Using Crowdsourced Data in Location-based Social Networks to Explore Influence Maximization Ji Li 1 Zhipeng Cai 1 Mingyuan Yan 2 Yingshu Li 1 1 Department of Computer Science, Georgia State University 2 Department of Computer Science and Information Systems, University of North Georgia IEEE INFOCOM 2016 1 / 48
Introduction Online social networks become a hot research topic One of the most important research issues is the influence maximization problem Many existing works: only the influence propagation in the online social network is considered Related Works The influence can also propagate in the physical world 2 / 48
Introduction Contribution Propose a network model and an influence propagation model Influence propagation in Online social network Physical world Propose an event activation position selection problem Designed a heuristic algorithm for position selection problem 3 / 48
Network Model Two-layer graph G t = (V, E f, Ep) t V : set of n users deployed in [0, 1) 2 E f : friendship in the online social network, remains the same Ep: t neighbour in the physical world at time t, changes over time Influence propagation An event is activated in the physical world, users around the activation position may be influenced The influence propagates in both online social networks and the physical world simultaneously 4 / 48
Network Model Online Social Network 1 3 6 5 2 4 7 7 5 2 1 3 6 4 Physical World u5 / IR 1, u5 may still be influenced since u3, u6 are u5 s friends and u3, u6 IR (u1, u7) / Ef,influence may propagate u1 u7 since (u1, u7) Ep t1 1 IR: influencing region 5 / 48
Measurements Datasets Two actual datasets named Brightkite and Gowalla Dataset origin: Stanford Large Network Dataset Collection [1] Findings Users positions in the physical world have high stability Influence of different users in an online social network varies a lot Convenient to propagate influence in the physical world High interdependency of geographical positions for friends in the online social networks Dataset details Measurement results 6 / 48
Influence Propagation Model Basic Influence Propagation Model E.t 0 E.t 0 + E.t init pro E.t 0 + E.t init pro + E.t add pro Initial propagation period Additional propagation period Initial propagation period: users around the activation position may be influenced Additional propagation period: influence propagates in online social networks and the physical world 7 / 48
Influence Propagation Model Initial Influence Propagation Physical World Influenced User Uninfluenced User In initial propagation period, users in the influencing region may be influenced Influencing probability: p(e, v, init inf) Details 8 / 48
Influence Propagation Model Influence Propagation in Online Social Networks Online Social Network Influenced User Newly Influenced User Uninfluenced User A influenced user v shares the event E with its friends with probability p(v, osn share) v s friend u be influenced with probability p(e, u, osn inf) Details 9 / 48
Influence Propagation Model Influence Propagation in the Physical World Physical World Influenced User Newly Influenced User Uninfluenced User Influenced user v propagates E with probability p(v, pw share) v will choose neighbours to share event E Neighbour u be influenced with probability p(e, u, phy inf) Details 10 / 48
Influence Propagation Model Cross Propagation Online social networks physical world User u Online Social Network user v User v P hysical W orld user w Physical world online social networks User u P hysical W orld user v User v Online Social Network user w 11 / 48
Optimal Event Activation Position Selection Problem Definition Problem Description A candidate position set C Select pos C to activate event E so that its influence can be maximized Other parameters of E are fixed Formalized Definition F (pos): number of influenced users if activate event E in pos Input: candidate position set C, event E, graph G t = (V, E f, E t p) Output: arg max pos C F (pos) 12 / 48
Optimal Event Activation Position Selection Heuristic Algorithm N s and N i : predefined constant P = randomly selected N s positions in C Iterate for N i times Replace pos 1 P with a new position pos 2 if F (pos 2 ) > F (pos 1 ) Return arg max pos P F (pos) F -based algorithm Details Algorithm code New position selection Why not other algorithms? 13 / 48
Experimental Results Distribution of Influenced Users 1200 1600 number of influenced users 1000 800 600 400 200 initial only initial and OSN initial and OSN and PW number of influenced users 1400 1200 1000 800 600 400 200 initial only initial and OSN initial and OSN and PW 0 0.2 0.3 0.4 influence probability 0 0.2 0.3 0.4 influence probability (a) Brightkite (b) Gowalla Figure 1: Comparison of different propagation models Parameters and candidate position sets Omitted results 14 / 48
Experimental Results Distribution of Influenced Users 60 70 55 50 Initial OSN PW 60 Initial OSN PW percentage 45 40 35 30 percentage 50 40 30 25 20 20 15 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 additional propagation time (a) Brightkite 10 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 additional propagation time (b) Gowalla Figure 2: Comparison of different influence manners 15 / 48
Experimental Results The Optimal Activation Position Selection Algorithm execution time (ms) 7000 6000 5000 4000 3000 2000 1000 F F number of influenced users 600 500 400 300 200 100 F F 0 Brightkite Gowalla different datasets (a) execution time 0 Brightkite Gowalla different datasets (b) number of influenced users Figure 3: Comparison between F -based and F -based heuristic algorithms 16 / 48
Conclusion Propose a new network model A new event influence propagation model is proposed based on the measurement results of two actual datasets An event activation position selection problem is defined A heuristic algorithm for the position selection problem is designed 17 / 48
Questions and Answers 18 / 48
Thank you very much 19 / 48
Appendix 20 / 48
Appendix: Measurements Introduction to the Datasets Basics Record formatte: (user-id, login-time, latitude, longitude, location-id) Use the random way point model to estimate users positions [7] Investigated login records period Brightkite: April 2008 through October 2010 Gowalla: December 2009 through October 2010 21 / 48
Appendix: Measurements Introduction to the Datasets Standardization Users positions in the physical world [0, 1) 2 Time stamps for the logins [0, 1) Data selection To make sure the users movements are correctly detected, we employ part of the original Brightkite and Gowalla datasets The users are distributed in 400km 400km rectangle regions These regions include New York, Washington and Philadelphia where users are densely distributed 22 / 48
Appendix: Measurements Introduction to the Datasets property Brightkite Gowalla # users 3551 5231 # edges 9317 10134 average degree 5.248 3.875 # CC 569 1778 # nodes in largest CC 2907 3114 # logins 430657 297104 average login 121.278 56.797 # triangles 6738 11580 average CC size 6.241 2.942 # edges in largest CC 9228 9676 Table 1: Dataset Details Return 23 / 48
Appendix: Measurements Users Positions and Number of Friends 0.7 0.8 0.6 0.7 distance 0.5 0.4 0.3 0.2 distance 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0 0 20 40 60 80 100 percentage of distances (a) Brightkite 0 0 20 40 60 80 100 percentage of distances (b) Gowalla Figure 4: The distribution of distances 24 / 48
Appendix: Measurements Users Positions and Number of Friends 45 40 number of friends 40 35 30 25 20 15 10 5 number of friends 35 30 25 20 15 10 5 0 0 20 40 60 80 100 percentage of users (a) Brightkite 0 0 20 40 60 80 100 percentage of users (b) Gowalla Figure 5: The distribution of numbers of friends 25 / 48
Appendix: Measurements Users Positions and Number of Friends 120 300 100 250 number of users 80 60 40 number of users 200 150 100 20 50 0 1 2 3 4 5 6 7 8 9 10 distance x 10 3 0 1 2 3 4 5 6 7 8 9 10 distance x 10 3 (a) Brightkite (b) Gowalla Figure 6: The distribution of number of neighbors 26 / 48
Appendix: Measurements Positions and Friendships 40 60 35 friend non friend 50 friend non friend 30 percentage 25 20 15 10 5 percentage 40 30 20 10 0 r=0.001 r=0.002 r=0.003 different distances 0 r=0.001 r=0.002 r=0.003 different distances (a) Brightkite (b) Gowalla Figure 7: The percentage of users within a given distance 27 / 48
Appendix: Measurements Positions and Friendships 0.9 0.8 0.8 0.7 friend non friend 0.7 0.6 non friend friend distance 0.6 0.5 0.4 0.3 distance 0.5 0.4 0.3 0.2 0.2 0.1 0.1 0 0 20 40 60 80 100 percentage of distances (a) Brightkite 0 0 20 40 60 80 100 percentage of distances (b) Gowalla Figure 8: The distribution of minimum distances 28 / 48
Appendix: Measurements Positions and Friendships 10 0 10 0 10 1 non friend friend 10 1 non friend friend similarity 10 2 10 3 similarity 10 2 10 4 10 3 10 5 40 50 60 70 80 90 100 percentage of distances 10 4 30 40 50 60 70 80 90 100 percentage of distances (a) Brightkite (b) Gowalla Figure 9: The distribution of trajectory similarities Return 29 / 48
Appendix: Influence Propagation Model Initial Influence Propagation p(e, v, init inf) = min(p 1 I 1 (E, v)i 2 (E, v), 1) I 1 (E, v) = I(J(E.type, v.interest), I max1 ) I(x, I max ) = (I max 1) 1 (1 x) 2 + 1 J(E.type, v.interest) = p 1 : base influence probability E.type v.interest E.type v.interest T (E, v) I 2 (E, v) = I(, I max2 ) E.t init pro I max1 & I max2 : upper bound of increase T (E, v): time v stays in the influencing region Return 30 / 48
Appendix: Influence Propagation Model Influence Propagation in Online Social Networks p(v, osn share) = min(p 2 I 1 (E, v), 1) p(e, u, osn inf) = min(p 3 I 1 (E, u)i 3 (u, t), 1) I 3 (u, t) = I(min( n r(e, u, t) 1 n max, 1), I max3 ) p 2 / p 3 : base sharing/influencing probability I max3 : upper bound of increase n r (E, u, t): the number of descriptions of event E received by user u at time t n max : predefined constant Return 31 / 48
Appendix: Influence Propagation Model Influence Propagation in the Physical World p(v, pw share) = min(p 4 I 1 (E, v), 1) p(e, u, phy inf) = min(p 5 I 1 (E, u)i 4 (v, u), 1) { c if (v, u) Ef I 4 (v, u) = 1 otherwise p 4 / p 5 : base sharing/influencing probability v.share phy: set of different time instances for v to share E in the physical world c: predefined constant which satisfies c > 1 The roulette wheel method[8] is used to decide which neighbour to be chosen and I 4 (v, u) is used to calculate the weight Return 32 / 48
Appendix: Optimal Event Activation Position Selection Option 1 Idea: select the position with most users Problem: little interdependency between The number of influenced users The number of users in the initial influencing region Option 2 Idea: existing algorithm+influence propagation in the physical world Problem: distributions of top influencing users may be dispersive 33 / 48
Appendix: Optimal Event Activation Position Selection Option 3 Idea: use the monotonicity of function F (pos) Problem: values of function F (pos) may distribute highly irregularly Option 4 Idea: test each position in C Problem: does not work if C is an infinite set 34 / 48
Appendix: Optimal Event Activation Position Selection 700 700 number of influenced users 600 500 400 300 200 number of influenced users 600 500 400 300 200 100 0 5 10 15 20 25 30 35 40 45 number of users in the initial influencing radius 100 0 10 20 30 40 50 number of users in the initial influencing radius (a) Brightkite (b) Gowalla Figure 10: The number of influenced users vs. the number of users in the initial influencing region. 35 / 48
Appendix: Optimal Event Activation Position Selection 0.9 0.9 y 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 y 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x (a) Brightkite 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x (b) Gowalla Figure 11: User distribution 36 / 48
Appendix: Optimal Event Activation Position Selection number of influenced users 140 120 100 80 60 40 20 0 0.56 0.54 0.52 0.5 0.48 y 0.46 0.44 0.52 0.5 0.6 0.58 0.56 0.54 x number of influenced users 300 250 200 150 100 50 0 0.7 0.68 0.66 0.64 y 0.62 0.6 0.7 0.8 0.78 0.76 0.74 0.72 x (a) Brightkite (b) Gowalla Figure 12: Function F (pos) s values Return 37 / 48
Appendix: Optimal Event Activation Position Selection N c [pos 1 ] records how many times pos 1 is selected init and α (α > 1) are predefined constants Calculate the upper bound of dis(pos 1, pos 2 ) by = init α Nc[pos 1 ] Randomly select pos 2 {pos C dis(pos, pos 1 ) } Return 38 / 48
Optimal Event Activation Position Selection Heuristic Algorithm Problem: high computation cost Reason: complexity of the influence propagation model Solution: use another objective function F F -based heuristic algorithm: use F as the objective to evaluate the event activation position 39 / 48
Appendix: Optimal Event Activation Position Selection F (pos) = u U u.f riends + v Neg(u,t) v.friends Neg(u, t) t a randomly selected time instance in [E.t 0 + E.t init pro, E.t 0 + E.t init pro + E.t add pro ) v.friends the set of user v s friends in the online social network pos.x / pos.y the x-coordinate / y-coordinate of position pos Neg(u, t) u s neighbors in the physical world at time t U Users in the influencing region Table 2: Symbols in Function F Return 40 / 48
Appendix: Optimal Event Activation Position Selection Algorithm 1 Optimal Activation Position Selection Algorithm Input: candidate position set C, event E, graph G t = (V, E f, Ep) t Output: position to activate event E for i = 1 to N s do P [i]= randomly selected element in C, N c [i] = 0; end for for i = 1 to N i do find the minimum j satisfying j k=1 F (P [k]) Ns > rand; k=1 F (P [k]) randomly select pos {pos C dis(pos, P [j]) init α Nc[j] }; replace P [j] with pos if F (pos ) > F (P [j]); N c [j]++; end for return arg max pos P F (pos); Return 41 / 48
Appendix: Experimental Results parameter value parameter value parameter value E.r 0 0.01 E.t 0 0.5 E.t init pro 0.02 E.t add pro 0.2 I max1 3 I max2 1.5 I max3 6 r p 0.01 c 5 n max 10 α 2 0.1 N s 10 N i 10 Table 3: Parameters for the Experiments dataset candidate position set Brightkite {(x, y) 0.5 x 0.6, 0.45 y 0.55} Gowalla {(x, y) 0.7 x 0.8, 0.6 y 0.7} Table 4: Candidate Position Set Return 42 / 48
Appendix: Experimental Results Number of Influenced Users number of influenced users 1400 1200 1000 800 600 400 200 0.04 0.03 0.4 0.5 number of influenced users 2000 1500 1000 500 0.04 0.03 0.4 0.5 0.02 0.3 0.02 0.3 initial propagation time 0.01 0.2 influence probability initial propagation time 0.01 0.2 influence probability (a) Brightkite (b) Gowalla Figure 13: The number of influenced users for different initial propagation time 43 / 48
Appendix: Experimental Results Number of Influenced Users number of influenced users 1400 1200 1000 800 600 400 200 0.5 0.4 0.3 additional propagation time 0.2 0.1 0.2 (a) Brightkite 0.3 0.4 0.5 influence probability 3000 2500 2000 1500 1000 500 0.5 0 0.4 0.3 0.2 0.1 0.2 additional propagation time number of influenced users (b) Gowalla 0.5 0.4 0.3 influence probability Figure 14: The number of influenced users for different additional propagation time 44 / 48
Appendix: Experimental Results Appendix: Number of Influenced Users number of influenced users 1500 1000 500 0 0.01 0.008 0.006 0.004 0.002 initial influence region 0 0.2 0.3 0.4 0.5 number of influenced users 2000 1500 1000 500 0 0.01 0.005 influence probability initial influence region 0 0.2 0.5 0.4 0.3 influence probability (a) Brightkite (b) Gowalla Figure 15: The number of influenced users for different initial influence radius Return 45 / 48
Appendix: Related Works [2] and [3] propose multiple influence maximization algorithms for LBSNs [4] uses the Brightkite and Gowalla datasets to study friendships in online social networks and users movements in the physical world [5] proposes a friendship prediction approach by fusing the topology and geographical features in LBSNs [6] studies the impact of social relations hidden in LBSNs Return 46 / 48
Appendix: References I [1] J. Leskovec and A. Krevl, Snap datasets: Stanford large network dataset collection, Jun. 2014. [2] Y.-T. Wen, P.-R. Lei, W.-C. Peng, and X.-F. Zhou, Exploring social influence on location-based social networks, in IEEE ICDM, 2014, pp. 1043 1048. [3] T. Zhou, J. Cao, B. Liu, S. Xu, Z. Zhu, and J. Luo, Location-based influence maximization in social networks, in ACM CIKM, 2015, pp. 1211 1220. [4] E. Cho, S. A. Myers, and J. Leskovec, Friendship and mobility: user movement in location-based social networks, in ACM SIGKDD, 2011, pp. 1082 1090. [5] H. Luo, B. Guo, Z. W. Yu, Z. Wang, and Y. Feng, Friendship prediction based on the fusion of topology and geographical features in lbsn, in IEEE HPCC EUC, 2013, pp. 2224 2230. 47 / 48
Appendix: References II [6] Y.-T. Wen, P.-R. Lei, W.-C. Peng, and X.-F. Zhou, Exploring social influence on location-based social networks, in IEEE ICDM, 2014, pp. 1043 1048. [7] D. B. Johnson and D. A. Maltz, Dynamic source routing in ad hoc wireless networks, in Mobile computing. Springer, 1996, pp. 153 181. [8] A. Lipowski and D. Lipowska, Roulette-wheel selection via stochastic acceptance, Physica A: Statistical Mechanics and its Applications, vol. 391, no. 6, pp. 2193 2196, 2012. 48 / 48