IDmining (version 1.0.7)

MINDEX_SP: 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 \(N \times 2\) matrix, data.frame or data.table containing the \(X\) and \(Y\) coordinates of \(N\) data points. The \(X\) coordinates must be given in the first column and the \(Y\) coordinates in the second column.

scaleQ

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

mMin

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

mMax

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

Wlim_x

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

Wlim_y

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

Value

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

Details

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

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

3. \(\delta\) is the diagonal length of the grid cells.

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<U+2013>202.

L. Telesca, J. Golay and M. Kanevski (2015). Morisita-based space-clustering analysis of Swiss seismicity, Physica A 419:40<U+2013>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

# NOT RUN {
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)
# }