MINDID {IDmining}

The (Multipoint) Morisita Index for Intrinsic Dimension Estimation

Description

Estimates the intrinsic dimension of data using the Morisita estimator of intrinsic dimension.

Usage

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

Arguments

X

A N \times 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

A vector (at least two values). It contains the values of \ell^{-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. \ell is the edge length of the grid cells (or quadrats). Since the variables (and consenquently the grid) are rescaled to the [0,1] interval, \ell is equal to 1 for a grid consisting of only one cell.

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

3. \ell^{-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. \ell^{-1} is directly related to \delta (see References).

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

Value

A list of two elements:

1. a data.frame containing the \ln value of the m-Morisita index for each value of \ln (\delta) and m. The values of \ln (\delta) are provided with regard to the [0,1] interval.

2. a data.frame containing the values of S_m and M_m for each value of m.

Author(s)

Jean Golay [e-mail]

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.

J. Golay, M. Leuenberger and M. Kanevski (2017). Feature selection for regression problems based on the Morisita estimator of intrinsic dimension, Pattern Recognition 70:126–138.

J. Golay and M. Kanevski (2017). Unsupervised feature selection based on the Morisita estimator of intrinsic dimension, Knowledge-Based Systems 135:125-134.

J. Golay, M. Leuenberger and M. Kanevski (2015). Morisita-based feature selection for regression problems. Proceedings of the 23rd European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN), Bruges (Belgium).

Examples

sim_dat <- SwissRoll(1000)

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).
mMI_ID <- MINDID(sim_dat, scaleQ[5:15])

print(paste("The ID estimate is equal to",round(mMI_ID[[1]][1,3],2)))