Tuia Hsom V2

lundi 30 juin 2008

Socio-economic data analysis withself-organizing maps

Tuia, D., Kaiser, C., da Cunha, A., Kanevski, M.

lundi 30 juin 2008Tuia, Kaiser, da Cunha, Kanevski, ICCSA 082

Urban metamorphosis

• Metropolization process

• Peri-urbanization, sub-urbanization

• Changes in the residential patterns

• Effects on the urban dynamics, on planning of transportnetworks,…


Understand the urban patterns

• To understand such patterns, the analysis of socio-economic landscape isnecessary

• 2 problems of interest:

– Find coherent ensembles of spatial unit in socio-economic space to learnthe socio-economic landscape : Classification! (today’s talk)

– Find areas where certain features are over-represented or emergingclusters of activities : Cluster detection! (paper)


Classification of socio-economic urbanfeatures

• Features are unequally distributed in space

• But they group in coherent socio-economic ensembles!

• High number of dimensions

• Non linear relationships

• Unsupervised problem– We don’t know the number of groups in advance– We do not have training information


What do we need?

• An efficient dimensionality reductor

• Capable of handling nonlinear relationships

• And an effective unsupervised classifier

SOM, PCA, Isomap, …

SOM, KPCA, …

HAC, K-means,,…


the HSOM


Self organizing maps

• SOM is a neural network used for nonlinear dimensionality reductionand unsupervised classification

• Gives a 2D-representation of a possibly high-dimensional data set

• Grid of neural cells. Each cell is associated with a n-dimensional vector(n is the data number of dimensions).

• Proposed by Kohonen (2001)


Self organizing maps (SOM)


Self organizing maps

• Initial weights are randomly attributed

• Neighbour hood function h(r) is used for updating BMU and itsneighbours to match better the input training data.

• h(r) decreases with distance to BMU.

• Radius r decreases during training(to 1 or even to 0 in the final stage).


Final result of SOM

Mapping of municipalitiesOn neurons: 75D to 2D.


Hierarchical clustering (HAC)

The neurons of the SOMare classified usingHierarchical clustering.

The number of classescan be easily found bythe analysis of thedendrogram


Dendrogram


Data

• Municipalities of canton de Vaud and Geneva(Switzerland)

• 427 municipalities

• 75 variables– 54 socio-economic (employment per branch)– 20 demographic (age structure)– 1 immigration (pct of foreigners)

• SOM size 16x16 neurons


Results (1)


Results (2)


Mapping of results

• Since each municipality can be mapped to a neuron,neurons’ classification can be transposed ingeographical space


Results (3)


Results (4)


Conclusion

• Complex socio-economic feature spaces can give informationabout urban patterns

• Nonlinear methods can reduce the dimensionality of suchspaces and allow their visualization.

• They produce a nonlinear transform of the input space

• Classification in the new space allow to group similarmunicipalities and draw tendencies of urban residentialpatterns.


Thank you for yourattention!

[email protected]://devis.tuia.googlepages.com

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