skater: Spatial 'K'luster Analysis by Tree Edge Removal

Description

This function implements a SKATER procedure for spatial clustering analysis. This procedure essentialy begins with an edges set, a data set and a number of cuts. The output is an object of 'skater' class and is valid for input again.

Usage

skater(edges, data, ncuts, crit, vec.crit, method = c("euclidean", 
    "maximum", "manhattan", "canberra", "binary", "minkowski", 
    "mahalanobis"), p = 2, cov, inverted = FALSE)

Arguments

edges

A matrix with 2 colums with each row is an edge

data

A data.frame with data observed over nodes.

ncuts

The number of cuts

crit

A scalar ow two dimensional vector with with criteria for groups. Examples: limits of group size or limits of population size. If scalar, is the minimum criteria for groups.

vec.crit

A vector for evaluating criteria.

method

Character or function to declare distance method. If method is character, method must be "mahalanobis" or "euclidean", "maximum", "manhattan", "canberra", "binary" or "minkowisk". If method is one of "euclidean", "maximum", "manhattan", "canberra", "binary" or "minkowski", see dist for details, because this function as used to compute the distance. If method="mahalanobis", the mahalanobis distance is computed between neighbour areas. If method is a function, this function is used to compute the distance.

The power of the Minkowski distance.

cov

The covariance matrix used to compute the mahalanobis distance.

inverted

logical. If 'TRUE', 'cov' is supposed to contain the inverse of the covariance matrix.

Value

A object of skater class with:

groups

A vector with length equal the number of nodes. Each position identifies the group of node

edges.groups

A list of length equal the number of groups with each element is a set of edges

not.prune

A vector identifying the groups with are not candidates to partition.

candidates

A vector identifying the groups with are candidates to partition.

ssto

The total dissimilarity in each step of edge removal.

References

Assuncao, R.M., Lage J.P., and Reis, E.A. (2002). Analise de conglomerados espaciais via arvore geradora minima. Revista Brasileira de Estatistica, 62, 1-23.

Assuncao, R. M, Neves, M. C., Camara, G. and Freitas, C. da C. (2006). Efficient regionalization techniques for socio-economic geographical units using minimum spanning trees. International Journal of Geographical Information Science Vol. 20, No. 7, August 2006, 797-811

Examples

Run this code

# NOT RUN {
### loading data
require(maptools)
bh <- readShapePoly(system.file("etc/shapes/bhicv.shp",
      package="spdep")[1])
### data standardized 
dpad <- data.frame(scale(bh@data[,5:8]))

### neighboorhod list
bh.nb <- poly2nb(bh)

### calculating costs
lcosts <- nbcosts(bh.nb, dpad)

### making listw
nb.w <- nb2listw(bh.nb, lcosts, style="B")

### find a minimum spanning tree
mst.bh <- mstree(nb.w,5)

### the mstree plot
par(mar=c(0,0,0,0))
plot(mst.bh, coordinates(bh), col=2,       
     cex.lab=.7, cex.circles=0.035, fg="blue")
plot(bh, border=gray(.5), add=TRUE)

### three groups with no restriction
res1 <- skater(mst.bh[,1:2], dpad, 2)

### groups size
table(res1$groups)

### the skater plot
par(mar=c(0,0,0,0))
plot(res1, coordinates(bh), cex.circles=0.035, cex.lab=.7)

### the skater plot, using other colors
plot(res1, coordinates(bh), cex.circles=0.035, cex.lab=.7,
     groups.colors=rainbow(length(res1$ed)))

### the Spatial Polygons plot
plot(bh, col=heat.colors(length(res1$edg))[res1$groups])

### EXPERT OPTIONS

### more one partition
res1b <- skater(res1, dpad, 1)

### length groups frequency
table(res1$groups)
table(res1b$groups)

### thee groups with minimum population 
res2 <- skater(mst.bh[,1:2], dpad, 2, 200000, bh@data$Pop)

### thee groups with minimun number of areas
res3 <- skater(mst.bh[,1:2], dpad, 2, 3, rep(1,nrow(bh@data)))

### thee groups with minimun and maximun number of areas
res4 <- skater(mst.bh[,1:2], dpad, 2, c(20,50), rep(1,nrow(bh@data)))

table(res2$groups)
table(res3$groups)
table(res4$groups)

### if I want to get groups with 20 to 40 elements
res5 <- skater(mst.bh[,1:2], dpad, 2,
   c(20,40), rep(1,nrow(bh@data))) ## DON'T MAKE DIVISIONS 
table(res5$groups)

### In this MST don't have groups with this restrictions
### In this case, first I do one division
### with the minimun criteria
res5a <- skater(mst.bh[,1:2], dpad, 1, 20, rep(1,nrow(bh@data))) 
table(res5a$groups)

### and do more one division with the full criteria
res5b <- skater(res5a, dpad, 1, c(20, 40), rep(1,nrow(bh@data)))
table(res5b$groups)

### and do more one division with the full criteria
res5c <- skater(res5b, dpad, 1, c(20, 40), rep(1,nrow(bh@data)))
table(res5c$groups)

### It don't have another divison with this criteria
res5d <- skater(res5c, dpad, 1, c(20, 40), rep(1,nrow(bh@data)))
table(res5d$groups)

# }
# NOT RUN {
data(boston)
bh.nb <- boston.soi
dpad <- data.frame(scale(boston.c[,c(7:10)]))
### calculating costs
system.time(lcosts <- nbcosts(bh.nb, dpad))
### making listw
nb.w <- nb2listw(bh.nb, lcosts, style="B")
### find a minimum spanning tree
mst.bh <- mstree(nb.w,5)
### three groups with no restriction
system.time(res1 <- skater(mst.bh[,1:2], dpad, 2))
library(parallel)
nc <- detectCores(logical=FALSE)
# set nc to 1L here
if (nc > 1L) nc <- 1L
coresOpt <- get.coresOption()
invisible(set.coresOption(nc))
if(!get.mcOption()) {
# no-op, "snow" parallel calculation not available
  cl <- makeCluster(get.coresOption())
  set.ClusterOption(cl)
}
### calculating costs
system.time(plcosts <- nbcosts(bh.nb, dpad))
all.equal(lcosts, plcosts, check.attributes=FALSE)
### making listw
pnb.w <- nb2listw(bh.nb, plcosts, style="B")
### find a minimum spanning tree
pmst.bh <- mstree(pnb.w,5)
### three groups with no restriction
system.time(pres1 <- skater(pmst.bh[,1:2], dpad, 2))
if(!get.mcOption()) {
  set.ClusterOption(NULL)
  stopCluster(cl)
}
all.equal(res1, pres1, check.attributes=FALSE)
invisible(set.coresOption(coresOpt))
# }