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

## Description

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

## Usage

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

## Arguments

 `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).

## Details

1. 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.

2. l^(-1) is the number of grid cells (or quadrats) along each axis of the Euclidean space in which the data points are embedded.

3. 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).

4. l^(-1) is directly related to delta (see References).

5. delta is the diagonal length of the grid cells.

## Value

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

## 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.

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.

## 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``` ```## 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")-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) ```

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