1. By Venkata Sai Pulluri (10957537) Narendra Muppavarapu (10926835)
Friendship and Mobility: User Movement In Location-Based Social Networks By
Venkata Sai Pulluri ( )
Narendra Muppavarapu ( )

2. Outline: 1) Abstract 2) Introduction 3) Characteristics of Check-Ins
4) Friendship and Mobility
5) Model of Human Mobility
6)Experimental Evaluations
7) Conclusion

3. Abstract
Human mobility tends to show different structural patterns due to geographical and social constraints.
Analysis depicts that social relationships explains about % of human movement, and periodic behavior explains about 50-70%
The authors developed a model that can predict the location and dynamics of future human movements based on above statistics.
This model predicts the reliability of future human movement based on Cellphone location data and two location based social networks.

4. Introduction
Human Mobility exhibits structural patterns subject to geographic and social constraints.
It is very hard to get human mobility data, Traditional way of gathering data was from cell phone data, with the explosion of internet location based online social network applications have emerged.
Data allows us for studying 3 main aspects
Geographic movement (where do we move)
Temporal Dynamics (How often do we move)
Social Network ( how social ties interact with movement)
Understanding and modeling human mobility has many applications like improving large scale systems such as cloud computing. Accurate models of human mobility are essential for urban planning, understanding human migration patterns and spread of diseases.

5. Working Model
The authors study the relation between the three aspects, Tries to answer questions such as how likely is a person going to a place because he has a friend? How often person makes a friend by visiting a place? How probability increases or decrease when travelling long distances?
Authors observed that influence of friendship on one’s mobility is twice times stronger than influence of mobility on creating new friends.
Based on the findings authors develop a periodic and social mobility models for predicting mobility of individuals. Model has three components
spatial location user regularly visits.
Temporal movements---- between these locations (Home and work)
Social ties Movement influenced by friends

6. Characteristics of Check-Ins
Authors uses three different datasets that capture human mobility.
Two online location-based social networks (Gowalla and Brightkite) and one cell phone location trace data. The data is recorded based on the check-ins (time and location of the particular user is recorded).
Check-In behavior of users: Spatial and social characteristics of user check-ins are analyzed like how far they tend to move and meet social N/W friends at location they travel.

7. First observation is on How far from their homes users tends to travel.
The above figure shows that the distribution decreases faster for the travel less that 100km and then flattens.

8. Friendship and Mobility
The main focus here is about the interaction of the person’s social network structure and their mobility.
The different scenarios considered are
Moving close to a friend’s home
Influence of friends on an individual’s mobility
Moving to where a friend has checked-in before
Limits of using friendship for predicting mobility
Temporal and geographical periodicity of human movement

9. Moving close to a friend’s home
The observations begins by investigating the sociability of human movement, Authors considered A and B and how A’s movement is influenced by B.
Author considers model with social relationship (Pdata(d)) and null model (Pnull(d)).

10. Influence of friends on an individual’s mobility
The author considered two cases like friendship created before movement and after movement.
Authors considered two time frames and examined the patterns of user.
Observations shows that on an average 61% probability that user will visit an existing friend and 24% it leads to new friendship i.e, influence of friendship is 2.5 times greater than influence of mobility on creating friendship.

11. Moving to where a friend has checked-in before
Here the authors considered that both friends simultaneously moving and probability that they meet.
The observations shows that the more farther user travels is more influenced by friends.
The amount that the friendship influences movement when travelling long distances is an order of magnitude higher than the influence when travelled short distances.
we also observe that for movement farther than 100km from home the probability of checking-in at the exact same location as a friend has checked-in in the past remains constant at around 10%.

12. Limits of using friendship for predicting mobility
Observations shows strong correspondence between trajectory similarity of users and probability of friendship, in general only a small fraction of users have high overlap in check-ins with their friends.

13. Temporal and geographical periodicity of human movement
In this scenario authors considered non-social factors particularly periodicity ( temporal and geographical).
Quantifying periodicity is to measure the fraction of user check-ins that are visits to previously already visited. Considering the observation of Brightkite effect is 5 times more than the effect of social network (10% chance).
The above fig shows the entropy of check in locations over time. It describes entropy in mornings and rush hours, in weekends.

14. MODEL OF HUMAN MOBILITY
This model was developed by incorporating three ingredients, which are essential to predict human mobility.
Temporal periodic movement
Geographical periodic movement
Periodic movement with Social network structure.

15. Periodic Mobility Model(PMM):
This model build based on majority of human movement is periodic between a small set of latent states.
“Home”
“Work”
The movement is between either “home and work” or between two locations.
A user can also determines his/her location by
Identifying his/her state.
Finding location based on state.

16. Formal representation of PMM model:
P [x(t) = x] =P [Xu(t) = x|Cu(t) = H] · P [Cu(t) = H]
+P [Xu(t) = x|Cu(t) = W] · P [Cu(t) = W]
This calculates the probability for a user in either “work” or “home” state.
Where
‘t’ is the current time of the day.
‘Xu(t)’ denotes the geographic position of user ‘u’ at time t .
‘Cu(t)’ be the “state” at time t .
‘H,W’ denotes home and work respectively.

17. Temporal Component of PMM model:
In this, by using temporal component we can calculate the state of the User. Equation for calculating the probability for a state of the User is: Temporal component for “Home” state. Temporal component for “Work” state. And can be calculated by using..

18. The Following figure represent temporal component of a PMM model.

19. Spatial component of PMM model:
This is used to calculate the Geographical position of User.
This model uses the time-independent Gaussian distribution
Figure: spatial component
Fig: User transition over time

20. Periodic and Social Mobility Model(PSMM):
Extended from PMM model.
For the social network information, they introduce another state represented by ‘Zu(t)’.
Equation for finding probability.
User check in determine by two factors
Check-in period of his/her friend.
Distance

21. Fitting PMM and PSMM models:
Fitting PMM model:
PMM model fitted using “Expectation-Maximization(EM)”.
E-step:
Fitting parameters of model using maximum. likelihood estimation.
M-step:
Reassigning check-in state.
Iterative process
Fitting PSMM model:
By extending PMM model(“outlier check-in”)
Check-ins that are not fit to periodic model.

22. Experimental Evaluation.
Comparison by using Evaluation metrics and Baseline models.
Evaluation metrics:
Log-likelihood:
How well test set fits the model.
Predictive accuracy:
How accurately each model predict the exact location
Expected distance error:
by considering spatial proximities of predictions to actual location. It is uninformative when comparing different scales.

23. Baseline models:
Most Frequent Location Model:
predicts most likely location of a particular User.
Gaussian Model:
Proposed by Gonzalez.
Models human mobility as stochastic process.
Static in time and captures user movements.
RW Model
Predicts next location of user.
Experimental setup:
Users with at least 10 check-ins on each day
80% check-ins for build a model, 20% for test the model.
For each user they build 7 models for each day of week.

24. Predicting mobility:
This model gives 83.1% improvement over Gaussian and 11% relative improvement over MF model in Brightkite.
This model calculates exact location of check-in up to 40% of time.

25. Predictive performance of Social Model:
PSMM shows 10% relative improvement for expected distance error and 25% relative improvement for log-likelihood in case of both Brightkite and Cellphones.
Number of Latent States:
Two latent states so far..
Performance gained by adding 3rd state to model is minor compare to difference between two state model and single state model.

26. Conclusion
Human mobility was investigated on three different large datasets, i.e, two online location based social networks and one cell phone data, even though both are of different we found many common patterns.
Found that human experience a combination of strong short range spatially and temporally periodic movement that is not impacted by the social network structure, And long distance travel is more influenced by social network ties.
We developed a model of human mobility dynamics, this model reliably captures and predicts human mobility patterns and outperforms current mobility model by factor of two.