Hierarchical Clustering through SpatialHierarchical Clustering through SpatialInteraction Data. The Case of Commuting Flows inInteraction Data. The Case of Commuting Flows in

South-Eastern FranceSouth-Eastern France

Giovanni FUSCO, Matteo CAGLIONIUMR 6012 ESPACE, Université de Nice-Sophia Antipolis

ICCSA 2011 June 20-23 2011, University of Cantabria, Santander, Spain.

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Regional Science: Functional Area Detection

1. Deductive 2. Inductive

Overall : the importance of centres acting as focal points in the structuring of functional regions.

Centres are defined a priori

3. Hybrid

centres explicitlysearched for

centres notnecessary

Centres are determined as part of the algorithm

A priori list of centres which can be modified

A long disciplinary tradition identifying urban phenomena as the main force defining and shaping functional regions.

DOMINANT FLOWS(Nystuen and Dacey 1961)

3 families of methods :

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Complex Network Analysis: Community Detection

1. Local 2. Global

Communities = clusters of nodes having stronger ties within them than with the rest of the networkCommunities = mesoscopic structures averaging microscopic properties of individual nodes and interacting in order to explain macroscopic structures

3. NodeSimilarity

divisive optimisationspectralanalysis

MODULARITY OPTIMIZATION(Newman 2004)

Analogy with the geographic problem : spatial interaction matrices define complex relational networks among spatial units units = nodes flows = edges functional areas = communities

3 families of (inductive) methods :

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Hierarchical Clustering in Space

A shared interest of RS and CNA : the hierarchical structure of the partitioning.

Objective : detect nested partitions within space

Porter (2009) two notions make up the “structure” of a network:- Communities- Hierarchy

... Iterative application of partition methods

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Communities through Modularity Optimization

Density of links inside communities

MODULARITY, one of the most widely used objective functionsQ = C ( C in / 2m – (C tot / 2m)2 )

Density of links between communities

Blondel (2008) : a two step greedy algorithm repeated iteratively

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Matrix of Flows between Spatial Units

Detection of Dominant Flows: largest outflow towards a bigger unit

A

B F

Dominant Flows define hierarchical networks among spatial units (1st level networks).Units are clustered within networks.

Detection of networks of networks(2nd level networks)

Iteration of the method for flows between clusters

Functional Areas through Dominant Flows (Nystuen and Dacey 1961)

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Rank of Flow

Empirical Profile

. . .

Search of R2 max

1 Flow model

F 2 Flows model

F/2 F/23 Flows model

F/3F/3F/3

Are Dominant Flows Significant?

Threshold approach(Kipnis 1985, Rabino and

Occelli 1997)

MLA approach(Hagget et al. 1977)

Comparison of empirical profile with theoretical models where the total flow is concentrated on the first k flows

Only dominant flows beyond given absolute threshold and relative threshold (as % of total out-flow, resident population, etc.) are significant

Only dominant flows concerning mono-polarized units are significant

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Official Employment Areas in the PACA Region

An approximation of functional areas defined through a spurious deductive method (main job centres + commuter containment + administrative boundaries)

Briançon

Embrun

Gap

Barcelonnette

Sisteron

Digne

Avignon

Arles

Aix

Marseille

Toulon

NiceMonaco

Menton

DraguignanCannes

Salon

Orange

Manosque

Carpentras

BrignolesFréjus

Pertuis

Martigues

Châteaurenard

Antibes

Marignane

Manosque

Digne-les-Bains

Briançon

Gap

Cannes-Antibes

Menton

Nice

Arles

Aix-en-Provence

Marignane

Châteaurenard

Martigues

Salon-de-Provence

Marseille

Toulon

Fréjus

Draguignan

Brignoles

Orange

Carpentras

Pertuis

Avignon

Employment Areas by INSEE for the 1999 census

0 30 60 Km

Alpes de Haute Provence Department:

Hautes Alpes Department:

Alpes Maritimes Department:

Bouches du Rhone Department:

Var Department:

Vaucluse Department:

G. Fusco - UMR ESPAC

3rd region in France.Recent emergence of two metropolitan systems reshaping urban structures.

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Modularity Optimization

Compact communities at both levels of analysis

Matteo CAGLIONI, Giovanni FUSCO - UMR ESPACE - 2010

Alpes Maritimes

Var

Bouches du Rhône

Vaucluse

Alpes de Haute Provence

Department boundary(and official names)

Functional Areas defined by ModularityOptimisation of Commuting Flows in 1999

Boundary of level 2 communities

Level 1 communities

Level 2 communities

0 5025 Km

Hautes Alpes

5 level 2 communities :- 2 roughly correspond to Department boundaries- a unified alpine space- a vast metropolitan area in the South-West

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Significant Dominant Flows (Thresholds)

Comparing the two methods : - very good agreement (Avignon, Marseille)- the Nice network stretches in the West- the alpine space is fragmented in two main networks.

The internal structure of networks :- Morphological differences between the complex structure around Marseille and the simpler one around Nice.

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Significant Dominant Flows (MLA)

Not a complete partition of space, only cores of functional area which are strictly dominated.

Only Marseille and Nice are capable of structuring large networks.

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Iterating the MLA Algorithm further

The only method not converging to a unified coverage of the regional space.

The role of interface multipolarized units.

3 different spatial structures :- a vast hierarchical metropolitan area around Marseille- 4 relatively independent networks in the French Riviera- a highly fragmented alpine space

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Conclusions

Complementary pictures for a given regional space...near the insight of the analysis to the complexity of the geographical reality under investigation

Modularity Optimisation Dominant Flows

- a global method: optimizes the partition of space- produces compact areas

- detects the internal structure of functional areas at every level- a local method: detects the percolation of domination basins- MLA approach: hinders percolation detection but highlights interfaces

Perspectives : extending the comparison of methods regional science / complex network analysis. Evaluating optimality of RS methods and geographical meaning of CNA methods.

2 methods detecting hierarchically nested partitions of space

G. Fusco, M. Caglioni “Hierarchical Clustering through Spatial Interaction Data”

Thank youThank youfor your attentionfor your attention

giovanni.fusco @ unice.frgiovanni.fusco @ unice.frmatteo.caglioni @ unice.frmatteo.caglioni @ unice.fr