Hierarchical clustering through spatial interaction data. The case of commuting flows in South-Eastern France Giovanni Fusco, Matteo Caglioni - University of Nice Sophia-Antipolis

1. Hierarchical Clustering through Spatial Interaction Data. The Case of Commuting Flows in South-Eastern France Giovanni FUSCO, Matteo CAGLIONI UMR 6012 ESPACE, Université de Nice-Sophia Antipolis ICCSA 2011 June 20-23 2011, University of Cantabria, Santander, Spain.

2. 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 explicitly searched for centres not necessary 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 :

3. Complex Network Analysis: Community Detection 1. Local 2. Global Communities = clusters of nodes having stronger ties within them than with the rest of the network Communities = mesoscopic structures averaging microscopic properties of individual nodes and interacting in order to explain macroscopic structures 3. Node Similarity divisive optimisation spectral analysis 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 :

5. Communities through Modularity Optimization Density of links inside communities MODULARITY , one of the most widely used objective functions Q =  C (  C in / 2m – (  C tot / 2m) 2 ) Density of links between communities Blondel (2008) : a two step greedy algorithm repeated iteratively

6. Matrix of Flows between Spatial Units Detection of Dominant Flows : largest outflow towards a bigger unit Functional Areas through Dominant Flows (Nystuen and Dacey 1961) A B F Dominant Flows define hierarchical networks among spatial units (1 st level networks). Units are clustered within networks. Detection of networks of networks (2 nd level networks) Iteration of the method for flows between clusters

7. . . . Search of R 2 max 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 Rank of Flow Empirical Profile 1 Flow model  F 2 Flows model  F/2  F/2 3 Flows model  F/3  F/3  F/3

8. 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) 3 rd region in France. Recent emergence of two metropolitan systems reshaping urban structures.

11. 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.

14. Thank you for your attention giovanni.fusco @ unice.fr matteo.caglioni @ unice.fr