Friendship and Mobility: User Movement
In Location-Based Social Networks
By
Venkata Sai Pulluri (10957537)
Narendra Muppavarapu (10926835)
Outline:
1) Abstract
2) Introduction
3) Characteristics of Check-Ins
4) Friendship and Mobility
5) Model of Human Mobility
6)Experimental Evaluations
7) Conclusion
Abstract
 Human mobility tends to show different structural patterns
due to geographical and social constraints.
 Analysis depicts that social relationships explains about 1030% 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.
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.
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
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.
 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.
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
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)).
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.
Moving to where a friend has checkedin 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%.
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.
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.
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.
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.
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.
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..
 The Following figure represent temporal component of a PMM model.
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
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
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.
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.
 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.
 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.
 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.
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.