MINDID_FMC: Functional Measure of Clustering Using the Morisita Estimator...
In jeangolay/IDmining: Intrinsic Dimension for Data Mining

Description Usage Arguments Details Value Author(s) References Examples

Computes the functional m-Morisita index for a given set of threshold values.

1	MINDID_FMC(XY, scaleQ, m=2, thd)

`XY`	A N x E `matrix`, `data.frame` or `data.table` where N is the number of data points and E is the number of variables (i.e. the input variables + the variable measured at each measurement station). The last column contains the variable measured at each measurement station. And each input variable is rescaled to the [0,1] interval by the function. Typically, the input variables are the X and Y coordinates of the measurement stations, but other or additional variables can be considered as well.
`scaleQ`	A vector containing the values of l^(-1) chosen by the user (see Details).
`m`	The value of the parameter m (by default: `m=2`).
`thd`	Either a single value or a vector. It contains the value(s) of the threshold(s).

l is the edge length of the grid cells (or quadrats). Since the input variables (and consenquently the grid) are rescaled to the [0,1] interval, l is equal to 1 for a grid consisting of only one cell.
l^(-1) is the number of grid cells (or quadrats) along each axis of the Euclidean space in which the data points are embedded.
l^(-1) is equal to Q^(1/E) where Q is the number of grid cells and E is the number of variables (or features).
l^(-1) is directly related to delta (see References).
delta is the diagonal length of the grid cells.

A vector containing the value(s) of the m-Morisita slope, Sm, for each threshold value.

Jean Golay jeangolay@gmail.com

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.

J. Golay and M. Kanevski (2015). A new estimator of intrinsic dimension based on the multipoint Morisita index, Pattern Recognition 48 (12):4070–4081.

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

## Not run: 
bf    <- Butterfly(10000)
bf_SP <- bf[,c(1,2,9)]

m      <- 2
scaleQ <- 5:25
thd    <- quantile(bf_SP$Y,probs=c(0,0.1,0.2,0.3,
                                   0.4,0.5,0.6,
                                   0.7,0.8,0.9))

nbr_shuf    <- 100
Sm_thd_shuf <- matrix(0,length(thd),nbr_shuf)
for (i in 1:nbr_shuf){
  bf_SP_shuf      <- cbind(bf_SP[,1:2],sample(bf_SP$Y,length(bf_SP$Y)))
  Sm_thd_shuf[,i] <- MINDID_FMC(bf_SP_shuf, scaleQ, m, thd)
}
mean_shuf <- apply(Sm_thd_shuf,1,mean)

dev.new(width=6, height=4)
matplot(1:10,Sm_thd_shuf,type="l",lty=1,col=rgb(1,0,0,0.25),
        ylim=c(-0.05,0.05),ylab=bquote(S[.(m)]),xaxt="n",
        xlab="",cex.lab=1.2)
axis(1,1:10,labels = FALSE)
text(1:10,par("usr")[3]-0.01,srt=45,ad=1,
     labels=c("0_100", "10_100","20_100","30_100",
              "40_100","50_100","60_100",
              "70_100","80_100","90_100"),xpd=T,font=2,cex=1)
mtext("Thresholds",side=1,line=3.5,cex=1.2)
lines(1:10,mean_shuf,type="b",col="blue",pch=19)

legend.text<-c("Shuffled","mean")
legend.pch=c(NA,19)
legend.lwd=c(2,2)
legend.col=c("red","blue")
legend("topleft",legend=legend.text,pch=legend.pch,lwd=legend.lwd,
       col=legend.col,ncol=1,text.col="black",cex=1,box.lwd=1,bg="white")

## End(Not run)