exploratory interactive tools for spatial data analysis interactive tools for spatial data analysis...

Exploratory interactive tools for spatial data analysis

Exploratory interactive tools for spatial dataanalysis

Thibault LAURENT, Anne RUIZ-GAZEN and ChristineTHOMAS-AGNAN

GREMAQ, Toulouse School of Economics

8 juillet 2009

T. Laurent, A. Ruiz-Gazen and C. Thomas-Agnan Exploratory interactive tools for spatial data analysis


Introduction

Plan

1 Introduction

2 GeoXp : Interactivity between statistic plots with maps

3 Innovations of GeoXp

4 Perspectives



Introduction

Data Set

A data set of n observations and p variables (discrete, continuous) :

VariablesIndividuals 1 . . . p

1 x11 . . . x1p

2 x21 . . . x2p...

... . . ....

n xn1 . . . xnp

Each observation is associated to a a spatial object (a point, a lineor a polygon).



Introduction

Definition and objectives of Spatial Exploratory DataAnalysis (SEDA)

Definition : combine information given by techniques of EDAwith spatial information using mapping, interactivity betweenstatistical plots with maps or by creating new methods usingfor example neighborhood matrices.

Objectives : give qualitative response to the usual problems ofspatial analysis like detection of spatial autocorrelation,detection of local or global extreme values, detection ofspatial heterogeneity...



Introduction

Mapping with maptools packages

Soil Sample near the Meuse river

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Type of soil

123

0 1000 m

E

N

W

S

Income

<=8.7]8.7;11.8]]11.8;16]]16;22.2]>22.2

Income discretisated by Jenks' method



Introduction

Mapping with maptools and PBSmapping packages

Core−periphery dummy

01

Core−periphery / Income in Columbus OH

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Income

2.13.23.74.35.6

−127.5 −127 −126.5 −12648

.549

49.5

Longitude (°)

Latit

ude

(°)

500−800 m800−1200 m

1200−1600 m

LTS Survey Tracks

VancouverIsland



Introduction

Some advices

Which projection system ? Which reference system (veryimportant to give units to the distances) ?

Choice of palettes is important (see RColorBrewer package).

How find class intervals for continuous numerical variables :classInt package (“equal interval”, “quantile”, “K-means”,etc).

Interpolation can be useful to have a global view of spatialdistribution of : variables, residuals, coefficients of GWRmodel, etc (see package akima).



Interactivity

Interactivity between statistic plots with maps

1 Introduction



4 Perspectives



Interactivity

Package GeoXp

GeoXp (C. Thomas-Agnan et al.), an R package for interactiveexploratory spatial data analysis : it links dynamicallystatistical plots like boxplot, histogram, scatterplot, etc. witha map.

Selection of a zone on the map results in the automatichighlighting of the corresponding points on the statisticalgraph.

Selection of a portion of the graph results in the automatichighlighting of the corresponding sites on the map.



Interactivity

EDA functions

The main statistical plots of EDA have been included in GeoXp :

Descriptive functions : univariate or bivariate graphs such ashistogram, barplot, scatterplot, etc.

Multivariate functions : principal component analysis, clusteranalysis.



Interactivity

Example 1 : Kernel Density function estimate (1)

Plot kernel density function estimates for the whole distributionand for the distribution of the sites selected by the user (by pointsor polygons) on the map (see function bkde in packageKernSmooth) in red on the graphic.

densitymap(longitude,latitude,variable,...)

0 2000 4000 6000 8000

0e+

002e

−04

4e−

046e

−04

8e−

04

Average selling price per m2 in 2007



Interactivity

Example 1 : Kernel Density function estimate (2)

User selects an interval on the density curve by mouse clicking onthe graph on the extremities of interval and selected sites are thenrepresented in red on the map.

0 2000 4000 6000 8000

0.00

000

0.00

010

0.00

020

0.00

030

Average selling price per m2 in 2007



Interactivity

Example 2 : Principal component analysis (1)

The function pcamap draws the plots summarizing a generalizedPrincipal Component Analysis (PCA) and permits aninteractivity between the scatterplot of the individuals projected ona chosen principal component plane with the map.

pcamap(longitude,latitude,mat.var,...)

−1.0 −0.5 0.0 0.5 1.0

−1.

0−

0.5

0.0

0.5

1.0

component 1 : 52%

com

pone

nt 2

: 18

%

HOVAL : 82%

INC : 81%

CRIME : 75%

OPEN : 81%

PLUMB : 92%

DISCBD : 91%

−2 0 2 4

−1

01

23

4component 1 : 52%

com

pone

nt 2

: 18

%

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94%

mat.var=log(1+c("HOVAL","INC","CRIME","OPEN","PLUMB","DISCBD"))T. Laurent, A. Ruiz-Gazen and C. Thomas-Agnan Exploratory interactive tools for spatial data analysis


Interactivity

Example 2 : Principal component analysis (1)

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01

1005

1017

1016

1048

0 1

CP

05

1015

2025



Interactivity

Other Examples



Interactivity

Specific statistical plots

Statistical plots specific to spatial analysis :

Geostatistic functions : angle plot, drift plot.

Spatial Econometric functions : Moran plot, neighbour plot



Interactivity

Drift map (Cressie, 1993)

driftmap(longitude,latitude,variable,...)



Interactivity

Angle plot (Brunsdon, 1998)

represents the absolute difference between the values of avariable at two sites si and sj as a function of the anglebetween vector ~si sj and the x-axis,

possibility to draw only couples of sites whose absolutedifference is larger than some α regression quantile smoothingsplines.



Interactivity

Angle plot (Brunsdon, 1998)

angleplotmap(longitude,latitude,variable,...)

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copper

1254010

topsoil copper concentration, ppm.

abso

lut m

agni

tude

0 ππ 4 ππ 2 3ππ 4 ππ

020

4060

8010

0

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Innovations

Innovations of GeoXp

1 Introduction



4 Perspectives



Innovations

Analysis of a neighborhood structure (1)

barnbmap(obj.nb, coords,...)

2 3 4 5 6 7 8 9 10Number of

neighbors by unit

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Innovations

Analysis of a neighborhood structure (2)

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Innovations

Moran plot

moranplotmap(long, lat, var, mat.W, ...)Test of spatial autocorrelation (gaussian version or permutation test)

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I = 0.49 (p − value < 0.0001)T. Laurent, A. Ruiz-Gazen and C. Thomas-Agnan Exploratory interactive tools for spatial data analysis


Innovations

Pairwise map (Filmozer et al.)

“Local outliers” : observations which differ from their neighbours.We propose to use pairwise robust Mahalanobis distances :

MD(xi ; xj ; C ) = {(xi − xj)′C−1(xi − xj)}1/2

R-packages : mvoutliers and rrcov.



Innovations

Pairwise map (Filmozer et al.)

pairwisemap(long, lat, obj.nb, mat.var,...)

Pairwise spatial distances

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mat.var=log(1+c("HOVAL","INC","CRIME","OPEN","PLUMB","DISCBD"))T. Laurent, A. Ruiz-Gazen and C. Thomas-Agnan Exploratory interactive tools for spatial data analysis


Perspectives

Perspectives

1 Introduction



4 Perspectives



Perspectives

Perspectives (1)

Use the sp norm (with the help of Roger Bivand)

0 20 40 60

02

46

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residential burglaries and vehicle thefts per thousand



Perspectives

Perspectives (2)

Add zoom

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Perspectives

Perspectives (3)

A new interface (close to Rcmdr window)

Add a number “unlimited” of interactive graphic window as inGeoDa

Add origin-destination flow graphics

A R vignette should appear on CRAN soon

Thanks for attention ! (my e-mail :[email protected])


exploratory interactive tools for spatial data analysis interactive tools for spatial data analysis...

Documents