neig {ade4}R Documentation

Neighbourhood Graphs

Description

neig creates objects of class neig with :
a list of edges
a binary square matrix
a list of vectors of neighbours
an integer (linear and circular graphs)
a data frame of polygons (area)

scores.neig returns the eigenvectors of neighbouring,
orthonormalized scores (null average, unit variance 1/n and null covariances) of maximal autocorrelation.

nb2neig returns an object of class neig using an object of class nb in the library 'spdep'

neig2nb returns an object of class nb using an object of class neig

neig2mat returns the incidence matrix between edges (1 = neighbour ; 0 = no neighbour)

neig.util.GtoL and neig.util.LtoG are utilities.

Usage

neig(list = NULL, mat01 = NULL, edges = NULL,
    n.line = NULL, n.circle = NULL, area = NULL)

scores.neig  (obj) 
## S3 method for class 'neig':
print(x, ...) 
## S3 method for class 'neig':
summary(object, ...)
nb2neig (nb)
neig2nb (neig)
neig2mat (neig)

Arguments

list a list which each component gives the number of neighbours
mat01 a symmetric square matrix of 0-1 values
edges a matrix of 2 columns with integer values giving a list of edges
n.line the number of points for a linear plot
n.circle the number of points for a circular plot
area a data frame containing a polygon set (see area.plot)
nb an object of class 'nb'
neig, x, obj, object an object of class 'neig'
... further arguments passed to or from other methods

Author(s)

Daniel Chessel

References

Thioulouse, J., D. Chessel, and S. Champely. 1995. Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environmental and Ecological Statistics, 2, 1–14.

Examples

data(mafragh)
if (require(deldir, quietly=TRUE)) {
    par(mfrow = c(2,1))
    provi <- deldir(mafragh$xy)
    provi.neig <- neig(edges = provi$delsgs[,5:6])
    
    s.label(mafragh$xy, neig = provi.neig, inc = FALSE, 
        addax = FALSE, clab = 0, cnei = 2)
    dist <- apply(provi.neig, 1, function(x) 
        sqrt(sum((mafragh$xy[x[1],] - mafragh$xy[x[2],])^2)))
    #hist(dist, nclass = 50)
    mafragh.neig <- neig(edges = provi.neig[dist<50,])
    s.label(mafragh$xy, neig = mafragh.neig, inc = FALSE, 
        addax = FALSE, clab = 0, cnei = 2)
    par(mfrow = c(1,1))
    
    data(irishdata)
    irish.neig <- neig(area = irishdata$area)
      summary(irish.neig)
      print(irish.neig)
    s.label(irishdata$xy, neig = irish.neig, cneig = 3,
        area = irishdata$area, clab = 0.8, inc = FALSE)
    
    irish.scores <- scores.neig(irish.neig)
    par(mfrow = c(2,3))
    for (i in 1:6) s.value(irishdata$xy, irish.scores[,i],
        inc = FALSE, grid = FALSE, addax = FALSE,
        neig = irish.neig,
        csi = 2, cleg = 0, sub = paste("Eigenvector ",i), csub = 2)
    par(mfrow = c(1,1))
    
    a.neig <- neig(n.circle = 16)
    a.scores <- scores.neig(a.neig)
    xy <- cbind.data.frame(cos((1:16) * pi / 8), sin((1:16) * pi / 8))
    par(mfrow = c(4,4))
    for (i in 1:15) s.value(xy, a.scores[,i], neig = a.neig, 
        csi = 3, cleg = 0)
    par(mfrow = c(1,1))
    
    a.neig <- neig(n.line = 28)
    a.scores <- scores.neig(a.neig)
    par(mfrow = c(7,4))
    par(mar = c(1.1,2.1,0.1,0.1))
    for (i in 1:27) barplot(a.scores[,i], col = grey(0.8))
}
par(mfrow = c(1,1))

if (require(maptools, quiet = TRUE) & require(spdep, quiet = TRUE)) {
    data(columbus)
    par(mfrow = c(2,1))
    par(mar = c(0.1,0.1,0.1,0.1))
    plot(col.gal.nb, coords)
    s.label(data.frame(coords), neig = neig(list = col.gal.nb),
        inc = FALSE, clab = 0.6, cneig = 1)
    par(mfrow = c(1,1))
    
    data(mafragh)
    maf.rel <- relativeneigh(as.matrix(mafragh$xy))
    maf.rel <- graph2nb(maf.rel)
    s.label(mafragh$xy, neig = neig(list = maf.rel), inc = FALSE,
        clab = 0, addax = FALSE, cne = 1, cpo = 2)
    
    par(mfrow = c(2,2))
    w <- matrix(runif(100), 50, 2)
    x.gab <- gabrielneigh(w)
    x.gab <- graph2nb(x.gab)
    s.label(data.frame(w), neig = neig(list = x.gab), inc = FALSE,
        clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "relative")
    x.rel <- relativeneigh(w)
    x.rel <- graph2nb(x.rel)
    s.label(data.frame(w), neig = neig(list = x.rel), inc = FALSE,
        clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "Gabriel")
    k1 <- knn2nb(knearneigh(w))
    s.label(data.frame(w), neig = neig(list = k1), inc = FALSE,
        clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "k nearest neighbours")
    
    all.linked <- max(unlist(nbdists(k1, w)))
    z <- dnearneigh(w, 0, all.linked)
    s.label(data.frame(w), neig = neig(list = z), inc = FALSE,
        clab = 0, addax = FALSE, cne = 1, cpo = 2, 
        sub = "Neighbourhood contiguity by distance")
}
par(mfrow = c(1,1))

Worked out examples


> library(ade4)
> ### Name: neig
> ### Title: Neighbourhood Graphs
> ### Aliases: neig neig.util.GtoL neig.util.LtoG print.neig summary.neig
> ###   scores.neig nb2neig neig2nb neig2mat
> ### Keywords: utilities
> 
> ### ** Examples
> 
> data(mafragh)
> if (require(deldir, quietly=TRUE)) {
+     par(mfrow = c(2,1))
+     provi <- deldir(mafragh$xy)
+     provi.neig <- neig(edges = provi$delsgs[,5:6])
+     
+     s.label(mafragh$xy, neig = provi.neig, inc = FALSE, 
+         addax = FALSE, clab = 0, cnei = 2)
+     dist <- apply(provi.neig, 1, function(x) 
+         sqrt(sum((mafragh$xy[x[1],] - mafragh$xy[x[2],])^2)))
+     #hist(dist, nclass = 50)
+     mafragh.neig <- neig(edges = provi.neig[dist<50,])
+     s.label(mafragh$xy, neig = mafragh.neig, inc = FALSE, 
+         addax = FALSE, clab = 0, cnei = 2)
+     par(mfrow = c(1,1))
+     
+     data(irishdata)
+     irish.neig <- neig(area = irishdata$area)
+       summary(irish.neig)
+       print(irish.neig)
+     s.label(irishdata$xy, neig = irish.neig, cneig = 3,
+         area = irishdata$area, clab = 0.8, inc = FALSE)
+     
+     irish.scores <- scores.neig(irish.neig)
+     par(mfrow = c(2,3))
+     for (i in 1:6) s.value(irishdata$xy, irish.scores[,i],
+         inc = FALSE, grid = FALSE, addax = FALSE,
+         neig = irish.neig,
+         csi = 2, cleg = 0, sub = paste("Eigenvector ",i), csub = 2)
+     par(mfrow = c(1,1))
+     
+     a.neig <- neig(n.circle = 16)
+     a.scores <- scores.neig(a.neig)
+     xy <- cbind.data.frame(cos((1:16) * pi / 8), sin((1:16) * pi / 8))
+     par(mfrow = c(4,4))
+     for (i in 1:15) s.value(xy, a.scores[,i], neig = a.neig, 
+         csi = 3, cleg = 0)
+     par(mfrow = c(1,1))
+     
+     a.neig <- neig(n.line = 28)
+     a.scores <- scores.neig(a.neig)
+     par(mfrow = c(7,4))
+     par(mar = c(1.1,2.1,0.1,0.1))
+     for (i in 1:27) barplot(a.scores[,i], col = grey(0.8))
+ }
deldir 0.0-12 

     Please note: The process for determining duplicated points
     has changed from that used in version 0.0-9 (and previously).

Neigbourhood undirected graph
Vertices: 25 
Degrees: 5 5 4 4 1 5 3 6 5 5 5 4 4 2 3 7 3 7 7 3 8 4 6 4 4 
Edges (pairs of vertices): 57 
S01 .
S02 ..
S03 ...
S04 ....
S05 .....
S06 ..1...
S07 ..11...
S08 1.......
S09 1........
S10 1......11.
S11 .1..1......
S12 ..11..1.....
S13 .1........1..
S14 ..............
S15 .....1.........
S16 .1.....1.....1..
S17 .1...........1.1.
S18 .....1.1.1.....1..
S19 .....1....1.1.1..1.
S20 ..........1...1...1.
S21 ..11.1..11.1.....1...
S22 ...1....1...........1.
S23 .1.....1....1..1.11....
S24 1.......1............1..
S25 1......1.......1.......1.
> par(mfrow = c(1,1))
> 
> if (require(maptools, quiet = TRUE) & require(spdep, quiet = TRUE)) {
+     data(columbus)
+     par(mfrow = c(2,1))
+     par(mar = c(0.1,0.1,0.1,0.1))
+     plot(col.gal.nb, coords)
+     s.label(data.frame(coords), neig = neig(list = col.gal.nb),
+         inc = FALSE, clab = 0.6, cneig = 1)
+     par(mfrow = c(1,1))
+     
+     data(mafragh)
+     maf.rel <- relativeneigh(as.matrix(mafragh$xy))
+     maf.rel <- graph2nb(maf.rel)
+     s.label(mafragh$xy, neig = neig(list = maf.rel), inc = FALSE,
+         clab = 0, addax = FALSE, cne = 1, cpo = 2)
+     
+     par(mfrow = c(2,2))
+     w <- matrix(runif(100), 50, 2)
+     x.gab <- gabrielneigh(w)
+     x.gab <- graph2nb(x.gab)
+     s.label(data.frame(w), neig = neig(list = x.gab), inc = FALSE,
+         clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "relative")
+     x.rel <- relativeneigh(w)
+     x.rel <- graph2nb(x.rel)
+     s.label(data.frame(w), neig = neig(list = x.rel), inc = FALSE,
+         clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "Gabriel")
+     k1 <- knn2nb(knearneigh(w))
+     s.label(data.frame(w), neig = neig(list = k1), inc = FALSE,
+         clab = 0, addax = FALSE, cne = 1, cpo = 2, sub = "k nearest neighbours")
+     
+     all.linked <- max(unlist(nbdists(k1, w)))
+     z <- dnearneigh(w, 0, all.linked)
+     s.label(data.frame(w), neig = neig(list = z), inc = FALSE,
+         clab = 0, addax = FALSE, cne = 1, cpo = 2, 
+         sub = "Neighbourhood contiguity by distance")
+ }
> par(mfrow = c(1,1))
> 
> 
> 
> 

[Package ade4 Index]