MINDID: 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

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 $ℓ^{- 1}$ 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).

Value

A list of two elements:

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

Details

$ℓ$ 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.
$ℓ^{- 1}$ 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 $δ$ (see References).
$δ$ is the diagonal length of the grid cells.

References

J. Golay and M. Kanevski (2015). A new estimator of intrinsic dimension based on the multipoint Morisita index, Pattern Recognition 48 (12):4070<U+2013>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<U+2013>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

Run this code

# NOT RUN {
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)))
# }

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