Smart Card in Public Transportation: Designing a Analysis System at the Human Scale

E. Tonnelier, N. Baskiotis, V. Guigue and P. Gallinari

LIP6 - UPMC - Sorbonne Universit´es

November 3 ^rd , 2016

IEEE 19th International Conference on Intelligent Transportation

Systems

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

U RBAN MOBILITY – MANY ISSUES & SENSORS

◦ Data sources

- City / Smart City: cellphones, GPS, smart street furnitures . . .

- Explosion of available data, rich literature over the last decade

◦ Development policies [Black et al., 2002, Golias, 2002]

◦ Global view on traffic [Ceapa et al., 2012, Louail et al., 2014]

◦ Regularity of users

- Trip prediction [Song et al., 2010, Foell et al., 2013]

- Users representations [Poussevin et al., 2014]

Vincent Guigue Smart Card Analysis at the Human Scale 2/17

⇒ for a standard week day

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

C ONTRIBUTIONS AND CHALLENGES

◦ Logs = entries of 10k users during 13 weeks

◦ Characterize noisy users - Aggregation / Clustering - Habits modeling of week days:

8am Week days

7pm Week days

11pm Thursdays

⇒ Variance overestimate

0h 5h 10h 15h 20h

0h 5h 10h 15h 20h

0h 5h 10h 15h 20h

User 1

User 2

Population

New hypothesis: Habits are shared...

but with individual schedule

Vincent Guigue Smart Card Analysis at the Human Scale 4/17

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

C ONTRIBUTIONS AND CHALLENGES

◦ Logs = entries of 10k users during 13 weeks

◦ Characterize noisy users - Aggregation / Clustering - Habits modeling of week days:

0h 5h 10h 15h 20h

0h 5h 10h 15h 20h

0h 5h 10h 15h 20h

User 1

User 2

Population

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

C ONTRIBUTIONS AND CHALLENGES

◦ Logs = entries of 10k users during 13 weeks

◦ Characterize noisy users - Aggregation / Clustering - Habits modeling of week days:

8am Week days

7pm Week days

11pm Thursdays

⇒ Variance overestimate

0h 5h 10h 15h 20h

0h 5h 10h 15h 20h

0h 5h 10h 15h 20h

User 1

User 2

Population

New hypothesis:

Habits are shared...

but with individual schedule

Vincent Guigue Smart Card Analysis at the Human Scale 4/17

= ×

Data matrix (logs) Code matrix Dictionary

i-th row

Goal: optimizing both code & dictionary

◦ Variations SVD [Golub and Van Loan, 1996]

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

NMF ON AN EXAMPLE

5 random users

◦ 24h = 96 intervals of 15min

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Dictionary: (most used atoms)

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2.5e+01

0 5 10 15 20

E = 2.4e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2e+01

Code:

0 2 4 6 8

0 1 2 3 4

Vincent Guigue Smart Card Analysis at the Human Scale 6/17

5 random users

◦ 24h = 96 intervals of 15min

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2.5e+01

0 5 10 15 20

E = 2.4e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2e+01

Code:

0

1

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

NMF ON AN EXAMPLE

5 random users

◦ 24h = 96 intervals of 15min Focusing on user #1

0 5 10 15 20

Dictionary: (most used atoms)

0 5 10 15 20

E = 1.9e+01

0 5 10 15 20

E = 1.6e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2e+01

Code:

0 2 4 6 8

0 1 2 3 4

Vincent Guigue Smart Card Analysis at the Human Scale 6/17

5 random users

◦ 24h = 96 intervals of 15min Focusing on user #1

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

0 5 10 15 20

E = 1.9e+01

0 5 10 15 20

E = 1.6e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2e+01

Code:

0

1

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

NMF ON AN EXAMPLE

5 random users

◦ 24h = 96 intervals of 15min Focusing on user #1

0 5 10 15 20 25

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Dictionary: (most used atoms)

0 5 10 15 20

E = 1.9e+01

0 5 10 15 20

E = 1.6e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2e+01

Code:

0 2 4 6 8

0 1 2 3 4

Vincent Guigue Smart Card Analysis at the Human Scale 6/17

5 random users

◦ 24h = 96 intervals of 15min Focusing on user #1

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

0 5 10 15 20

E = 1.9e+01

0 5 10 15 20

E = 1.6e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2e+01

Code:

0

1

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

NMF ON AN EXAMPLE

5 random users

◦ 24h = 96 intervals of 15min Focusing on user #1

0 5 10 15 20 25

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Dictionary: (most used atoms)

0 5 10 15 20

E = 1.9e+01

0 5 10 15 20

E = 1.6e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2e+01

Code:

0 2 4 6 8

0 1 2 3 4

Vincent Guigue Smart Card Analysis at the Human Scale 6/17

5 random users

◦ 24h = 96 intervals of 15min Focusing on user #1

0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

0 5 10 15 20

E = 1.9e+01

0 5 10 15 20

E = 1.6e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2e+01

Code:

0

1

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

NMF ON AN EXAMPLE

5 random users

◦ 24h = 96 intervals of 15min Focusing on user #1

0 5 10 15 20

Dictionary: (most used atoms)

0 5 10 15 20

E = 1.9e+01

0 5 10 15 20

E = 1.6e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2e+01

Code:

0 2 4 6 8

0 1 2 3 4

Vincent Guigue Smart Card Analysis at the Human Scale 6/17

0 5 10 15 20

E = 3.1e+01

0 5 10 15 20

E = 2.9e+01

0 5 10 15 20

E = 2.5e+01

0 5 10 15 20

E = 2.3e+01

0 5 10 15 20

E = 2.2e+01

0 5 10 15 20

E = 2.6e+01

0 5 10 15 20

E = 2.5e+01

0 5 10 15 20

E = 2.4e+01

0 5 10 15 20

E = 2.1e+01

0 5 10 15 20

E = 2e+01

0 5 10 15 20

E = 1.8e+01

0 5 10 15 20

E = 1.8e+01

0 5 10 15 20

E = 1.8e+01

0 5 10 15 20

E = 1.6e+01

0 5 10 15 20

E = 1.3e+01

- More atoms = finer reconstruction...

+reconstruction of the noise...

+ meaningless atoms - Less atoms = no longer local event modeling (variance

overestimate)

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

NMF: ANALYSIS

◦ Number of atoms in the dictionary (rank constraint) - More atoms = finer reconstruction...

+reconstruction of the noise...

+ meaningless atoms - Less atoms = no longer local event modeling (variance

overestimate) Reconstruction (poor

dictionary)

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Reconstruction (standard dictionary)

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Reconstruction (rich dictionary)

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

◦ Parameters are wasted modeling translated events

◦ Evaluation ?

Vincent Guigue Smart Card Analysis at the Human Scale 7/17

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

C ONTRIBUTION : TS-NMF

Idea:

◦ Keeping the NMF framework

◦ Defining compact atoms

which shapes are learned on all users (=NMF) which can be positioned for each user

Signal

Atom

Shift

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

C ONTRIBUTION : TS-NMF

Idea:

◦ Keeping the NMF framework

◦ Defining compact atoms

which shapes are learned on all users (=NMF) which can be positioned for each user

u = X

z

τ _u,z (w u,z d z ) = w u,z d z (t + φ _u,z )

= ⊕ ( ^× )

Data matrix (logs) φ matrix Code matrix Dictionary

i-th row

Vincent Guigue Smart Card Analysis at the Human Scale 8/17

Algorithm 1: TS NMF learning algorithm

Data: X ∈ R ^U×T + , Z, max iter , α Φ

1 max iter : to reach convergence

α Φ : window of search in the atom shift procedure Result: Optimized matrix Φ, D and W

2 D, W, Φ = init(X, Z)

D and W randomly initialized, Φ regularly scat- tered along time band

3 for it ∈ 0...max iter do

4 for u ∈ range(0, U) do

5 x u = X[u, .]

6 atoms = descendingEntropy(D)

return atoms indexes sort in descending order

7 for a ∈ atoms do

8 Φ _u,a = minimizeLocalCost t (x u , D a )

finding optimal time-shift t in a window of size α Φ 9 W u,a = update W(x u , W u,. , D, Φ u,a )

Simple gradient descent

10 x u = x u − f (D a , Φ u,a )W u,a

Vincent Guigue Smart Card Analysis at the Human Scale 9/17

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

A LGORITHM

Algorithm 2: TS NMF learning algorithm

Data: X ∈ R ^U + ^{× T} , Z, max iter , α Φ

1 max iter : to reach convergence

α Φ : window of search in the atom shift procedure Result: Optimized matrix Φ, D and W

2 D, W, Φ = init(X, Z)

D and W randomly initialized, Φ regularly scat- tered along time band

3 for it ∈ 0...max iter do

4 for u ∈ range(0, U) do

5 x u = X[u, .]

6 atoms = descendingEntropy(D)

return atoms indexes sort in descending order

7 for a ∈ atoms do

8 Φ _u,a = minimizeLocalCost t (x u , D a )

finding optimal time-shift t in a window of size α Φ 9 W u,a = update W(x u , W u,. , D, Φ _u,a )

Simple gradient descent

10 x u = x u − f (D a , Φ u,a )W u,a

Matching pursuit like update

11 D = update D(W, D, Φ)

12 D = centerAtoms(D)

Centering procedure to make atoms comparable

Vincent Guigue Smart Card Analysis at the Human Scale 9/17

Reconstructed users:

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Code:

0 1 2 3 4 5 6

0 1 2 3 4

φ: 0

1

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

TS-NMF: OUTPUTS

Reconstruction process:

Atom selection ...

0 5 10 15 20 25

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Dictionary:

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Code:

0 1 2 3 4 5 6

0 1 2 3 4

φ:

0 1 2 3 4 5 6

0 1 2 3 4

Vincent Guigue Smart Card Analysis at the Human Scale 10/17

Reconstruction process:

+ shift

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Code:

0 1 2 3 4 5 6

0 1 2 3 4

φ: 0

1

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

TS-NMF: OUTPUTS

Reconstruction process:

0 5 10 15 20 25

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Dictionary:

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Code:

0 1 2 3 4 5 6

0 1 2 3 4

φ:

0 1 2 3 4 5 6

0 1 2 3 4

Vincent Guigue Smart Card Analysis at the Human Scale 10/17

Reconstruction process:

0 5 10 15 20 25

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Code:

0 1 2 3 4 5 6

0 1 2 3 4

φ: 0

1

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

TS-NMF: OUTPUTS

Reconstruction process:

0 5 10 15 20 25

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Dictionary:

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Code:

0 1 2 3 4 5 6

0 1 2 3 4

φ:

0 1 2 3 4 5 6

0 1 2 3 4

Vincent Guigue Smart Card Analysis at the Human Scale 10/17

Reconstruction process:

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

0 5 10 15 20

Code:

0 1 2 3 4 5 6

0 1 2 3 4

φ: 0

1

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

E VALUATION

◦ Impossible on training data:

- more degrees of freedom ⇒ less reconstruction error

◦ 9 weeks for learning, 4 weeks for testing

- Random initialization + non convex optimization ⇒ averaging performance on 5 runs

- Reconstruction of unseen data (=predictive skills) - Necessary but not sufficient

◦ ⇒ meaning/interpretation of the model is required - link with the number of parameters

Vincent Guigue Smart Card Analysis at the Human Scale 11/17

◦ 480 time intervals (3 minutes)

# parameters

◦ General model = 1-mean model ⇒ 0

◦ k-means, k = 16:

- 16 prototypes ∈ R ⁴⁸⁰ + 10k assignments ⇒ 17,680

◦ NMF, Z = 16:

- 16 prototypes ∈ R ⁴⁸⁰ + 10k × 16 weights ⇒ 167,680

◦ GMM = 3 Gaussian atoms (µ, σ ₁ ), (µ, σ ₂ ), (µ, σ ₃ ) centered

on each of the 480 time interval & weighted ⇒ 14,400,003

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

C OMPARISON

2 metrics

MSE Mean Squared Error (between real & estimated pdf) ML Likelihood of the logs according to the model

Model # param. MSE -train- (mean (std)) MSE -test- (mean (std))

General model 0 0.033 (0) 0.040 (0)

KMeans (16 clusters) 17,680 0.027 (6.3e-6) 0.038 (1.5e-5)

NMF 167,680 0.024 (7.7e-5) 0.036 (6.7e-5)

GMM 14,400,003 0.023 (0) 0.050 (0)

TS-NMF 320,960 0.016 (5.8e-4) 0.042 (8.9e-4)

Model # param. ML -train- (mean (std)) ML -test- (mean (std))

General 0 0.0038 (0) 0.0036(0)

KMeans (16 clusters) 17,680 0.010 (6.3e-6) 0.008 (5.7e-6)

NMF 167,680 0.013 (8.3e-5) 0.009 (3.8e-5)

GMM 14,400,003 0.027 (0) 0.018 (0)

TS-NMF 320,960 0.026 (9.3e-4) 0.016 (4.8e-4)

Vincent Guigue Smart Card Analysis at the Human Scale 13/17

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

10 20 30 40 50

0min 1h 2h 3h

◦ +/- variance

the population)

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

100 200 300 400

0h 5h 10h 15h 20h

◦ Most atoms correspond to

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

U SER MAPPING ON P ARIS MAP

According to the shapes of the atoms [Poussevin et al., 2014]

gare de lyon marcadet poissonniers

montgallet ranelagh

villejuif louis aragon aubervilliers pantin

porte de la chapelle

campo formio billancourt

chardon lagache

pyramides

couronnes danube

volontaires

saint maur telegraphe kleber

monceau

gare de l'est

lourmel

reaumur sebastopol ternes

maraichers

creteil pointe du lac charonne

porte de bagnolet

commerce

tuileries villiersrome

saint fargeau

vaugirard ecole militaire

buzenval chateau landon

bir hakeim

trinite d'estienne d'orves

olympiades bel air gaite

bolivar

pyrenees

pont marie rambuteau

sevres lecourbe pont de levallois becon

jacques bonsergent botzaris

porte de vincennes montparnasse

belleville franklin roosevelt

pigalle

reuilly diderot felix faure

convention

picpus

nationale pont de sevres

victor hugo

plaisance

jaures pont de neuilly

blanche jules joffrin les agnettes

ourcq

palais royal trocadero

madeleine

colonel fabien

le kremlin bicetre richelieu drouot

la chapelle europe

charenton ecoles porte doree saint michel

duroc bourse

varenne

mairie de montreuil

vaneau

creteil universite filles du calvaire

odeon temple wagram

8 mai 1945

porte de charenton sevres babylone

george v

pelleport concorde

malakoff rue etienne dolet

creteil prefecture rennes

porte de pantin

dupleix

michel bizot charles de gaulle etoile

bastille

mirabeau

corentin cariou

chaussee d'antin chateau rouge

chevaleret brochant

miromesnil

crimee

alexandre dumas

avenue emile zola opera saint philippe du roule

menilmontant place des fetes

edgar quinet chateau d'eau

saint sulpice la defense

mairie de clichy

gare du nord courcelles

glaciere

creteil l'echat porte de vanves

poissonniere

pont neuf notre dame de lorette gabriel peri

quai de la rapee javel

saint marcel

corvisart charles michels

maisons alfort stade louis blanc

basilique de saint denis

assemblee nationale

michel ange auteuil les sablons

cambronne malesherbes

goncourt strasbourg saint denis

maisons alfort les juilliottes porte des lilas

les gobelins

pierre et marie curie hoche porte de la villette

place monge argentine

saint sebastien froissartpere lachaise

boulogne pont de saint cloud eglise d'auteuil

gallieni

bibliotheque francois mitterrand place d'italie

bobigny pantin

jourdain laumiere

etienne marcel buttes chaumont place de clichy

bonne nouvelle

villejuif leo lagrange corentin celton

louise michel

rue des boulets

falguiere

riquet mairie de saint ouen

iena

louvre rivoli

la motte picquet grenelle sully morland

bobigny pablo picasso

berault avron sentier

austerlitz la muette

stalingrad carrefour pleyel

maubert mutualite

exelmans

quatre septembre boissiere

maison blanche bercy rue de la pompe

grands boulevards porte de clignancourt

michel ange molitor

fort d'aubervilliers

les halles

segur

saint jacques

ecole veterinaire de maisons alfort

villejuif paul vaillant couturier

saint francois xavier porte de montreuil

porte de versailles

quai de la gare champs elysees clemenceau

saint germain des pres

mairie des lilas

alma marceau

pre saint gervais saint lazare

pereire

porte d'orleans

chatillon montrouge anatole france

lamarck caulaincourt

pasteur raspail pernety

alesia marcel sembat

cardinal lemoine

denfert rochereau republique

mouton duvernet le peletier

eglise de pantin les courtilles asnieres gennevilliers

mabillon

croix de chavaux saint ambroise

porte de saint ouen

notre dame des champs

breguet sabin

saint mande porte de clichy

invalides

boucicaut

havre caumartin marx dormoy

porte de choisy liege

porte de saint cloud

vavin

liberte cour saint emilion saint placide

porte d'ivry mairie d'issy

porte maillot

la tour maubourg

censier daubenton cadet

jasmin

barbes rochechouart

jussieu porte dauphine

richard lenoir

ledru rollin arts et metiers

porte d'italie saint georges esplanade de la defense

saint denis universite

mairie d'ivry oberkampf

faidherbe chaligny

balard

saint paul

malakoff plateau de vanves

simplon

daumesnil

chateau de vincennes saint augustin

guy moquet

robespierre voltaire

porte de champerret garibaldi

hotel de ville

gambetta

rue du bac cite

saint denis porte de paris

parmentier

solferino chatelet

porte d'auteuil

tolbiac

dugommier anvers

nation abbesses

boulogne jean jaures

passy chemin vert

la fourche

philippe auguste

c01 c02 c03 c04 c05

Vincent Guigue Smart Card Analysis at the Human Scale 15/17

GLACIERE SAINT-JACQUES RASPAIL DENFERT-ROCHEREAU FALGUIERE PASTEUR VOLONTAIRES VAUGIRARD (ADOLPHE CHERIOU) CONVENTION PORTE DE VERSAILLES BALARDLOURMELBOUCICAUTFELIX FAURE

CHARLES MICHELS JAVEL PORTE DAUPHINE

LA MOTTE-PICQUET-GRENELLE COMMERCEAVENUE EMILE ZOLA DUPLEIX PASSY RANELAGHLA MUETTE

RUE DE LA POMPE (AVENUE GEORGES MANDEL)BOISSIERE TROCADEROIENAALMA-MARCEAU

MIROMESNIL SAINT-PHILIPPE-DU-ROULE FRANKLIN-D.ROOSEVELT GEORGE V KLEBER VICTOR HUGO

ARGENTINECHARLES DE GAULLE ETOILETERNESCOURCELLES MAIRIE DE CLICHY GABRIEL PERI-ASNIERES-GENNEVILLIERS LES AGNETTES-ASNIERES-GENNEVILLIERS LES COURTILLES-ASNIERES-GENNEVILLIERS

GARIBALDI MAIRIE DE SAINT-OUEN

CARREFOUR PLEYEL SAINT-DENIS-PORTE DE PARIS

BASILIQUE DE SAINT-DENIS

PORTE DE CLIGNANCOURTPORTE DE LA CHAPELLE

MARX DORMOY MARCADET-POISSONNIERS SIMPLON JULES JOFFRIN LAMARCK-CAULAINCOURT

CHAUSSEE D'ANTIN (LA FAYETTE)LE PELETIERCADET CHATEAU ROUGE

BARBES-ROCHECHOUART GARE DU NORD GARE DE L'EST POISSONNIERECHATEAU-LANDON

PORTE DE PANTIN OURCQ CORENTIN CARIOU CRIMEE RIQUET LA CHAPELLE

LOUIS BLANC STALINGRAD JAURES

LAUMIERE BOLIVAR

COLONEL FABIEN PORTE DES LILASMAIRIE DES LILAS

PORTE DE BAGNOLETGALLIENI (PARC DE BAGNOLET) PLACE DES FETES

BOTZARISDANUBE PRE SAINT-GERVAIS BUTTES-CHAUMONT

JOURDAIN TELEGRAPHE

VOLTAIRE (LEON BLUM) CHARONNE

PERE LACHAISE MENILMONTANT SAINT-MAUR

PHILIPPE AUGUSTE SAINT-FARGEAU PELLEPORT GAMBETTA BELLEVILLE

COURONNES PYRENEES

CROIX DE CHAVAUX (JACQUES DUCLOS) MAIRIE DE MONTREUIL

SAINT-MANDE-TOURELLEBERAULT CHATEAU DE VINCENNES

LIBERTE CHARENTON-ECOLES PORTE D'IVRY

PORTE DE VANVES MALAKOFF-PLATEAU DE VANVES CORENTIN-CELTON

MAIRIE D'ISSY MARCEL SEMBAT BILLANCOURT PONT DE SEVRES

BOULOGNE-JEAN JAURES BOULOGNE-PONT DE SAINT CLOUD

LES SABLONS (JARDIN D'ACCLIMATATION) PONT DE NEUILLY (AVENUE DE MADRID) ESPLANADE DE LA DEFENSE LA DEFENSE-GRANDE ARCHE

PORTE DE CHAMPERRET LOUISE MICHEL ANATOLE FRANCE PONT DE LEVALLOIS-BECON

PORTE MAILLOT WAGRAM PEREIRE-LEVALLOIS

BROCHANT PORTE DE CLICHYGUY MOQUET

PORTE DE SAINT-OUEN

ANVERS ABBESSES PIGALLE BLANCHE

TRINITE-D'ESTIENNE D'ORVESSAINT-GEORGESNOTRE-DAME-DE-LORETTE ROMEPLACE DE CLICHY

LA FOURCHE

CHATELET-LES HALLES AUBER

GARE DE LYON NATION CHARLES DE GAULLE ETOILE

LA DEFENSE-GRANDE ARCHE

SAINT-MICHEL NOTRE DAME

DENFERT-ROCHEREAU SAINT-MICHEL ODEON

MAUBERT-MUTUALITE CHATELET LES HALLES LOUVRE-RIVOLI

PONT-NEUF (LA MONNAIE) CITEHOTEL DE VILLE

CAMBRONNE SEVRES-LECOURBE SEGUR

SAINT-FRANCOIS-XAVIER DUROCVANEAUSEVRES-BABYLONE

RUE DU BAC

RENNES SAINT-SULPICESAINT-GERMAIN-DES-PRESMABILLON

PORTE DE LA VILLETTE AUBERVILLIERS-PANTIN (QUATRE CHEMINS)

FORT D'AUBERVILLIERS 8 MAI 1945

HOCHE EGLISE DE PANTINBOBIGNY-PANTIN (RAYMOND QUENEAU) BOBIGNY-PABLO PICASSO

PERNETY PLAISANCE

GAITEMONTPARNASSEEDGAR QUINETVAVIN SAINT-PLACIDE

NOTRE-DAME-DES-CHAMPS

ROBESPIERRE PORTE DE MONTREUIL MARAICHERS BUZENVAL RUE DES BOULETS - RUE DE MONTREUIL

PORTE DE VINCENNES PICPUS NATION

AVRON ALEXANDRE DUMAS MALESHERBES

MONCEAUVILLIERS

QUATRE SEPTEMBRE OPERA HAVRE-CAUMARTIN SAINT-LAZARE SAINT-LAZARE SAINT-AUGUSTIN EUROPELIEGE

PORTE DE SAINT-CLOUD PORTE D'AUTEUILMICHEL-ANGE-AUTEUILEGLISE D'AUTEUIL

MICHEL-ANGE-MOLITORCHARDON-LAGACHEMIRABEAU EXELMANS

JASMIN

RAMBUTEAU ARTS ET METIERS

JACQUES BONSERGENTGONCOURT (HOPITAL SAINT-LOUIS) TEMPLEREPUBLIQUE

OBERKAMPFPARMENTIER FILLES DU CALVAIRE SAINT-SEBASTIEN FROISSARTRICHARD LENOIRSAINT-AMBROISE

QUAI DE LA GARE CHEVALERET SAINT-MARCEL

AUSTERLITZQUAI DE LA RAPEEGARE DE LYON CHAMPS-ELYSEES-CLEMENCEAU

CONCORDE MADELEINE

BIR-HAKEIM (GRENELLE)ECOLE MILITAIRE LA TOUR MAUBOURG

INVALIDES

SAINT-DENIS-UNIVERSITE

VARENNE ASSEMBLEE NATIONALE

SOLFERINO TUILERIES

PALAIS ROYAL-MUSEE DU LOUVRE PYRAMIDESBOURSE

GRANDS BOULEVARDS (RUE MONTMARTRE) RICHELIEU-DROUOTBONNE NOUVELLESTRASBOURG-SAINT-DENIS

CHATEAU D'EAU SENTIERREAUMUR-SEBASTOPOL

ETIENNE-MARCEL

FAIDHERBE-CHALIGNY REUILLY-DIDEROT

MONTGALLET CENSIER-DAUBENTON

PLACE MONGE (JARDIN DES PLANTES) CARDINAL-LEMOINEJUSSIEU

SULLY-MORLAND PONT-MARIE (CITE DES ARTS)SAINT-PAUL (LE MARAIS)

BASTILLE CHEMIN VERTBREGUET-SABIN

LEDRU-ROLLIN

PORTE DOREE PORTE DE CHARENTON BERCY DUGOMMIER

MICHEL BIZOT DAUMESNILBEL-AIR

PORTE DE CHOISY PORTE D'ITALIE MAISON BLANCHE TOLBIAC

NATIONALE CAMPO-FORMIO LES GOBELINS

PLACE D'ITALIE CORVISART

COUR SAINT-EMILION

PORTE D'ORLEANS

BIBLIOTHEQUE FRANCOIS MITTERRAND MOUTON-DUVERNET

ALESIA OLYMPIADES

6h55 7h05 7h 6h46 7h23

I NTRODUCTION H ABITS / NMF T IME S HIFT -NMF Evaluation Conclusion

C ONCLUSION

Characterizing both habits and their schedules

◦ ... at the individual scale

◦ ⇒ valuable information on users

◦ Costly, but scalable for a transportation system

Perspective

◦ Work on the cost function...

◦ ... to discover less compact atoms (more meaningful)

Vincent Guigue Smart Card Analysis at the Human Scale 16/17

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