2013.10.24y. yuan and m. raubal1 investigating the distribution of human activity space from mobile...

2013.10.24 Y. Yuan and M. Raubal 1

Investigating the distribution of human activity space from mobile

phone usage

Yihong Yuan1,2 and Martin Raubal11Institute of Cartography and Geoinformation, ETH Zurich

2Department of Geography, University of California, Santa Barbara

[email protected], [email protected]


Background• Information and communication

technologies (ICTs)– Greater mobility flexibility– A wide range of Spatio-temporal data sources

• Modeling the activity pattern of phone users– Call Detailed Records (CDRs)– Low resolution / precision– Uncertainty?


Background

• Activity space of human beings– “the local areas within which people travel

during their daily activities”– How to measure an activity space

• Size• Shape• Regularly visited places (e.g., home, work)• ……


Objective & Motivation

• Explore the distribution of activity space of phone users based on (CDRs)

• Why is this important?– Large scale, urban oriented research– Model fitting

• Abstract and generalized indicators• Provide reference for various fields• A neat fitted distribution can facilitate comparison

between cities/countries/cultures, etc…


Methodology

• Three measures of Activity space– Radius -> Scale

– Eccentricity -> Shape• Shape Index: 1- Eccentricity

– Entropy->Regularity

Transformation of Trajectories (Gonzalez et al. 2008).


Example dataset

• Mobile Phone Connections in 10 cities in Northeast China– 3 large, 5 median, 2 small– Time, duration, and locations of mobile phone

connections over 9 days


Descriptive plots(Probability density functions)

• Radius

• (b)


Probability distribution functions

• Shape Index


Probability distribution functions

• Entropy


Model Fitting

• Various models– Why model fitting is needed sometimes– Exponential…– Skewed normal…

• Cross-variable comparison– One flexible model for all three variables– Weibull distribution

• For exploratory analysis• Both cross-city and cross-variable comparison


Weibull distribution

• An effective model in various applications such as industrial engineering

– where k > 0 is the shape parameter and λ > 0 is the scale parameter of the distribution.

– With k=1, the Weibull distribution turns into an exponential distribution

• The combination of simplicity and flexibility in the shape of the Weibull distribution

( )1( ; , ) ( )kx

kk xf x k e

0x

()


Weibull Distribution (Cont.)

• Scale parameter lamda–How much the curve stretches out–When k stays the same, The larger lamda is, , the distribution gets stretched out to the right and its height decreases, while maintaining its shape and location.


Weibull distribution fitting


Discussion

• The distribution of radius is close to an exponential distribution (k2≈1)

• The decay of Shape Index is faster than exponential (k3<1). It also shows that the distribution of Entropy is similar to a skewed normal distribution (k1≈2).


Application

• We have also constructed a regression model showing that – k2 is significantly correlated with the size of

the cities, indicating that bigger cities have a faster decay trend for individual activity radii.

– city size is not significantly correlated with either entropy or SI.


Summary

• Weibull distribution– Fit into three variables

• The distribution of radius is close to an exponential distribution


Future Work

• Further examine other potential factors

• Test the robust of the method– Apply to other data

• Applications


Acknowledgement

• This research is funded by:– Swiss National Science Foundation, Grant

No. 141284

2013.10.24y. yuan and m. raubal1 investigating the distribution of human activity space from mobile...

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