Modeling the Social, Spatial, and Temporal dimensions of Human Mobility in a unifying framework
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This document proposes a framework for modeling human mobility that unifies the social, spatial, and temporal dimensions. It summarizes existing models and their limitations in capturing all dimensions. The proposed framework models visits as sequences rather than trajectories. It takes a social graph and arrival processes as input and outputs contact statistics. Case studies show it can generate different inter-contact time distributions by varying the arrival rates. The framework is customizable and allows analytical analysis of temporal dependencies. It was tested on a real mobility dataset.
Modeling the Social, Spatial, and Temporal dimensions of Human Mobility in a unifying framework
- 1. Modeling the Social, Spatial, and Temporal dimensions of Human Mobility in a unifying framework Dmytro Karamshuk IMT - Institutions Markets Technologies Institute for Advanced Studies, Lucca January 2013
- 2. Why 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
- 3. Opportunistic 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
- 4. Properties of Human Mobility ● in human mobility we study how people visit different places ● we are interested in social, spatial, and temporal characteristics of the visits
- 5. Mobility Properties - Spatial How far we travel from place to place? M. Gonzalez, C. Hidalgo, A. Barabasi, Understanding individual human mobility patterns, Nature
- 6. Mobility Properties – Temporal ● returning time probability ● visits of top k-th location How frequently we visit different places? C. Song, T. Koren, P. Wang, A. Barabasi, Modelling the scaling properties of human mobility, Nature Physics
- 7. Mobility Properties - Social ● 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? How our social ties influence the choice of the places we visit?
- 8. Mobility Properties – Social (another view) ● inter-contact time i.e. time between two consecutive contacts of two persons (mobile devices) ● this in t e r-c o n ta c t tim e s characteristic is crucial for studying mobile social networks, particularly opportunistic networks based on p2p communications ● usually this is the o u tpu t o f th e m o b ilit y m o de lin g T. Karagiannis, J. Le Boudec, M. Vojnovic, Power law and exponential decay of intercontact times between mobile devices, Mobile Computing
- 9. Mobility Models ● existing models does not combine all directions ● existing models are neither flexible nor controllable A survey of existing models: D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. Human mobility models for opportunistic networks. IEEE Commun. Mag, 2011
- 10. Arrival 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
- 11. Adding 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 algorithm that: ● takes a social graph as input ● partitions the graph into a set of overlapping and hierarchically organized cliques ● generates arrival network by assigning each clique a separate meeting place
- 12. Adding Spatial Dimension to Social Graphs The clique partitioning algorithm consists of two main parts: ● finding the cover of the maximum overlapping cliques in the input social graph (we use BronKerbosch algorithm) ● reproducing hierarchical cliques structure by randomly splitting the cliques
- 13. Example step N1 step N2 step N3 result
- 14. Adding Temporal Dimension To characterize the temporal dimension of human mobility we model time sequences of users' arrivals to places with stochastic point 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.
- 15. Customizing the model Input: Output: ● social graph ● statistics of contact sequences ● link removal probability ● arrival processes
- 16. 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
- 17. 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
- 18. Flexibility of the Framework Input: Output: ● social graph and link removal ● statistics of contact sequences 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
- 19. Analytical analysis - Prerequisites A: Does aggregate power-law imply power-law for individual components? Q: Not necessarily ●A. Passarella and M. Conti. Characterizing aggregate inter-contact times in heterogeneous opportunistic networks. NETWORKING 2011
- 20. Analytical analysis - Idea In the same network with the same arrival processes we can obtain very different inter-contact times distributions.
- 21. Analytical Analysis – Contact Process Contacts between two users in a Contacts between two users in all single meeting place. shared meeting places. The rate of the resulting contact process depends on arrival rates as:
- 22. Analytical 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)
- 23. Case study N1 – long-tail ICT Input: Output: ● random graph with number of nodes ● long-tail distribution of inter-contact n and probability of link χ times ● removal probability α ● Bernoulli arrival processes with rates where Y is a standard normal random variable
- 24. Case study N2 – exponential ICT Input: Output: ● similar as in the first case but the ● inter-contact times distribution with Bernoulli arrival processes with exponential shape identical rates
- 25. Conclusion ● 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 framework for human mobility modeling. WoWMoM, 2012 D. Karamshuk, C. Boldrini, M. Conti, and A. Passarella. SPoT: Representing the Social, Spatial, and Temporal Dimensions of Human Mobility with a Unifying Framework. Under submission.
- 26. Thank you for attention! Dmytro Karamshuk PhD student @ IMT Lucca Research Associate @ IIT CNR di Pisa email: [email protected] follow me on Twitter: @karamshuk