher layergeographically contains those in lower layers. Forexample, BUPT Campus geographically covers theBUPT library and the third teaching building, so thenode representing BUPT library is the parent nodeof the latter two. Similarly, since BUPT Campusand Tsinghua University are both located in Haid-ian District, they are both child nodes of HaidianDistrict. Population density is unevenly distributedin different regions, so persons with constant privacylevel k are not associated to certain node fixedly. Forexample, a user in region 1 may transfer to region2 in the next timestamp (see Fig. 4).

D. Weights of Semantic Regions

In our previous work, we consider that all the re-gions expose the same influence on similarity calcu-lation. Actually, different regions should contributedifferent influences when measuring the similarityof users’ trajectories. For example, people checkingin a bar may share more similar characteristics.Since a bar is a less popular region, but people hereare more likely to have social ties. In our model, weconsider that the popularity of a region decides itsweight in similarity calculations, and less popularregions should be assigned a higher weight.

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In order to determine the weight of each region,we propose an approach to set regions’ weightsbased on mathematical expectation and standard de-viation. Mathematical expectation could reflect theprobability-weighted average of all possible valuesof a discrete random variable. Standard deviationis used to quantify the amount of variation ordispersion of a set of data values.

First of all, we need to calculate the probability ofevery region being checked in. We count the numberof check-ins of each region, and then calculate thepercentage of the check-ins of each region on eachlevel by Eq. 3. The set of percentages is denoted asPj = {Pji : i = 1, 2, ..., |Pj|}, where |Pj| denotesthe number of nodes in the jth level. This percentagecould represent the probability that a region hasbeen checked in.

Pji =Cji∑|Cj |i=1Cji

, (3)

where the set of the check-ins in the jth level isdenoted as Cj = {Cji : i = 1, 2, ..., |Cj|}, and Cji

represents the number of check-ins of the ith nodein the jth level.

Next, we calculate the expectation and standarddeviation denoted as EV and SD in each level ofthe tree. For the jth level, we could get the expecta-tion value via Eq. 4, and get the standard deviationby Eq. 5. The mathematical expectation is theprobability-weighted average of different amountsof check-ins of all regions in this level.

EV =

|Cj |∑i=1

Pji × Cji, (4)

where |Cj| is the number of nodes in the jth levelof the tree.

SD =

√√√√ 1

|Cj|

|Cj |∑i=1

(Cji − EV)2, (5)

where EV could be obtained from Eq. 4.Observing the distribution of the check-in num-

bers could help classify the regions into differentgrades. The distribution curve of the number ofcheck-ins in certain level of the tree is demonstratedin Fig. 5. We found that the distribution curve issimilar to the normal distribution, and the peakof the curve corresponds to the expectation value.In Fig. 5, the horizontal axis is the number ofcheck-ins, and the vertical axis is the percentage.The area encompassed by the curve and two lines

perpendicular to the horizontal axis represents thepercentage of regions whose check-ins numbers fallinto the range of two lines. For example, the areaof the shaded part could represent the percentageof regions whose number of check-ins fall intobetween x = 0 and x = EV − 2SD, which is p%in this case.

Fig. 5: The distribution curve of check-in numbers.

According to the mathematical expectation value,the standard deviation, and the distribution analy-sis, all of the regions in the same level could beclustered into multiple grades, and different weightvalues should be assigned to different grades accord-ingly. In this way, regions could be differentiatedbased on popularity.

Next, we would illustrate the details of classifyingregions under the premise of not changing thestructure of the hierarchical semantic tree. Whenclustering regions of a level, k-means method isadopted. In further details, we set the clusters andweights as follows:

• Determine typical values as the center pointsof k-means. Instead of selecting initial center-ing points randomly in a traditional k-meansmethod, we select them according to EV andSD. It is known that the standard deviationdoes measure how far typical values tend tobe from the expectation value, and thus theinitial center points could be set based onthe standard deviations of expectation value(mathematically, EV ± SD, or EV ± 2SD).In this way, some errors caused by selectingcenter points randomly could be reduced.

• Cluster regions for each level. In each levelof the tree, we cluster regions by a k-meansmethod. In the k-means method, items are clus-tered mainly by the distance between the itemand center points. In our work, the distance isthe difference between the number of check-ins

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in every region, and that of center points.• Assign different weight values to different

clusters. We rank the clusters according to thepercentage of their corresponding center point,and this rank could reflect their popularity. Alower value of a center point indicates thatthe regions in this cluster are relatively lesspopular, so we should assign a higher weightvalue to this class, and vice versa.

Fig. 6: The example of clustering regions.

As shown in Fig. 6, regions of certain level areclustered into five clusters according to the check-innumbers. In this example, the EV is equal to 260,and the SD is equal to 150. The points with thesame color and shape belong to a cluster. In Fig.6, we could observe that the numbers of regions indifferent clusters are uneven. Furthermore, a clustercontains more regions if the value of center point iscloser to the expectation value, and vice versa. Inthis case, we should assign different weight valuesto five clusters. Regions in the cluster within whichthe check-in numbers of the center point is thelowest, are assigned the biggest weight, and viceversa. For example, if the center point values offive clusters are v1, v2, v3, v4 and v5, respectively,where v1 < v2 < v3 < v4 < v5, their weights shouldbe w1, w2, w3, w4 and w5, where w1 > w2 > w3 >w4 > w5.

E. Temporal SimilarityWhen calculating similarity of two trajectories, it

is necessary to ensure they are aligned in temporaldimension. It makes sense only if the two regionsto be compared fall in a same time slot.

Definition 3.1: (Pair regions) Suppose pi andpj are two spatial-temporal semantic portions fromtwo trajectories t1 and t2 respectively, they aredefined as pair regions if and only if the temporalconstraint TimeDiff is satisfied. More specifically,TimeDiff (Epi , Epj ) 6 δt and TimeDiff (Lpi ,

Lpj ) 6 δt should be satisfied simultaneously for piand pj , where δt is a given temporal implying theoptimal time span.

In order to guarantee the mobility of individualsand the amount of pair regions on two trajectories,δt is set as one hour. Two considerations should befine-tuned to better determine the parameter δt. Forone thing, in order to ensure semantic regions in atrajectory are meaningful, the time span should notbe too long. For example, making a comparison be-tween trajectories in different years makes no sense.For another, the alignment of different trajectoriesin a same day is not mandatory. This ensures thatregions with similar patterns in different days shouldstill be considered as pair regions. For example,Jack and John are colleagues and know each other.However, Jack goes to the company every workday,while John does not come to the company every day.Although Jack and John may not meet everyday, westill observe similar mobility patterns between them.

t1

t2

6:00 a.m. 8:00 a.m. 10:00 a.m. 12:00 a.m.

P1

P1

P2 P3

P3

P4 P5

P4P2

Fig. 7: Pair regions in two trajectories.

Fig. 7 illustrates the concept of pair regions,where pair regions are indicated with same shape.It is possible that a region on a trajectory maybe paired with more than one regions on anothertrajectory, i.e. p4, p5, and p6 circled in Fig. 7.This is because multiple regions may satisfy thesame temporal constraint δt. For this case, similaritybetween all pair regions is measured.

F. The Relationship between Trajectories’ Similar-ity and Social Ties

It is supposed that the similarity of individuals’trajectories can imply, to a large extent, their com-mon preference of behaviors and mobility patterns.Therefore, a high similarity score of trajectories mayindicate that social tie may exist between users.

Hierarchical semantic tree is adopted as a fea-sible model for inferring social ties in this paper.The underlying concept is twofold. First, if users’trajectories match well, they are likely to share samepattern in the hierarchical semantic tree. Second, to

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say the least, even though their trajectories are notexactly the same, social tie may still exist if their tra-jectories are close in the hierarchical semantic tree,or if there exists containment relationship betweentheir semantic regions.

IV. THE PROPOSED SOCIAL TIE DISCOVERYALGORITHM

The existence of social ties mainly depends onthe similarity of trajectories between users. We cancalculate the similarity of two trajectories based onpair regions. Several relevant metrics, including thelowest common ancestor node and the length of theshortest path, can be obtained from the hierarchicalsemantic tree:

• The level of the lowest common ancestor node.The level of the lowest common ancestor nodeof pair regions determines how relevant the pairregions are in the hierarchical semantic tree.Lower level may lead to greater impact on sim-ilarity measurement, since a lower level noderepresents a more specific semantic region. Ifthe pair regions are located in the same nodein the tree, it, itself, is the lowest commonancestor node.

• The shortest length between two semantic re-gions. The shortest length between two regionsin the hierarchical semantic tree reflects howclose the two regions are. Intuitively, they arecloser if they are more geographically adjacent.

• The level of the semantic regions themselves. Ifthe semantic regions are located in a lower levelin the hierarchical semantic tree, their locationsare more accurately indicated.

• The popularity of each region. We consider thatpersons checking in the less popular region aremore likely to have social ties.

Based on the consideration mentioned above, themetrics are defined accordingly:

1) len(Ri, Rj): the length of the shortest pathbetween region Ri and region Rj .

2) lca(Ri, Rj): the lowest common ancestor n-ode of Ri and Rj .

3) depth(Ri): the level of region Ri in hierarchi-cal semantic tree.

4) deep max: the maximum level of the tree.5) sim(Ri, Rj): the similarity between cloaking

regions Ri and Rj in the tree.6) inf(Ri): the influence of Ri in social ties

prediction, which is decided by the level ofregion Ri. Intuitively, inf(Ri) increases withdepth(Ri) monotonically.

7) W (Ri): the weight of Ri, which reflects thepopularity of this region.

We measure the similarity of trajectories based onthese three metrics: the length of the shortest path,the level of the lowest common ancestor, and theinfluence of the semantic region. It is illustrated inthe following equation:

simPair(Ri, Rj) = e−α×len(Ri,Rj)

×{inf(Ri)× inf(Rj)× e−γ(W (Ri)×W (Rj))

×eβ×depth(lca(Ri,Rj)) − e−β×depth(lca(Ri,Rj))

eβ×depth(lca(Ri,Rj)) + e−β×depth(lca(Ri,Rj))}

(6)

Apparently, the value of Eq. 6 increasesmonotonically with respect to depth(lca(Ri, Rj)),but decreases with len(Ri, Rj). The smaller thelen(Ri, Rj) is or the greater the depth(lca(Ri, Rj))is, user A and user B are more likely to locate inregions of a lower level in the hierarchical semantictree. Such that, they will have greater influence andachieve a maximum sim(Ri, Rj). On the contrary,if len(Ri, Rj) is closer to 2 × deep max anddepth(lca(Ri, Rj)) is equal to 1 (i.e. root node),then sim(Ri, Rj) will be close to 0. Besides, αand β are parameters scaling the contribution of thelength of the shortest path and the level of the lowestcommon ancestor respectively, and γ is scalingthe contribution of the weight of a region. Theoptimal setting of α, β and γ should be decided bythe experimental results. Also, inf(Ri) × inf(Rj)represents the mutual influence contributed to thesimilarity. To derive the similarity of two cloakedtrajectories, the hierarchical semantic tree and theset of pair regions in two trajectories (t1 and t2),denoted as PR are taken as input. Then, the metricsdefined above are derived for each pair of regions.According to Eq. 6, the similarity of each pair regionis then obtained. Finally, by taking the weightedaverage of the similarities of all pair regions, thesimilarity of two cloaked trajectories is achieved.The detail description is illustrated in Alg. 1.

We take Fig. 8 as an example. Two users, Jackand John are involved in this scenario. At time m1,the semantic region of Jack is covered by regionA, and the semantic region of John is in region B.Region C is their lowest common ancestor, which isin the second level of the semantic tree. Accordingto this tree, the length of shortest path is equal to 5.Then, we can calculate the similarity of the first pairregions of these two trajectories. In the next times-tamp m2, Jack and John arrive at region D and Erespectively. The second similarity score can also be

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Algorithm 1 The algorithm of calculating twotrajectories’ similarity.Require:

The hierarchical semantic tree, HST ;The set of pair regions of trajectories t1 and t2, PR;

Ensure:The similarity of trajectories t1 and t2, Sim;

1: Sim = 0;2: Num = |PR|;3: for all (Ri, Rj ) ∈ PR do4: LCANode = searchLCA(Ri, Rj , HST );5: SP = ShortestPathLength(Ri, Rj , HST );6: LCALevel = LocatedLevel(LCANode,HST );7: Level1 = LocatedLevel(Ri, HST );8: Level2 = LocatedLevel(Rj , HST );9: W1 = Weight(Ri)

10: W2 = Weight(Rj)11: Inf1 = Infulence(Level1);12: Inf2 = Infulence(Level2);13: Update simPair according to Eq. 6;14: Sim = Sim + simPair;15: end for16: Sim = Sim / Num;17: return Sim;

calculated based on Eq. 6 above. After calculatingthe similarity scores of all pair regions, we set −→s asthe similarity vector to record the similarity score ofeach pair of regions from the two trajectories, denot-ed by −→s = (simPair1, simPair2, ..., simPairn).

ROOT

C

F

D A

level = 1

level = 2

level = 3

level = 4

E B level = 5

Jack

John

Semantic Region Path to Lowest Common

Ancestor

Jack

John

Fig. 8: Calculate the similarity of regions.

Finally, the similarity score of the two trajectories(t1, t2) can be calculated by:

Sim(t1, t2) =1

|−→s |×

n∑i=1

simPairi. (7)

If more than one trajectory exists for an individ-ual, each pair of trajectories between users shouldbe compared. We assume that the set of trajectoriesof Jack is T1, and the set of trajectories of Johnis T2. For each trajectory ti ∈ T1, we calculate atrajectory similarity score of ti and every trajectorytj ∈ T2. Then, an average value of all the known

trajectory similarity scores can be combined toobtain an overall similarity score of two individuals.This score can be used to measure their degree ofcloseness. In order to decide whether there existsocial ties between two individuals, a threshold δsis set. If the score is greater than threshold δs, weconsider that it is more likely to have social tiesbetween them. δs is determined by estimating theF-measure when it achieves optimal value.

V. PERFORMANCE EVALUATION

A. Setup

In this paper, the proposed algorithm is verifiedwith a real-world dataset collected by Gowalla[18],[19]. It is a location-based social networkingwebsite where users share their locations by check-in. The friendship network is undirected and wascollected using their public API. This dataset con-sists of 196,591 nodes and 950,327 edges. A totalnumber of 6,442,890 check-ins from these usershave been collected from February 2009 to October2010.

Wang et. al have found that the similarity betweentwo individuals’ movements strongly correlates withtheir relationship in the social network, and theprobability could reach almost 80% [8]. Thus, weselect some users with high movement similarityfrom the original dataset, and it is considered thatthese users really have social ties. So, we use thedataset of these users as our dataset. We adopt thefollowing procedures to set up our simulation:

• We consider that users’ trajectories with toofew records could not reflect their mobilityroutine. It will be difficult to discover social tiesamong the users with little information. Thus,we ignore users with less than 20 check-ins.

• For all of the retained users, we randomly set kfor each of them to represent individual privacyprotection level (3 6 k 6 10). We select con-secutive check-ins within a defined time inter-val as a trajectory, and only choose trajectorieshaving at least 20 locations. Then, we storeall retained trajectory information, friendshipinformation, and the correspondences betweenusers and k in a local MySQL database.

• For a given trajectory comprised of GPS check-in locations, we transform it to a cloaked tra-jectory. Next, we transform all of the cloakingregions to semantic regions.

• We divide the dataset into two partitions: atraining set containing the previous 75% of

10

consecutive records in each trajectory, and atesting set containing the remaining 25% ofrecords in each trajectory. All of the trajectoriesare processed by the k-anonymity cloakingmethod.

Precision, Recall and F-measure are main mea-surements for the experimental evaluation. Theyare usually used in information retrieval tasks. Ininformation retrieval contexts, precision and recallare defined in terms of a set of retrieved documentsand a set of relevant documents. Precision is thefraction of retrieved instances that are relevant,while recall is the fraction of relevant instances thatare retrieved. F-measure is the harmonic mean ofprecision and recall. In this work, the precision rate,recall rate, and F-measure are redefined by Eqs. 8,9, and 10.

Precision =p+

p+ + p−, (8)

Recall =p+

|R|, (9)

F −measure =2× Precision×Recall

Precision+Recall, (10)

where p+ and p− indicate the number of correct pre-dictions and incorrect predictions of the existenceof social ties, respectively. |R| indicates the totalnumber of social tie records in the social network.

Experiments are divided into two parts: 1) sen-sitivity tests; and 2) performance comparison. Thesensitivity tests evaluate the proposed algorithmunder various parameter settings (i.e., α, β and γ)in Eq. 6. In performance comparison, we mainlyevaluate the performance from three aspects. First,we analyze the performance of our approach with d-ifferent groups of people holding different values ofk. Second, we contrast our model with the KSTCMmodel [16]. The anonymity levels for different usersare varied in our paper. At last, we evaluate theperformance by using semantic trajectories withoutcloaking, and make a comparison with the perfor-mance using cloaked trajectories.

B. Sensitivity TestsThis test aims to evaluate the performance of the

proposed algorithm under different parameter set-tings. In order to investigate the impact of differentfactors, in each step, only one parameter would befine-tuned, while the others remain unchanged.

0.10 0.15 0.20 0.25 0.3030%

35%

40%

45%

50%

55%

Parameter ( )

Recall Precision F-measure

(a) Performance changing with α

0.10 0.15 0.20 0.25 0.3020%

40%

60%

80%

100%

Parameter ( )

Recall Precision F-measure

(b) Performance changing with β

0.10 0.15 0.20 0.25 0.3035%

40%

45%

50%

55%

Parameter ( )

Recall Precision F-measure

(c) Performance changing with γ

Fig. 9: Performance in various parameter settings.

As can be observed from Fig. 9, when α andγ grows, precision improves but recall decreases.Conversely, precision decreases, but recall improveswhen β grows. Meanwhile, it is interesting to findβ gains better impact to influence both precisionand recall, which suggests that the level of thelowest common ancestor node plays an importantrole in determining the performance of our proposedmechanism. Also, it could be concluded that thecontainment relationship among semantic regions isinfluenced in similarity calculation. In our previouswork [17], we consider that all regions have thesame weight values. In this paper, we could observethat the performance improves greatly when theregion popularity is taken into consideration.

In order to explore the best combination of α,β and γ, more experimental results with variousparameter settings are reported. Although, there isno causal relation between precision and recall, theyare regarded as two inter-constraint measures. In thissituation, the best performance would be obtained

11

when F-measure achieves the highest value. This isbecause F-measure takes both precision and recallinto consideration. Precision and recall get closerwhen F-measure increases. From the parameter-setting experiment, we set α = 0.15, β = 0.1, andγ = 0.15 after this experiment, since it achieves thebest performance of F-measure, and precision andrecall are most harmonious. In this situation, our ap-proach could achieves 47.22% in terms of precisionand 49.05% in terms of recall, which reflects theperformance when considering all anonymity levelsof privacy protection.

C. Performance ComparisonsTo validate the performance of our proposed mod-

el, comparisons are conducted with previous works.More specifically, the experiments are divided intothe following steps:

1) We first validate the performance in termsof anonymity levels by grouping all usersaccording to their anonymity level k.

2) The performance is compared between our ap-proach and KSTCM model [16]. We calculateprecision, recall, and F-measure when k is setto 4, 6, 8, and 10.

3) In order to validate the influence of theweights of semantic regions, we comparethe performance with our previous work [17]which does not consider the impact of seman-tic regions’ popularity.

4) In order to evaluate the proposed algorithmunder the condition of ignoring the privacyprotection, we evaluate the performance us-ing purely semantic trajectories without k-anonymity cloaking. In this comparison, wetransform the raw GPS trajectories to seman-tic trajectories directly without cloaking.

4 5 6 7 8 9 1035%

40%

45%

50%

55%

60%

k-value (K)

Precision Recall F-measure

Fig. 10: The influence of k on performance.

Apparently, the size of cloaking regions growswhen k increases. The growing size of cloaking

regions will inevitably lead to an indefinite represen-tation of the region and finally cause a degradationof performance. As illustrated in Fig. 10, precisionand recall deteriorate gradually as k increases, whichimplies that a better performance is available forusers with low privacy requirements.

In KSTCM model [16], the privacy protectionlevel of all the users are the same by default.Comparison of two models is given in Fig. 11.

As can be seen, our approach outperforms K-STCM in terms of precision, recall and F-measure.It demonstrates that our approach using semanticregions is more capable than that using raw cloakingregions. The result implies that semantic regionscould reveal more individuals’ interests and prefer-ences, and individuals usually have closer social tieswhen sharing similar semantic regions or locatingin the less popular regions. Comparison betweenthis model and our previous work [17], which doesnot take the difference of popularity of regions intoaccount, is shown in Fig. 12.

As shown in Fig. 12, the performance improvesalmost 5% when considering the weight of semanticregions based on their popularity. It suggests that thepopularity of regions is helpful to discover socialties, and less popular regions could better representusers’ interests and characteristics better.

Finally, we evaluate our proposed algorithm withsemantic trajectories without cloaking by transform-ing raw GPS trajectories to semantic regions di-rectly. In this way, we compare the performance ofour approach under the situations with and withoutproviding privacy preservation. From Fig. 13, weobserve that there is a significant improvement inprecision rate using accurate semantic trajectoriesrather than cloaked trajectories. It suggests thataccurate locations benefit improving the accuracyof social ties detection. Intuitively, raw GPS loca-tions carry more accurate semantic meanings, whichwould probably make the semantic regions locatein lower levels of the hierarchical semantic tree.From the results, we see that the three metrics donot degrade significantly, considering the challengeof using cloaked trajectories. We validate that ouralgorithm is capable of discovering social ties witha reasonable performance, while preserving locationprivacy effectively.

VI. CONCLUSIONS AND FUTURE WORK

In this paper, we have proposed a novel approachto infer social ties with cloaked trajectories insteadof accurate GPS trajectories for privacy preserving.

12

31.826.3 23.2

19.2

59.44

48.9741.31 39.16

4 6 8 100%

20%

40%

60%

80%

100%Precision

k-value (K)

KSTCM our model

(a) Precision Rate comparison

35.230.2 27.9 25.34

58.1253.42

44.7739.89

4 6 8 100%

20%

40%

60%

80%

100%

Rec

all

k-value (K)

KSTCM our model

(b) Recall Rate comparison

33.827.9 25.8 22.3

58.7751.2

42.97 39.52

4 6 8 100%

20%

40%

60%

80%

100%

F-mea

sure

k-value (K)

KSTCM our model

(c) F-measure comparison

Fig. 11: The comparison of precision, recall, and F-measure under different values of k.

42.7448.71 45.648.22 49.31 48.63

Precision Recall F-measure0%

20%

40%

60%

80%

100%

Indicator

Previous Model Weighted Model

Fig. 12: The performances of our previous modeland the weighted hierarchical semantic tree model.

47.22 49.05 48.12

65.57

49.4155.69

Precision Recall F-measure0%

20%

40%

60%

80%

100%

Indicator

Cloaked trajectories Semantic trajectories

Fig. 13: The performances using cloakedtrajectories and semantic trajectories.

Instead of matching historical locations directly ingeographic space, we presented a novel model totransform cloaking regions to semantic regions, andfurther proposed a weighted hierarchical semantictree model to make the containment relationship vis-ible. The weighted hierarchical semantic tree is thenused to calculate the similarity of the trajectoriesof individuals, and predict the existence of socialties. We have conducted extensive experiments toevaluate the performance of our approach with a realdataset. The evaluation results demonstrated thatour approach could infer social ties and effectively

preserve privacy of users. We have compared ourproposed model with existing work and demonstrat-ed that our approach could achieve much higherperformance in social tie detection.

In the future, we would like to further improvethe accuracy of discovering social ties by clusteringsimilar users based on their semantic patterns. Also,we plan to apply privacy preservation techniquesto new applications that require location privacyprotection, such as in participation sensing.

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Ye Tian (M’15) received the B.S. degree fromNanjing University of Posts and Telecommu-nications (NUPT), Nanjing, China, in 2003,later he received the M.S. and Ph.D. degree incomputer science and technology from BeijingUniversity of Posts and Telecommunications(BUPT), Beijing, China, in 2007 and 2013respectively. He is currently a post-doc inBUPT. He has published over twenty paper.He is the holder of 13 U.S./China patents. His

research interests include social network analysis, text mining andmobile computing.

Wendong Wang (M’02) received the B.S.and M.S. degrees from Beijing University ofPosts and Telecommunications (BUPT), Bei-jing, China, in 1985 and 1991, respective-ly.

He is currently a Full Professor with BUPT.He is currently on the Assessment Panel of theNational Natural Science Foundation Programand the National High Technology Researchand Development Program of China. He has

published more than 200 papers in various journals and conferenceproceedings. He is the holder of 14 U.S./China patents. His cur-rent research interests include next-generation network architecture,Internet-of-Things, participatory sensing, wireless ad hoc, sensor,mesh networks and mobile Internet.

14

Jie Wu (M’89-SM’94-F’09) received the B.S.and M.S. degrees from Shanghai Universityof Science and Technology (currently Shang-hai University), Shanghai, China, in 1982 and1985, respectively, and the Ph.D. degree incomputer engineering from Florida AtlanticUniversity, Boca Raton, FL, USA, in 1989.

He is the Chair of and a Laura H. CarnellProfessor with the Department of Computerand Information Sciences, Temple University,

Philadelphia, PA, USA. Prior to joining Temple University, he wasa Program Director with the National Science Foundation and aDistinguished Professor with Florida Atlantic University, Boca Raton,FL, USA. He has regularly published scholarly journals, conferenceproceedings, and books. His current research interests include mobilecomputing and wireless networks, routing protocols, cloud and greencomputing, network trust and security, and social network applica-tions.

Mr. Wu serves on several editorial boards, including that of theIEEE TRANSACTIONS ON COMPUTERS, the IEEE TRANSAC-TIONS ON SERVICE COMPUTING, and the Journal of Parallel andDistributed Computing. He was the general Cochair/Chair for theIEEE International Conference on Mobile Ad Hoc and Sensor Sys-tems (MASS 2006) and the IEEE International Symposium on Paral-lel and Distributed Processing (IPDPS 2008), the Program Co-chairfor the IEEE International Conference on Computer Communications(INFOCOM 2011), the General Chair for the IEEE InternationalConference on Distributed Computing Systems (ICDCS 2013) andthe Program Chair for the China Computer Federation (CCF) ChinaNational Computer Congress (CNCC 2013). He is currently servingas the General Chair for the Association for ComputingMachinery(ACM) International Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc 2014). He was an IEEE Computer SocietyDistinguished Visitor, an ACM Distinguished Speaker, and the Chairfor the IEEE Technical Committee on Distributed Processing. He isa CCF Distinguished Speaker. He received the 2011 CCF OverseasOutstanding Achievement Award.

Qinli Kou received the B.S. and M.S. degreefrom the State Key Laboratory of Networkingand Switching Technology, Beijing Universi-ty of Posts and Telecommunications (BUPT),Beijing, China, in 2013 and 2016 respective-ly. Her research interests include participatorysensing and social network analysis.

Zheng Song received the Ph.D. degree fromthe State Key Laboratory of Networking andSwitching Technology, Beijing University ofPosts and Telecommunications (BUPT), Bei-jing, China.

Prior to studying at BUPT, he was with theR&D Department of Sina Corporation. He isthe holder of ten U.S. and China patents. Hisresearch interests include participatory sens-ing, indoor localization, and the Internet-of-

Things.

Edith C. -H. Ngai is currently an Asso-ciate Professor in Department of InformationTechnology, Uppsala University, Sweden. Shereceived her Ph.D. from the Department ofComputer Science and Engineering, the Chi-nese University of Hong Kong in 2007. Shedid her post-doc in Department of Electricaland Electronic Engineering, Imperial CollegeLondon, United Kingdom in 2007-2008. Herresearch interests include wireless sensor and

mobile networks, information-centric networking, Internet-of-Thingsand cloud, network security and privacy, e-health and smart cityapplications.

Previously, she has conducted research in VIEW Laboratory,CUHK, Hong Kong; Multimedia and Wireless Networking Group,Simon Fraser University, Vancouver, Canada; Tsinghua NationalLaboratory for Information Science and Technology, Tsinghua U-niversity, Beijing, China; Intelligent and Systems Networks (ISN)Group, Imperial College London, United Kingdom; and Networkedand Embedded Systems Laboratory (NESL), UCLA, USA. She isalso a VINNMER Fellow (2009) awarded by VINNOVA, Sweden.