Social Event Detection

V.A. Traag1, A. Browet1, F. Calabrese2, F. Morlot3

1Department of Applied MathematicsUCL, Louvain-la-neuve, Belgium

2SENSEable City LabMIT, Cambridge, USA

3Orange LabsIssy-les-Moulineaux, France

24 February 2011

Outline

1 Motivation

2 Bayesian Location Inference

3 Identification of frequent location

4 Event detection

5 Presence probability

Introduction

Purpose

Analyze mobility and social behaviour of mobile phone users:

1 Detect social events i.e. unsual large gatherings of poeple.

2 Identify frequent location such as home or office.

Motivation

1 Between 70% & 80% of human mobility is explain by the dailyhome-office routine (Barabasi et al.). Analyze theout-of-ordinary behaviour.

2 Anticipate the impact of large events on urban transit for trafficregulation or public transportation.

3 Identification/Classification of users and their habits fortelecommunication company.

Introduction

Purpose

Analyze mobility and social behaviour of mobile phone users:

1 Detect social events i.e. unsual large gatherings of poeple.

2 Identify frequent location such as home or office.

Motivation

1 Between 70% & 80% of human mobility is explain by the dailyhome-office routine (Barabasi et al.). Analyze theout-of-ordinary behaviour.

2 Anticipate the impact of large events on urban transit for trafficregulation or public transportation.

3 Identification/Classification of users and their habits fortelecommunication company.

Introduction

Purpose

Analyze mobility and social behaviour of mobile phone users:

1 Detect social events i.e. unsual large gatherings of poeple.

2 Identify frequent location such as home or office.

Motivation

1 Between 70% & 80% of human mobility is explain by the dailyhome-office routine (Barabasi et al.). Analyze theout-of-ordinary behaviour.

2 Anticipate the impact of large events on urban transit for trafficregulation or public transportation.

3 Identification/Classification of users and their habits fortelecommunication company.

Introduction

Purpose

Analyze mobility and social behaviour of mobile phone users:

1 Detect social events i.e. unsual large gatherings of poeple.

2 Identify frequent location such as home or office.

Motivation

1 Between 70% & 80% of human mobility is explain by the dailyhome-office routine (Barabasi et al.). Analyze theout-of-ordinary behaviour.

2 Anticipate the impact of large events on urban transit for trafficregulation or public transportation.

3 Identification/Classification of users and their habits fortelecommunication company.

Introduction

Available data

1 Precise location of antennas but no orientation information.

2 Record for each connection to the networks (calls, textmessages, mobile internet,...)

Compute 2 probability measures

1 φi (x) to be connected to antenna i given a position x

2 ψi (x) to be in position x given that the user was connected toantenna i

Location Inference

The signal strength at position x of an antenna i at position Xi isdefined by:

• the power of the antenna pi ; but pi = p;

• the loss of signal strength over distance:

Li (x) =1

‖x − Xi‖β;

• a stochastic fading of the signal i.e. the Rayleigh fading Ri :

Pr(Ri ≤ r) = F (r) = 1− e−r .

Location Inference

The signal strength of antenna i is then given by

Si (x) = piLi (x)Ri .

Further assumptions:

• Ri ⊥⊥ Rj ∀i 6= j .

• given a position x , the user connects to the antenna i with thehighest signal strength:

Si (x) ≥ Sj(x) ∀j ∈ X

m

Si (x) = maxj∈X

Sj(x)

Location Inference

Let ai denote the fact that a user connects to antenna i .

Pr(ai |x) = Pr(Si (x) = maxj∈X Sj(x))

=∏j∈Xj 6=i

Pr (piLi (x)Ri ≥ pjLj(x)Rj)

If we assume that the random variable Ri realize a specific value r ,

Pr(ai |x ,Ri = r) =∏j∈Xj 6=i

Pr(Rj ≤ Li (x)

Lj (x)r)

=∏j∈Xj 6=i

F(Li (x)Lj (x)

r)

Location Inference

Then, it follows that

φi (x) = Pr(ai |x) =∞∫0

f (r)Pr(ai |x ,Ri = r)dr

=∞∫0

e−r∏j∈Xj 6=i

(1− exp

(−r ||x−Xj ||β||x−Xi ||β

))dr

≈∞∫0

e−r∏j∈Xi

(1− exp

(−r ||x−Xj ||β||x−Xi ||β

))dr

How to choose the local neighborhood and what is its impact ?

Location Inference

Delaunay Radius:

ρi = max{d(Xi ,Xj)| j Delaunay of i}

The domain Di is define by

Di = {x |rρi ≥ d(x ,Xi )}

The neighborhood is computed as

Xi = {j |Xj ∈ Di , j ∈ X}

Location Inference

Average error on 1000 random points

1 1.5 2 2.5 30

0.002

0.004

0.006

0.008

0.01

0.012

0.014

r

Avera

ge e

rror

Location Inference

Based on Bayes rule, we can obtain

ψi (x) = Pr(x |ai ) =Pr(ai |x)Pr(x)

Pr(ai )

The value Pr(x)Pr(ai )

is not known but can be assumed constant overthe domain Di . It follows that

ψi (x) =φi (x)∫

Di

φi (x)dx

Location Inference

Probability density ψi (x)

Frequent Location Indentification

Probability that a user connects to antenna i is φi (x)Probability that he made ki calls with antenna i is then φi (x)ki

The likelihood of observing those calling frequencies is

L(x |k) =∏i∈H

φi (x)ki

mlog L(x |k) =

∑i∈H

ki log φi (x)

Maximum Likelihood Estimator(MLE)

x̂h(u) = arg maxx

log L(x |k(u))

Overview Event Detection

General

• Looking for unusual large gatherings of people.

• Which people are likely to be attending an (possible) event?

• Should be present at the event location with high probability.

• Should not be often there.

Presence probability

Given calls in the neighbourhood, what is the probability the userwas present during the time interval of an event?

Ordinary probability

What is the average probability a user was present during otherweeks.

Presence probability

Derivation

• Probability user in area A at time tc for a call c is pc .

• Assume constant leave and arrival rate γ

• Then for t 6= tc we have e−γ|t−tc |pc .

• Take max over all calls c for a user

pp =1

te − ts

∫ te

ts

maxc

e−γ|t−tc |pcdt

Motivation

• More calls ⇒ higher presence probability

• Calls close by ⇒ higher presence probability

• Don’t take into account calls outside of area.

Presence probability

← First call

← Second call

Time

Pro

babili

ty

13 14 15 16 17 18 190

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Ordinary probability

How regularly is user in the area?(Consider only same weekday, same time of day)

Apr

il 1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 25 26 27 28 29 30

Was not present, i.e. pp(i) = 0

Was in area with probability pp(2)

Was in area with probability pp(5)

Ordinary probability

Ordinary probability defined as average probability, i.e.po = 1

W

∑Wi=1 pp(i)

Probability of attending

Maximum ordinary probability

• Should be present with relatively high probability

• Relatively rarely present ⇒ small po (i.e. only for the event)

• What is theoretical maximum ordinary probability p̄o?

• Theoretical maximum: make infinite number of calls with ‘best’antenna.

Probability of attending

• Probability user attended then calculated as

pa = pp(1− po/p̄o)

Event detection

Number of attendees

• Mark user as (possible) attendee if pa high enough

• Number of (possible) attendees at week w given by nw

• Mark week w as event if nw is high enough.

Example: Stadium

0 10 20 30 40 50 60−2

−1

0

1

2

3

4

5

Week

Z−

score

Example: Stadium

0 2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

250

300

350

Hour

No

. o

f C

alls

Not attending

Attending

Regular

Example: Park

0 10 20 30 40 50 60−4

−3

−2

−1

0

1

2

3

4

Week

Z−

score

Example: Park

0 2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

250

300

350

Hour

No

. o

f C

alls

Not Attending

Attending

Regular

Example: Rural area

0 10 20 30 40 50 60−4

−3

−2

−1

0

1

2

3

4

Week

Z−

score

Sensitivity

Conclusions

Conclusions

• Possible to detect ‘social events’ in mobile phone data

• Robust to antenna positioning and switching

• Interesting observation: non-routine behaviour seems massive

Further considerations

• Use simpler (faster) method to detect irregularities

• Refine location estimation by likelihood inference

Questions? Suggestions? Remarks?