# logMINDEX: The Multipoint Morisita Index in 1, 2 or Higher Dimensions In IDmining: Intrinsic Dimension for Data Mining

## Description

Computes the ln values of the multipoint Morisita index in 1, 2 or higher dimensional spaces.

## Usage

 `1` ```logMINDEX(X, scaleQ=1:5, mMin=2, mMax=2) ```

## Arguments

 `X` 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 (or features). Each variable is rescaled to the [0,1] interval by the function. `scaleQ` Either a single value or a vector. It contains the value(s) of l^(-1) chosen by the user (by default: `scaleQ = 1:5`). `mMin` The minimum value of m (by default: `mMin = 2`). `mMax` The maximum value of m (by default: `mMax = 2`).

## Details

1. l is the edge length of the grid cells (or quadrats). Since the 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 `data.frame` containing the ln value of the m-Morisita index for each value of ln(delta) and m. Notice also that the values of ln(delta) are provided with regard to the [0,1] interval.

## Author(s)

Jean Golay jeangolay@gmail.com

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```sim_dat <- SwissRoll(1000) m <- 2 scaleQ <- 1:15 # It starts with a grid of 1^E cell (or quadrat). # It ends with a grid of 15^E cells (or quadrats). lnmMI <- logMINDEX(sim_dat, scaleQ, m, m) dev.new(width=5, height=4) plot(exp(lnmMI[,1]),exp(lnmMI[,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) dev.new(width=5, height=4) plot(lnmMI[,1],lnmMI[,2],pch=19,col="black",xlab="",ylab="") title(xlab = expression(paste("log(",delta,")")), cex.lab = 1.5,line = 2.5) title(ylab = expression(paste("log(",I['2,'*delta],")")), cex.lab = 1.5,line = 2.5) ```

### Example output

```dev.new(): using pdf(file="Rplots1.pdf")
```

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