Limits of Predictability in Human Mobility Chaoming Song 1,2 , Zehui - - PowerPoint PPT Presentation

Chaoming Song1,2, Zehui Qu1,2,3, Nicholas Blumm1,2, Albert-Laszlo Barabasi1,2*

1 Center for Complex Network Research, Departments of Physics, Biology, and Computer Science, Northeastern University, Boston, MA 02115, USA. 2 Department of Medicine, Harvard Medical School, and Center for Cancer Systems Biology, Dana- Farber Cancer Institute, Boston, MA 02115, USA. 3 School of Computer Science and Engineering, University of Electric Science and Technology of China, Chengdu 610054, China.

Limits of Predictability in Human Mobility

Presenter: Rufeng Ma

Background

Why do people study human mobility?

Urban planning and traffic engineering human infectious disease

Curr rrent work rks

Brockmann, Nature, 2006

It turns out that the distribution of traveling distances decays algebraically, and is well reproduced within a two parameter continuous-time random-walk model.

Gonz´alez, Nature, 2008

In this case the distribution of displacements over all users is also well approximated by a truncated power-law and analyzed in terms of truncated Lévi flights, i.e., random walks with power-law distributed step sizes.

Obje jectiv ive A range of applications, from predicting the spread of human and electronic viruses to city planning and resource management in mobile communications, depend on our ability to foresee the whereabouts and mobility of individuals, raising a fundamental question: To what degree is human behavior predictable?

Data coll llectio ion

Mobile carriers record the closest mobile tower each time the user uses his or her phone.

• 50,000 individuals chosen from ~10 million anonymous
• 3-month-long record
• Visit more than 2 loations (tower vicinity)
• Average call frequency f is >=0.5/hour

Data coll llectio ion

The trajectories of two users with sidely different mobility patterns. Mobility networks associated with the two users shown in Figure A

A B

22 vicinities 76 vicinities

Entropy Entropy is probably the most fundamental quantity capturing the degree of predictability characterizing a time series.

• The random entropy

𝑇𝑗

𝑠𝑏𝑜𝑒 ≡ 𝑚𝑝𝑕2𝑂𝑗

• The temporal-uncorrelated entropy

𝑇𝑗

𝑣𝑜𝑑 ≡ − ෍ 𝑘=1 𝑂𝑗

𝑞𝑗 𝑘 𝑚𝑝𝑕2𝑞𝑗(𝑘)

• The actual entropy

𝐵𝑇𝑗 = − ෍

𝑈

𝑗 ′⊂𝑈𝑗

𝑄 𝑈𝑗

′ 𝑚𝑝𝑕2 [𝑄(𝑈𝑗 ′)]

In Incomple leteness

Users tend to place most of their calls in short bursts, followed by long periods with no call activity, during which we have no information about the user’s location. Distribution of the time intervals between consecutive calls τ Distribution of the fraction of unknown locations

Analy lysis is

Distribution of entropy Distribution of the predictability

Analy lysis is

The dependence of predictability Π𝑛𝑏𝑦 on the user’s radius of gyration The fraction of time a user spends in the top n most visited locations

Analy lysis is

Hourly regularity over a week-long time period The average number of visited locations N during each hourly time frame with in a week The averaged 𝑆/𝑆𝑠𝑏𝑜𝑒 versus the radius of gyration

Conclu lusio ion The authors explore the limits of predictability in human dynamics by studying the mobility patterns of anonymized mobile phone users. By measuring the entropy of each individual’s trajectory, we find a 93% potential predictability in user mobility across the whole user base. Despite the significant differences in the travel patterns, they find a remarkable lack

• f

variability in predictability, which is largely independent of the distance users cover on a regular basis.

Thank you!