# MINDEX_SP: The Multipoint Morisita Index for Spatial Patterns In IDmining: Intrinsic Dimension for Data Mining

## Description

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

## Usage

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

## Arguments

 `X` A N x 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]))`).

## 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.

## Value

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

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39``` ```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) ```

### Example output

```Loading required package: colorRamps
```

IDmining documentation built on May 3, 2021, 9:08 a.m.