Friendship and Mobility: User Movement In Location-Based Social Networks. Eunjoon Cho* Seth A. Myers* Jure Leskovec

Transcription

1 Friendship and Mobility: User Movement In Location-Based Social Networks Eunjoon Cho* Seth A. Myers* Jure Leskovec

2 Outline Introduction Related Work Data Observations from Data Model of Human Mobility Evaluation Summary

3 Introduction Human Mobility patterns have: A high degree of freedom and variation Show structural patterns due to: Geographic constraints Social constraints Short-ranged Travel is Periodic spatially and temporally Not affected by social network ties Long-distance Travel is influenced by social network ties

4 Introduction Contd.. Aim: To identify fundamental factors that govern Human Mobility. To develop a human mobility model capturing: Short-ranged Travel due to work Long-distance Travel due to social network To find answers to some interesting questions: Does mobility have an effect on human friendship? Does friendship have an effect on human mobility? Are people s visits periodic?

5 Introduction Contd.. Hypothesis: Mobility is, Periodic between home and work Constrained by distance travelable in a day Shaped by social relationships

6 Introduction Contd.. Hypothesis: Mobility is, Periodic between home and work Constrained by distance travelable in a day Shaped by social relationships Can be tested using check-ins from: Location Based Social Networks (Eg. Gowalla and Brightkite) Cellphone data

7 Introduction Contd.. Importance: Mobility Modelling is important for Urban Planning Understanding of Human Migration Patterns and spread of diseases Improving location based recommendations

8 Related Work Two categories of related work: Common Limitation: Do not consider geographic movement, temporal dynamics and social network together to build a model. Models of Human movement and Dynamics Consider mobility as a stochastic process centered about one fixed point Drawback: Poor accuracy Solution: Consider mobility a stochastic process around several fixed points Use wireless network or GPS data to model mobility Drawback: Studies limited to small geographic area (eg., college campus) Studies on impact of geography on social interaction

9 Data Cellphone Gowalla Brightkite Users 2,000, ,591 58,288 Friendships 4,500, , ,078 Check-ins 900,000,000 6,400,000 4,500,000

10 Data Contd.. Cellphone Social Media (Gowalla and Brightkite) Coarse location accuracy Implicit and frequent check-ins Implicit Social Network Data from one unnamed country Good location accuracy Explicit and sporadic check-ins Explicit Social Network Data from across the World

11 Data Contd.. Definitions for Cellphone Data: Check-in: Location and time of a phone call Friends: People who have called each other at least five times Home: Average position of check-ins in the cell with most check-ins Cell: 25km x 25km area section from a discretized world

12 Observations from Data

13 Observations from Data Kink at 100 Km mark!

14 Observations from Data Kink at 100 Km mark! Explained by: Non-uniform population distribution Radius of reach"

15 Observations from Data Contd..

16 Observations from Data Contd..

17 Observations from Data Contd.. Where P null (d) is the probability of being around a friend s home, given, movement is random with respect to population density.

18 Observations from Data Contd Where P null (d) is the probability of being around a friend s home, given, movement is random with respect to population density.

19 Observations from Data Contd.. Influence Graph 0.3 Where P null (d) is the probability of being around a friend s home, given, movement is random with respect to population density.

20 Observations from Data Contd.. Influence of friends on individual s mobility Friendship causing mobility Network before time t 1 considered Fraction of check-ins near friends in this network calculated 61% probability that a user visits a friend Mobility causing friendship Check-ins before time t 1 considered New friends created by these check-ins calculated 24% probability that a check-in will lead to new friendship

21 Observations from Data Contd.. Limits of using friendship to predict mobility

22 Observations from Data Contd.. Limits of using friendship to predict mobility %

23 Observations from Data Contd.. Limits of using friendship to predict mobility Element of time considered % 40%

24 Observations from Data Contd.. Temporal and geographic periodicity

25 Observations from Data Contd.. Temporal and geographic periodicity Evening Weekend Evening Weekend Morning Morning

26 Observations from Data Contd.. More Observations Brightkite 53% of check-ins in Brightkite previously visited by user Only 4.1% of check-ins previously visited by a friend Gowalla 31% of check-ins previously visited by user Only 9.6% of check-ins previously visited by a friend

27 Model of Human Mobility Periodic Mobility Model (PMM): Assuming Movement is based on periodic movement between two states (Home and Work) Probability Definition: Where, x u (t) is location of user u time t c u (t) is state of user u time t

28 Model of Human Mobility Contd.. Check-in of a user in San Fransicso (Red:Home, Blue:Work)

29 Model of Human Mobility Contd.. Temporal Component of PMM Model: Truncated Gaussian Distribution

30 Model of Human Mobility Contd.. Spatial Component of PMM Model: 2-dimensional time-independent Gaussian Distribution

31 Model of Human Mobility Contd.. Hence, PMM Model is: A two state mixture of Gaussians with time dependent state prior.

32 Model of Human Mobility Contd.. Hence, PMM Model is: A two state mixture of Gaussians with time dependent state prior. Probability density of user location over time from work to home in PMM

33 Model of Human Mobility Contd.. Periodic and Social Mobility Model (PSMM): Assuming Movement is based on movement between three states (Home, Work and Outlier). It captures both the non-periodic (social) movement and periodic movement. Probability Definition: Where, z u (t)=1 means check-in is social (non-periodic) z u (t)=0 means check-in is periodic

34 Model of Human Mobility Contd.. is the same as PMM (Periodic Mobility Model) Where J u is the set of check-ins by u s friends in the same day

35 Model of Human Mobility Contd.. Decay of Probability of a location based on time difference and distance from a friend s check-in

36 Model of Human Mobility Contd.. Fitting PMM and PSMM models: PMM: PSMM: Fitted using Random restart Expectation Maximization (EM) Overfitting avoided using regularization Minimum singular value of spatial covariance is set as 10-7 Minimum bound on temporal variance is set as 10-4 Train PMM with three latent states: home, work and outlier Fit social model to the outlier check-ins Fitting of decay variables, alpha and beta, done using (EM) for each user

37 Evaluation of PMM and PSMM Metrics used: Predictive Accuracy Average Log Likelihood Relative Expected Distance Error

38 Evaluation of PMM and PSMM Metrics used: Predictive Accuracy : Accuracy of exact prediction Average Log Likelihood Relative Expected Distance Error

39 Evaluation of PMM and PSMM Metrics used: Predictive Accuracy : Accuracy of exact prediction Average Log Likelihood : Fitment of test set in model Relative Expected Distance Error

40 Evaluation of PMM and PSMM Metrics used: Predictive Accuracy : Accuracy of exact prediction Average Log Likelihood : Fitment of test set in model Relative Expected Distance Error : (Expected Distance Error) / (Radius of Gyration of a user in a day) Where Expected Distance Error is:

41 Evaluation of PMM and PSMM Contd.. Baselines used: Most Frequented Location Model (MF): Probability is proportional to fraction of check-ins in that location at the same hour on previous days

42 Evaluation of PMM and PSMM Contd.. Baselines used: Gaussian Model (G): Probability is given by Gaussian distribution of check-ins on the same day of previous weeks centered around a single point RW Model: Predicts check-in location as last known check-in location

43 Evaluation of PMM and PSMM Contd.. `

44 Evaluation of PMM and PSMM Contd..

45 Evaluation of PMM and PSMM Contd..

46 Evaluation of PMM and PSMM Contd.. Similarity of Daily mobility patterns Similarity metric:

47 Evaluation of PMM and PSMM Contd..

48 Evaluation of PMM and PSMM Contd..

49 Evaluation of PMM and PSMM Contd..

50 Evaluation of PMM and PSMM Contd..

51 Evaluation of PMM and PSMM Contd.. Number of Latent States Accuracy % % %

52 Summary Social relationships can explain 10% to 30% of human movement Periodic behavior can explain 50% to 70% of human movement Short-range travel is periodic and not affected by social ties People are more likely to visit a distant place if a friend lives there Influence of friendship on mobility is 2x stronger than influence of mobility on friendship People are 5 times more likely to visit a place they previously visited than to visit a place previously visited by a friend The model captures both periodic short-range travel and social ties based long-distance travel The model can predict high precision user location with 40% accuracy Performance gained by adding additional latent states after 3 has marginal effect on accuracy

53 Thank You