Temporal Social Network: Group Query Processing

Transcription

1 Temporal Social Network: Grop Qery Processing Xiaoying Chen 1 Chong Zhang 2 Yanli H 3 Bin Ge 4 Weidong Xiao 5 Science and Technology on Information Systems Engineering Laboratory National University of Defense Technology, Changsha , P.R.China and Collaborative Innovation Center of Geospatial Technology, China { 1 chenxiaoying1991, 2 leocheng8286}@yahoo.com 3 smilelife1979@163.com 4 gebin1978@gmail.com 5 wilsonshaw@vip.sina.com Abstract With the development of on-line social networks, more and more sers and sellers are interested in grop analytics which provides insights into common interests with varios relationships. This paper addresses this problem from temporal aspect, i.e., temporal grop qery (TGQ) which gives people the historical view for grop forming and changing. To efficiently achieve or goal, we propose two strctres to index temporal social network (TSN), and then a simple naive searching method is designed to process the TGQ, after that we arge a more efficient approach can be implemented by pdate operations instead of iterative graph generations, which we call optimized method. We condct experiments on real-synthetic dataset, and the reslts show that or indexes and searching algorithms are capable, and optimized method is mch more efficient than the naive one. I. INTRODUCTION De to the increasing poplarity of social networks and vast amont of information in them, there have been many efforts in enhancing web search based on social data. Social networks contain data abot the network, i.e., data abot sers and their social relations, data abot the activities that sers participate in. Besides the graph strctre, another important dimension of social network is dynamic attribte. For instance, logins or logots of a ser represents changes in the sers on-line stats. Also, new content is added throgh ser activities (sch as posting text, photo) representing respective changes in the sers interests. This temporal aspect of information in social network wold inflence social network qery either explicitly by enabling sers to qery for particlar time points or periods, or implicitly by providing the fresher reslts, e.g., find some sers who are active dring a certain period, or find some activities posted at some time. Sch qeries add temporal axis to ser reqirement, we call it temporal social network qery. In or previos work, we introdced temporal social network, and address three qery types, namely Friends of Interesting Activities (FIA) qery, Users of Time Filter (UTF) qery and Grop of Users with Relationship Dration (GURD) qery. In GURD qery, it aims to find a set of grops, where the nmber of sers in each grop is eqal to a given nmber, and average intimate degree which is measred by average relationship dration of it satisfies a given vale, and all the members of it have taken part in some given activities. In this This work is spported by NSF of China grant and paper, we arge that GURD is not sfficient for analyzing the changes of grops, which is an essential modle for temporal social networks analytics. Ths, we intend to extend GURD qery to a more generalized and applicable one to adapt more temporal qeries in real world. Here, we call it Temporal Grop Qery (TGQ). TGQ is essential, for instance, when the system analyst wold like to observe and analyze the formation and changes of grops, historically. For example, they aim to find a set of grops, each grop with all member participating in the activity labeled with presidential election dring last two weeks, and average on-line dration is not less than 24 hors dring last two weeks. The reslt of this qery shold be appropriately in the form: {< g 1 ={ 1, 2,... }, t 1, t 2 >, <... >,...}, where g 1 is a satisfying grop valid dring [t 1, t 2 ]. For efficiently answer TGQ qery, we design two indexes, one is called Temporal Activity tree (TA-tree) indexing participating time and keywords activity, the other is Temporal Friendship tree (TF-tree) indexing versions of relationships. We first devise an approach naively iterate each relationship changing time point, and constrct the satisfying grop. However, we arge that the naive method is not efficient, ths we design a more efficient algorithm to accelerate the processing, in particlar, it is a series pdate operations to an initial graphs and check which pdated graph is satisfied. De to less time for constrcting connected graph, it is more efficient than the naive one. In this paper, we make the following contribtions: We propose a more applicable qery type, temporal grop qery, to answer grop qery in temporal social network. We design two approaches to process TGQ, one is naive iterative, the other is an optimized one. We condct experiments on real-synthetic hybrid dataset, and reslts show or method is efficient. The rest of this paper is organized as follows. Related works are srveyed in section 2. Problem is formally defined in section 3. In section 4, two index TA-tree and TF-tree are presented, followed by qery processing in section 5. In section 6, we carry ot or experiments. Finally, section 7 concldes the paper with directions for ftre works.

2 II. RELATED WORKS Some of the relevant works of temporal social network stdy focs on efficient algorithms and data strctre for searching data. And some others propose some typical kinds of temporalsocial qery that can be applied to life application. We have proposed three kinds of qeries, namely FIA, UTF and GURD qery in [1]. GURD qery is a kind of temporal grop qery, which aims to find a set of grops, where the nmber of sers in each grop is eqal to a given nmber, and average intimate degree of it satisfies a given vale, and all the members of it have taken part in some given activities. We propose two index strctres, TUR-tree and TUA-tree for accelerating qery process. Algorithms of qery processing for the three qeries are finally proposed. There are many other works introdce many kinds of grop qeries, sch as [2], [3], [4]. Social-Temporal Grop Qery (STGQ) [2], which considers the available time of candidate attendees and their social relation, aims to find activity time and attendees with minimm total distance to the initiator. However, in STSG, the time dimension is only considered as available time for attendees, which can be dealt with after Social-Grop Qery (SGQ). In the other hand, adding the spatial dimension into social network wold bring abot different grop qeries. Socio- Spatial Grop Qery (SSGQ) [3] finds a grop of attendees close to rally point and ensre that the selected attendees have a good social relationship to create a good atmosphere in the activity. There are many similar qeries, for example, Circle of Friends (CoF) [4] finds a grop of friends whose members are close to each other both socially and geographically. These two qery problem are both NP-hard (becase social restrictions diverse), bt withot time dimension. As there are many kinds of temporal social network qeries, it is impossible to stdy all of them. So Kostas Stefanidis et.al.[5] define a logical algebra that provides a set of operators reqired for temporal social network qery evalation. However, this work only provides a logical algebra withot any storage model and qery processing detail which is the important factor to the effectiveness of this framework. As we have introdced above, there are few previos stdies consider the efficient qery processing in temporal social grop qery in historical view. III. PROBLEM DEFINITIONS Given an ndirected graph G=(V, E), V =U A. Each vertex i in U represents a ser in the commnity and is associated with a time interval [t s, t e ), meaning the valid period dring which i exists (or being logon stats) in commnity, and [t s, ) means i is still in the commnity now. For a given social network graph G, there is also a set A V, in this paper, we se term activity to denote social event in the social network, e.g., pblishing a post, sharing a link and etc. Withot loss generality, each activity can be represented as < aid, W a >, where aid is the activity identifier, W a is a keyword set to describe the activity. Each edge (v i, v j ) in E has two forms: ( i, j ) and ( i, a j ). ( i, j ) represents a friend relationship between ser i and j, and it is also associated with a time interval [et s, et e ), in which et s means the time when the relationship is established and et e means the time when the relationship is removed. Each i in G can connect to an activity a k in A, which means that i gets involved in a k, formed as ( i, a k ). We se term participation to describe relationship between ser and activity, e.g., in social network, ser may post some texts, or forward other s post, or share a link of web page, or comment other s activity, or add some activity into favorite, in general, we call these actions as participations. (t 10, *) 10 (t 2, *) (t 1, *) 2 1 (et 1, et 3) 3 (et 3, *) t 1 (et 2, *) t 6 (et 4, *) (t 3, t 5) 5 (t 5, *) t 2 t 4 4 t 3 W 2 a 2 (t 4, *) a 1 W 1 t (et 5, *) (et 6, *) 6 (t 9, *) (t 7, *) (t 6, t 9) Fig. 1. Temporal Social Network Example Figre 1 illstrates a temporal social network, where sers and activities are plotted as dots and triangles, respectively. The relationship are divided into two categories: ser-to-ser (solid line) and ser-to-activity (dashed line). And the label on edge indicates time interval of relationship or time stamp when a ser participate in an activity. For instance, ser 1 logins commnity at time t 1 and does not logot at crrent, and ser 1 and 2 become friends at et 1 and nfriend each other at et 3, and 4, 7 and 2 participate in a 2 at t 4, t 5 and t 6, respectively. Then we formally give definition of TGQ, a TGQ (W, [t s, t e ], t ol ) aims to find a set of grops, in which, each grop is a connected graph, and all members have participated in the activities with keywords in W dring period [t s, t e ], and the average on-line dration (AOD) (dring [t s, t e ]) of the members is not less t ol. Here on-line dration (AOD) is defined as: n i=1 AOD = onlinedration( i) (1) n where n is the cardinality of the grop, onlinedration( i ) calclates on-line dration of ser i. IV. INDEXES DESIGN AND FUNCTIONS We believe that for a TGQ (W, [t s, t e ], t ol ), two kinds of temporal predicates shold be taken into consideration of bilding indexes. One is the temporal predicate [t s, t e ] for participation time, and the other is friendship valid period predicate for generating grops with valid period. Ths, we design two indexes to accelerate qery processing. One index is for finding which sers participating in the activities with keywords in W dring [t s, t e ], and the other one aims to

3 process the qery given a time period, find pairs of sers who are friends dring the period. The first index we call it Temporal Activity tree (TA-tree), which is actally a B + -tree injected with Bloom Filter[6]. In particlar, the data item (entry in leaf node) to be indexed is in the form < i, t p, a k,w ak >, where i is a ser identifier, t p represents the time ser i participates in activity a k, and W ak is the keyword set describing a k. B + -tree is bilt according to the key t p, and the keyword sets of all entries in each leaf node constitte a Bloom Filter BF, and BF serves as filter with pointers in internal nodes. Figre 2 illstrates an example of TA-tree. We se a qerying fnction to represent retrieval fnction of TA-tree, R=T ARetrv([t s, t e ], W ), which means to find ser set R participating in the activities with keywords in W dring [t s, t e ]. BF5 BF1 t 2 BF2 t 3 BF3 t 5 BF4 t 3 1,t 1,a 1, 2,t 2,a 2, 3,t 3,a 3, 4,t 4,a 4, 5,t 5,a 5, 6,t 6,a 6, 7,t 7,a 7, W 1 W 2 W 3 W 4 W 5 W 6 W 7 Fig. 2. TA-Tree Example The second index is Temporal Friendship tree (TF-tree), which is a kind of MVB-tree[7], indexing the temporal friend relationship. In particlar, data item to be indexed is in the form < i j, [t f, t ]>, where i j is concatenation of a pair of friends serving as the search key, and [t f, t ] is the valid friendship period of i and j. Ths, TF-tree s fnction is to find which pairs of sers are valid friends dring the given time period, and the retrieval fnction can be represented as R=T F Retrv([t f, t ]), which means to retrieve pairs of friends associated with corresponding valid time period dring [t f, t ]. BF6 V. QUERY PROCESSING In this section, we handle the qery processing for TGQ. First we propose a straightforward approach, after that, we optimize it to improve the efficiency. A. Searching For a TGQ (W, [t s, t e ], t ol ), the basic workflow is as following: firstly, TA-tree is sed to retrieve the ser set (say U c ) participating in the activities containing the keyword set W dring [t s, t e ], then for each candidate ser i in U c, sm of on-line dration dring [t s, t e ] is calclated. Then, the difficlty lies in how to retrn the satisfied grop with valid time period. Throgh observation, we get that the grop s valid period depends on each relationship s changing time, e.g., a temporal interval for a relationship is [t f, t ], which wold contribte the valid period of the grop. Ths we can se TFtree to retrieve all pairs of friends dring [t s, t e ], say F c, and we can generate pairs of friends in U c associated with valid time period by intersecting U c and F c, after that, for each time point when friendship change happens in U c, we calclate the satisfied snapshots of grops (i.e., connected graph), and then form the reslts. For accelerating the processing, we se a max-qee storing sers in U c sorted by on-line dration, ths we can terminate the loop as early as possible. In particlar, on each time point t i, we calclate a set of snapshot connected graph whose AOD is larger than or eqal to t ol, i.e., top element top of the maxqee is popped and checked whether on-line dration is not less than t ol, if so, that is to say it is possible for finding a satisfied connected graph containing top, then a connected graph G ti on time t is generated, and check whether AOD of G ti is larger than or eqal to t ol, if so, G ti is a reslt, after that, all sers in G ti are removed from the qee, and next top element is popped and the similar processing is contined. Otherwise, i.e., on-line dration of top is less than t ol, which means it is impossible to find a satisfied connected graph for the elements following top, so the loop for the qee is terminated and processing is moved to the next time point. Algorithm 1 presents the psedo-code of naive searching. Algorithm 1 Searching Inpt: q=(w, [t s, t e], t ol ) Otpt: Rlist 1: U c=t ARetrv([t s, t e], W ) 2: Q=generateQee(U c) 3: F c=t F Retrv([t s, t e]) 4: T P =extractt imep oints(f c, U c) 5: for each tp T P do 6: replq=q 7: while replq φ do 8: =deqee(replq) 9: if.od t ol then 10: CQ=geneCQ(, tp) 11: if AOD(CQ) t ol then 12: Rlist (CQ, tp) 13: end if 14: else 15: break 16: end if 17: end while 18: end for 19: retrn Rlist For example, after retrieving the sers that satisfied the keywords and time constristant, U c ={ 1, 2,..., 15 } is fond, and t ol =300. The relationships between these sers, F c is showed in Figre 3 with time interval tags. Meanwhile, a timeline containing t i, and the sm of on-line dration of each i is also showed in this figre [20.*) [0,1100) 7 [10.*) [400,*) [0,*) [200,*) [0,800) [0,*) [400,800) Fig. 3. Example of TGQ

4 As shown in Figre [20.*) 4, on time 2 t 1 =300, top = 6 (show [0,1100) in bold), we form a connected 7 [10.*) graph for , and then check that AOD=382>300, so we add it 14 to 13 the 270 reslt list. And then { 6, 3, [400,*) 10, 15, 13 } are removed. 4 top changes to 9, 13 we simply form a a connected graph for 9, and check that AOD=291.7<300, 15 this reslt does not satisfy. Until the 11 top = 2, the on-line dration of 2 =300, is not less than t ol. So the processing [0,*) [200,*) [0,800) is jmped 10 to the [0,*) next time 10 point 10 t 2 =400. De to space limitations [400,800) we do not show 9 the processing 14 5 at time 500 and Avg=382>300 g 1={ 6, 3, 10, 15, 13} Avg=261.6<300 Fig Avg=291.7<300 T= Avg=291.7< Searching T=500Example B Processing We optimize the naive searching in this section, throgh 14 5 observation, we can see 10 that, it is not necessary to constrct connected 3 graphs at each time 9 point. On the contrary, all the connected 10 graphs can be constrcted Avg=271.6<300 Avg=197.5<300 initially, and at each time point, according to the changes of relationship, we pdate T=800 the corresponding graph and make jdgment whether it is a satisfied 9 450grop. In particlar, we arge that the 13 key 270 techniqes lie in the pdate operations to connected graphs. On each time point, 13 there are one or more operations to previos connected graphs, 3 170and we distingish 10 the following 11 cases: (1) 5 Addition 130 of relationship between nodes both in a connected Avg=331.6>300 Avg=197.5< graph cg. For this case, no jdgment need to make, i.e., g the reslts are 1={the 6, 3,same 10, 15, 9, with 8} the previos step. (2) Addition of relationship between a node in a connected graph and an isolating node inode. For sch a case, a new connected graph containing inode is generated, which shold be inspected whether it is a satisfied grop, i.e., whether average on-line dration is not less the given vale. (3) Addition of relationship between two isolating nodes. For sch a case, a new connected graph is formed, the processing is the same with case (2). (4) Addition of relationship between one node in a connected graph and the other node in another connected graph. For sch a case, a new connected graph is formed, the processing is the same with case (2). (5) Removal of relationship between two nodes, reslting no split in a connected graph. For this case, no jdgment need to make, and reslts are nchanged. (6) Removal of relationship between two nodes, reslting a connected graph split. For this case, the two emerging connected graphs shold both be inspected whether they are still satisfied grops. Unlike the naive searching, the optimized processing only consider the changes of relationship in the graph, also take Figre 3 as an example, the processing is shown in Figre 5. Firstly, we form connected graphs at t 1 =300. Then at t 2 =400, the changes of relationship are addition of relationship { 4, 13 } (case 2) and { 3, 10 } (case 1). Adding the relationship { 3, 10 } in case 1 have no effect on the previos step, while adding the relationship { 4, 13 }, a new connected graph is formed. In this case, a new member 4 (on-line dration is 160) is added to G t1 in time 300 which reslts to AOD changing and G t1 is no longer the satisfied reslt. At t 3 =500, the changes of relationship are establishment relationship { 1, 14 } (case 3) and { 9, 10 } (case 4). At t 4 =800, the changes of relationship are removal of relationship { 3, 10 } (case 5) and { 13, 15 }, { 9, 11 } (case 6). VI. EXPERIMENTAL EVALUATION We implement the indexes and processing algorithms, and experimentally evalate them on a synthetic-real-hybrid dataset. De to the fact that there is no real dataset containing temporal information on on-line stats, relationship and activity participation. Ths we have to synthetically generate dataset based on some real datasets which contain partial temporal attribtes. Table I lists some properties of these datasets. Datasets U sers is generated according to the case of YoTbe, which owing 3,223,589 sers. Then according to birthday information of Users, we randomly prodced the login time list of each ser, which forms the login dataset. Datasets Relation is prodced based on the real dataset 1, which contains 9,375,374 pairs of relation of YoTbe. For the dataset of Activity, firstly, we download the dataset abot food theme on GCZX server, formed in xml file of 25 classes of Amazon commodities, 1759 review on the hotel and some web crawling data, etc. Secondly, we extract the sefl text as part of the text of activity, and randomly generated sers who involved in this activity and the time participate in the activities. TABLE I DATASET DESCRIPTION Dataset Record nmber Data size User 3,223, M Relation 9,375, G Login 3,223, G Activity 6,980, G We implement or algorithms in Java. To make comparison, the naive searching approach is sed as a baseline. We vary the qery parameters and at each testing point, 10 qeries are issed to collect the average reslts. The experiments are condcted on a DELL server with Intel(R) Xeon(R) 2.40GHz 1

5 [0,*) [200,*) [0,800) [0,*) [400,800) Avg= Avg=382 Avg= g1={6,3,10,15,13} 9 5 Avg= T=400 +(4,13) +(3,10) Avg=190 Avg= Avg= Avg= T=500 +(1,14) +(9,10) Avg= Avg=190 5 Avg= T=800 -(13,15) -(3,10) -(9,11) 2 Avg= Avg= g1={6,3,10,15,9,8} 11 Fig. 5. Processing Example processor, 8GB memory and 500GB disk. Table II describes the qery parameters. TABLE II PARAMETERS IN EXPERIMENT qeries parameters domain defalt TGQ t ol W q s cardinality length [ts,te] /temporal extent 0.1%-3% 1% Firstly, we vary t ol to compare the performances of two algorithms. We increase t ol from 1 to 5, while the response time of qery decreases (see Figre 6(a)), this is de to or terminating condition, i.e., a larger t ol will terminate loop earlier, ths the processing delay is redced. For the detail, we can see the effectiveness of or optimization, i.e., the optimized approach tilizes the pdates to the graphs, which redces the simple repeated grop forming procedre, ths it cost less time to retrieve the reslts. Next, we increase the nmber of qerying keywords to test performances. We can see from Figre 6(b), the response time also increases with the nmber of keywords. This can be explained that a larger nmber of keywords wold involve more tree nodes in the TA-tree to be traversed, ths more time wold be cost. Similarly, the optimized approach otperforms the naive searching. Figre 6(c) illstrates the reslts of varying parameter time selectivity, a larger vale cases more candidates to be inspected, ths the response time increases correspondingly. And still, the reslts show that a series of pdate operations is more efficient than exhasted method. VII. CONCLUSION With applications continosly developing, more and more temporal social network grop qeries will be paid attention. In this paper, we focs on temporal analytics on social grop qery, and arge Temporal Grop Qery (TGQ) is sefl and applicable. To efficiently address the qery, we design two indexing strctres to accelerate the qery processing, and two processing algorithms, one is simple, the other is optimized, to accomplish the processing. We condct experiments on realsynthetic hybrid dataset, and the reslts show or methods are capable and optimized method is efficient. In the ftre, we wold like to stdy on social grop qery with geographic attribtes Average On-line Dration (a) Effect of t ol Nmber of Keywords (b) Effect of keywords Fig. 6. Experimental Reslts 5000 ACKNOWLEDGMENT Time Selectivity(%) (c) Effect of time selectivity This work is spported by NSF of China grant and We wold like to thank Prof. Dai and Dr. H for helping with the proof. REFERENCES [1] X. Chen, C. Zhang, B. Ge, and W. Xiao, Temporal social network: Storage, indexing and qery processing, EDBT, [2] D. N. Yang, Y. L. Chen, W. C. Lee, and M. S. Chen, On socialtemporal grop qery with acqaintance constraint, Proceedings of the Vldb Endowment, vol. 4, no. 6, [3] D. N. Yang, C. Y. Shen, W. C. Lee, and M. S. Chen, On socio-spatial grop qery for location-based social networks, in Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining, 2012, pp [4] W. Li, W. Sn, C. Chen, Y. Hang, Y. Jing, and K. Chen, Circle of friend qery in geo-social networks, in International Conference on Database Systems for Advanced Applications, 2012, pp [5] K. Stefanidis and G. Koloniari, Enabling social search in time throgh graphs, in Proceedings of the 5th International Workshop on Web-scale Knowledge Representation Retrieval & Reasoning, 2014, pp [6] I. De Felipe, V. Hristidis, and N. Rishe, Keyword search on spatial databases, in Data Engineering, ICDE IEEE 24th International Conference on. IEEE, 2008, pp [7] B. Becker, S. Gschwind, T. Ohler, B. Seeger, and P. Widmayer, An asymptotically optimal mltiversion b-tree, The VLDB JornalThe International Jornal on Very Large Data Bases, vol. 5, no. 4, pp , 1996.