policentrometer

Lorenzo GabrielliDaniele Fadda • Giulio RossettiMirco Nanni • Fosca Giannotti

Dino Pedreschi • Leonardo Piccini

State of the art

Morphological analysis Functional analysis

A big data proposal

Example of individual mobility observation

Tuscany municipalitiesCoverage space

150KNumber of Vehicles

February March 2014Time

12 mlnTrips

MobilityOD MATRIX

Problem definition (by domain expert)

◉ Q1: How can we automatically identify groups of contiguous areas having inner mobility higher than the surrounding network?

◉ Q2: How many communities we are able to identify by looking at human vehicular Mobility?

◉ Q3: Which are the most relevant characteristics of such communities? Which are their sizes and internal densities?

Requirement: maximise self-contained traffic

i=1 i=10 i=20

Our proposal: Agglomerative process

Red Communities/Regions created in the last iterationGrey Communities/Regions created in previous iterations

Iteration n

Local quality score: self containment index

Iteration n

Local quality score: self containment index

Evaluationn (t,z)= tUz/(t*+*z)

Iteration n

Local quality score: self containment index

Evaluationn (t,z)= tUz/(t*+*z)

50%52%

48% 40%

aUb = 50% bUc = 52% cUd = 48% dUe = 40%

Iteration n

Local quality score: self containment index

Evaluationn (t,z)= tUz/(t*+*z)

Iteration n+1

50%52%

48% 40%

aUb = 50% bUc = 52% cUd = 48% dUe = 40%

Cut criteria: maximise global quality scoreOptimum iteration to end the algorithm is suggested by the first local maximum of S

Real Expected

Flows of vehicles by the municipality i to municipality j

Cut criteria: maximise global quality scoreOptimum iteration to end the algorithm is suggested by the first local maximum of S

Real Expected

Flows of vehicles by the municipality i to municipality j

Cut criteria: maximise global quality score

Total outgoing flows starting from Municipality i

Optimum iteration to end the algorithm is suggested by the first local maximum of S

Real Expected

Flows of vehicles by the municipality i to municipality j

Cut criteria: maximise global quality score

Total outgoing flows starting from Municipality i

incoming flows in Municipality j

Optimum iteration to end the algorithm is suggested by the first local maximum of S

Real Expected

Flows of vehicles by the municipality i to municipality j

Cut criteria: maximise global quality score

Total outgoing flows starting from Municipality i

incoming flows in Municipality j

Total flows in the network

Optimum iteration to end the algorithm is suggested by the first local maximum of S

Real Expected

Policentric cities RESULTS161

24 Communities discovered

State-of-the-art

◉ Clustering problem similarity using Distance Matrix

◉ Community detection problem Network built using trips [OD Matrix]

Competitors

Network Based

◉Louvain MODULARITY BASED

◉Demon EGO NETWORK BASED

◉Infohiermap CONDUCTANCE BASED

Cluster Based

◉DBSCAN

◉KMedoid

NETWORK approachIn order to compare our approach with the state of art we observe those measures: internal density conductance modularity

Measure min/max/avg/std

Louvain Policentrometer

Internal Edge Density 0.15/0.32/0.21/0.07 0.27/0.75/0.49/0.20

Conductance 0.014/0.58/0.38/0.27 0.014/0.97/0.88/0.19

Modularity 0.16 -0.06

Network approach LOUVAIN

Drawback too few and too big communities

Measure min/max/avg/std

Louvain Policentrometer

Internal Edge Density 0.15/0.32/0.21/0.07 0.27/0.75/0.49/0.20

Conductance 0.014/0.58/0.38/0.27 0.014/0.97/0.88/0.19

Modularity 0.16 -0.06

Network approach LOUVAIN

Measure min/max/avg/std

Demon Policentrometer

Internal Edge Density 0.12/0.50/0.28/0.18 0.27/0.75/0.49/0.20

Conductance 0.37/0.90/0.50/0.17 0.014/0.97/0.88/0.19

Modularity -0.38 -0.06

Network approach DEMON

Drawback too overlapping communities

Measure min/max/avg/std

Demon Policentrometer

Internal Edge Density 0.12/0.50/0.28/0.18 0.27/0.75/0.49/0.20

Conductance 0.37/0.90/0.50/0.17 0.014/0.97/0.88/0.19

Modularity -0.38 -0.06

Network approach DEMON

Measure min/max/avg/std

INFOHIERMAP Policentrometer

Internal Edge Density

0.09/0.50/0.18/0.10 0.27/0.75/0.49/0.20

Conductance 0.90/0.98/0.95/0.24 0.014/0.97/0.88/0.19

Modularity 0.006 -0.06

Network approach INFOHIERMAP

Drawback non contiguous communities

Measure min/max/avg/std

INFOHIERMAP Policentrometer

Internal Edge Density

0.09/0.50/0.18/0.10 0.27/0.75/0.49/0.20

Conductance 0.90/0.98/0.95/0.24 0.014/0.97/0.88/0.19

Modularity 0.006 -0.06

Network approach INFOHIERMAP

Lesson Learned

Comparison with network algorithms:

◉ Too few communities

◉ Too big

◉ Not contiguos

CLUSTERING approachpartitions obtained with K-medoid and DBSCAN cluster methods

K MEDOIDDrawback non contiguous communities

k=2 k=3 k=6

DBSCAN

dbscan communities

DBSCAN

optimal choice for the two methods

Drawback: Policentrometer get a higher global score than DBSCAN

dbscan communities

◉ Flow inclusion based problem definition

◉ Ad hoc algorithm that outperforms state-of-the-art methods

◉ Preliminary evaluation of results

Conclusion

Ongoing work: validation24 communities

Population density systematic Non systematic

ADDITIONS◉ Comparison with optimization methods◉ Seeding using municipalities with more than 50.000 people

INTEGRATIONS

NEW APPLICATIONS

◉ Public transport system data

◉ Domain indipendent◉ All Geo OD Matrix can be used

Any questions ?

Thanks!