Modeling the Social, Spatial, and Temporal dimensions of Human Mobility in a unifying framework
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Transcript of Modeling the Social, Spatial, and Temporal dimensions of Human Mobility in a unifying framework
Modeling the Social, Spatial, and Temporal dimensions of Human Mobility in a unifying framework
Dmytro Karamshuk
IMT - Institutions Markets TechnologiesInstitute for Advanced Studies, Lucca
January 2013
Why do we study human mobilityWhy do we study human mobility
● modeling ad-hoc wireless networks● modeling information propagation, disease
spreading etc. ● developing new mobile services, e.g., location
recommendation systems● security systems in location based social networks● transportation, urban infrastructure
Opportunistic NetworksOpportunistic Networks
● Motivation: 5,3 billion mobile devices, 10 billion ARM processors in embedded systems of vehicles, street cameras etc.
● Approach: based on 'stare, carry and forward' principle● Main challenge: forwarding (routing) protocols and more
generally information dissemination
Properties of Human MobilityProperties of Human Mobility
● in human mobility we study in human mobility we study howhow people visitpeople visit different different placesplaces● we are interested in we are interested in socialsocial, , spatialspatial, and , and temporaltemporal characteristics of the characteristics of the visitsvisits
Mobility Properties - SpatialMobility Properties - Spatial
How far we travel from place to place?How far we travel from place to place?
M. Gonzalez, C. Hidalgo, A. Barabasi, Understanding individual human mobility patterns, Nature
Mobility Properties – TemporalMobility Properties – Temporal● returning time probability ● visits of top k-th location
How frequently we visit different places?How frequently we visit different places?C. Song, T. Koren, P. Wang, A. Barabasi, Modelling the scaling propertiesof human mobility, Nature Physics
Mobility Properties - SocialMobility Properties - Social
How our social ties influence the choice of the places we visit?How our social ties influence the choice of the places we visit?
● To what extend our movements depend on our social ties?
● How the influence of our social ties depend on time?
● How the places associated with different social communities are spatially distributed?
Mobility Properties – Social (another view)Mobility Properties – Social (another view)● inter-contact time
i.e. time between two consecutive contacts of two persons (mobile devices)
● this this inte r-c o nta c t t im e sinte r-c o nta c t t im e s characteristic is crucial for studying mobile social characteristic is crucial for studying mobile social networks, particularly opportunistic networks based on p2p communications networks, particularly opportunistic networks based on p2p communications
● usually this is the usually this is the o utput o f the m o b ility o utput o f the m o b ility m o de lingm o de ling T. Karagiannis, J. Le Boudec, M. Vojnovic, Power law and exponentialdecay of intercontact times between mobile devices, Mobile Computing
Mobility Models Mobility Models
D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. Human mobility models for opportunistic networks. IEEE Commun. Mag, 2011
● existing models does not combine all directions ● existing models are neither flexible nor controllable
A survey of existing models:
Arrival Based Mobility FrameworkArrival Based Mobility Framework
● defines mobility in terms of visits sequences not trajectories● customizable for any temporal patterns of visits ● provides a framework for analytical analysis of the temporal
dependencies between visits and contacts
Adding Spatial Dimension to Social GraphsAdding Spatial Dimension to Social Graphs● cliques (i.e., fully connected
sub-graphs) of users share common meeting places
● cliques are overlapping and hierarchically organized
● example: a company has meeting rooms shared by all employees, while each subdivision of the company has their own offices, shared only by the members of the subdivision. The subdivisions might share common members.
We develop an We develop an algorithmalgorithm that: that:● takes a social graph as inputtakes a social graph as input● partitions the graph into a set of overlapping and hierarchically organized cliquespartitions the graph into a set of overlapping and hierarchically organized cliques● generates arrival network by assigning each clique a separate meeting placegenerates arrival network by assigning each clique a separate meeting place
Adding Spatial Dimension to Social GraphsAdding Spatial Dimension to Social GraphsThe The clique partitioningclique partitioning algorithm consists of two main parts: algorithm consists of two main parts:
● finding the cover of the finding the cover of the maximum overlapping cliquesmaximum overlapping cliques in the input social graph (we in the input social graph (we use BronKerbosch algorithm) use BronKerbosch algorithm)
● reproducing reproducing hierarchical cliqueshierarchical cliques structure by randomly splitting the cliques structure by randomly splitting the cliques
Adding Temporal DimensionAdding Temporal Dimension
To To characterizecharacterize the temporal dimension of the temporal dimension of human mobility we model time sequences of human mobility we model time sequences of users' arrivals to places with stochastic point users' arrivals to places with stochastic point processes. processes.
For simplicity we consider that arrival processes are:
● discrete (e.g., with the time unit equal to one day)
● the contact between persons happen if they both arrive in the same place in the same time slot
Although, the framework could be extended to other cases.
Customizing the modelCustomizing the model
Input: ● social graph
● link removal probability
● arrival processes
Output:● statistics of contact sequences
Data Analysis
● 27M check-in records ● 619K users● 2.4M venues● 15M user-place pairs and 94K of them
with at least 20 repeats● 1.3K user pairs with at least 20
contacts● time period from 21.01.09 to 07.08.11
T. Hossmann, T. Spyropoulos, F. Legendre, Putting contacts into context: Mobility modeling beyond inter-contact times
Individual arrival sequences
● fitting geometric distribution with Maximum Likelihood Estimation
● Pearson's chi-squared test to attest the quality of approximation
● 70% of individual inter-arrivals sequences follows a geometric distribution
● arrival sequences can be potentially approximated by a simple Bernoulli process
Flexibility of the FrameworkOutput:
● statistics of contact sequences
Input: ● social graph and link removal
probability measured from the Gowalla data
● homogenous Bernoulli arrival processes with the distribution of rates measured from the Gowalla data
model is in agreement with data
Analytical analysis - PrerequisitesAnalytical analysis - Prerequisites
● A. Passarella and M. Conti. Characterizing aggregate inter-contact times in heterogeneous opportunistic networks. NETWORKING 2011
A: Does aggregate power-law imply power-law for individual
components?
Q: Not necessarily
Analytical analysis - IdeaAnalytical analysis - Idea
In the same network with the same arrival processes
we can obtain very different inter-contact times
distributions.
Analytical Analysis – Contact ProcessAnalytical Analysis – Contact ProcessContacts between two users in a
single meeting place.Contacts between two users in all
shared meeting places.
The rate of the resulting contact process depends on arrival rates as:The rate of the resulting contact process depends on arrival rates as:
Analytical Analysis – SchemeAnalytical Analysis – Scheme
where
● different shapes of the inter-contact times distribution can be obtained by tuning the distribution of arrival rates
● although we cannot derive a closed-form expression for a general case, we can do for specific cases, e.g., for exponential or long-tail F(τ)
Case study N1 – long-tail ICTCase study N1 – long-tail ICT
Output:● long-tail distribution of inter-contact
times
Input:● random graph with number of nodes n and probability of link χ
● removal probability α
● Bernoulli arrival processes with rates where Y is a standard normal random variable
Case study N2 – exponential ICTCase study N2 – exponential ICT
Input:● similar as in the first case but the
Bernoulli arrival processes with identical rates
Output:● inter-contact times distribution with
exponential shape
ConclusionConclusion● The framework allows us to model the way users visit different
places and contact each other in those places ● The framework is customizable for any social environment by
taking social graph as an input parameter ● The framework is customizable for any temporal patterns of
users' visits to places by taking arrival stochastic processes as an input parameter
● Temporal characteristics of the contact sequences can be analyzed analytically
D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. An arrival based D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. An arrival based framework for human mobility modeling. WoWMoM, 2012framework for human mobility modeling. WoWMoM, 2012
D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. SPoT: Representing D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. SPoT: Representing the Social, Spatial, and Temporal Dimensions of Human Mobility with a the Social, Spatial, and Temporal Dimensions of Human Mobility with a Unifying Framework. Under submission.Unifying Framework. Under submission.
Thank you for attention!
Dmytro KaramshukPhD student @ IMT Lucca
Research Associate @ IIT CNR di Pisaemail: [email protected]
follow me on Twitter: @karamshuk