SOM based index

The methodology for the spatial segregation indicator is based on 2 publications ((Cottrell et al. 2017),(Olteanu et al. 2019)).This section reproduces the method of how to calculate the indicator for 81 neurons.

library(sp)
library(rgeos)
library(rgdal)
library(ggplot2)

Reading spatial database

CLUSTER<-readOGR('data/CLUSTER.shp')

Chess distance for each neuron

o<-as.data.frame(matrix(0,81,81))
colnames(o)<-1:81
t<-as.matrix(cbind(9:1,18:10,27:19,36:28,45:37,54:46,63:55,72:64,81:73))
C<-1
for(j in 1:dim(t)[2]){
  for(i in 1:dim(t)[1]){
    F<-1
    for(l in 1:dim(t)[2]){
      for(k in 1:dim(t)[1]){
        d<-max(c(abs(i-k),abs(j-l)))
        o[F,C]<-d
        F<-F+1
      }
    }
    C<-C+1
  }
}

Geographic distance matrix

centroides<-gCentroid(CLUSTER,byid = TRUE)
dist<-spDists(centroides)
dist<-as.data.frame(dist)
colnames(dist)<-as.numeric(rownames(centroides@coords))+1
rownames(dist)<-as.numeric(rownames(centroides@coords))+1

O<-as.data.frame(matrix(0,length(colnames(dist)),length(colnames(dist))))
colnames(O)<-colnames(dist)
rownames(O)<-colnames(dist)

for(i in 1:dim(O)[1]){
  for(j in 1:dim(O)[2]){
    Nf<-CLUSTER$NEUR[i]
    Nc<-CLUSTER$NEUR[j]
    D<-o[Nf,Nc]
    O[i,j]<-D
  }
}

DGEO<-NULL
for(i in 2:dim(dist)[1]){
  for(j in 1:(i-1)){
    DGEO<-c(DGEO,dist[i,j])
  }
}

DSOM<-NULL
for(i in 2:dim(O)[1]){
  for(j in 1:(i-1)){
    DSOM<-c(DSOM,O[i,j])
  }
}

plot(DSOM,DGEO)

ggplot(data=data.frame(DSOM,DGEO),aes(x=DSOM,y=DGEO)) +
    geom_bin2d(bin=20) +
    scale_fill_continuous(type = "viridis") +
    geom_smooth(method=lm, se=FALSE, fullrange=TRUE)

## `geom_smooth()` using formula 'y ~ x'

cor(DSOM,DGEO)

## [1] 0.3347225

SOM based index

References