MINDEX_SP {IDmining}R Documentation

The Multipoint Morisita Index for Spatial Patterns

Description

Computes the multipoint Morisita index for spatial patterns (i.e. 2-dimensional patterns).

Usage

MINDEX_SP(X, scaleQ=1:5, mMin=2, mMax=5, Wlim_x=NULL, Wlim_y=NULL)

Arguments

X

A N×2N \times 2 matrix, data.frame or data.table containing the XX and YY coordinates of NN data points. The XX coordinates must be given in the first column and the YY coordinates in the second column.

scaleQ

Either a single value or a vector. It contains the value(s) of Q(1/2)Q^{(1/2)} chosen by the user where QQ is the number of cells (or quadrats) of the 2D2D grid (by default: scaleQ = 1:5).

mMin

The minimum value of mm (by default: mMin = 2).

mMax

The maximum value of mm (by default: mMax = 5).

Wlim_x

A vector controlling the spatial extent of the 2D2D gird along the XX axis. It consists of two real values, i.e. Wlim_x <- c(a,b) where b>ab > a (by default: Wlim_x <- c(min(X[,1]),max(X[,1]))).

Wlim_y

A vector controlling the spatial extent of the 2D2D gird along the YY axis. It consists of two real values, i.e. Wlim_y <- c(a,b) where b>ab > a (by default: Wlim_y <- c(min(X[,2]),max(X[,2]))).

Details

  1. Q(1/2)Q^{(1/2)} is the number of grid cells (or quadrats) along each of the two axes.

  2. Q(1/2)Q^{(1/2)} is directly related to δ\delta (see References).

  3. δ\delta is the diagonal length of the grid cells.

Value

A data.frame containing the value of the m-Morisita index for each value of δ\delta and mm.

Author(s)

Jean Golay jeangolay@gmail.com

References

J. Golay, M. Kanevski, C. D. Vega Orozco and M. Leuenberger (2014). The multipoint Morisita index for the analysis of spatial patterns, Physica A 406:191–202.

L. Telesca, J. Golay and M. Kanevski (2015). Morisita-based space-clustering analysis of Swiss seismicity, Physica A 419:40–47.

L. Telesca, M. Lovallo, J. Golay and M. Kanevski (2016). Comparing seismicity declustering techniques by means of the joint use of Allan Factor and Morisita index, Stochastic Environmental Research and Risk Assessment 30(1):77-90.

Examples

sim_dat <- SwissRoll(1000)

m <- 2
scaleQ <- 1:15 # It starts with a grid of 1^2 cell (or quadrat).
               # It ends with a grid of 15^2 cells (or quadrats).
mMI <- MINDEX_SP(sim_dat[,c(1,2)], scaleQ, m, 5)

plot(mMI[,1],mMI[,2],pch=19,col="black",xlab="",ylab="")
title(xlab=expression(delta),cex.lab=1.5,line=2.5)
title(ylab=expression(I['2,'*delta]),cex.lab=1.5,line=2.5)

## Not run: 
require(colorRamps)
colfunc <- colorRampPalette(c("blue","red"))
color <- colfunc(4)
dev.new(width=5,height=4)
plot(mMI[5:15,1],mMI[5:15,2],pch=19,col=color[1],xlab="",ylab="",
     ylim=c(1,max(mMI[,5])))
title(xlab=expression(delta),cex.lab=1.5,line=2.5)
title(ylab=expression(I['2,'*delta]),cex.lab=1.5,line=2.5)
for(i in 3:5){
  points(mMI[5:15,1],mMI[5:15,i],pch=19,col=color[i-1])
}
legend.text<-c("m=2","m=3","m=4","m=5")
legend.pch=c(19,19,19,19)
legend.lwd=c(NA,NA,NA,NA)
legend.col=c(color[1],color[2],color[3],color[4])
legend("topright",legend=legend.text,pch=legend.pch,lwd=legend.lwd,
       col=legend.col,ncol=1,text.col="black",cex=0.9,box.lwd=1,bg="white")

xlim_l <- c(-5,5)     # By default, the spatial extent of the grid is set so
ylim_l <- c(-6,6)     # that it is the same as the spatial extent of the data.
xlim_s <- c(-0.6,0.2) # But it can be modified to cover either a larger (l)
ylim_s <- c(-1,0.5)   # or a smaller (s) study area (or validity domain).

mMI_l <- MINDEX_SP(sim_dat[,c(1,2)], scaleQ, m, 5, xlim_l, ylim_l)
mMI_s <- MINDEX_SP(sim_dat[,c(1,2)], scaleQ, m, 5, xlim_s, ylim_s)

## End(Not run)

[Package IDmining version 1.0.7 Index]