CRE: Cumulative Residual Entropy (CRE)

In rasterdiv: Diversity Indices for Numerical Matrices

Cumulative Residual Entropy (CRE)

Description

Computes Cumulative Residual Entropy (CRE) on different classes of numeric matrices using a moving window algorithm.

Usage

CRE(x, window=3, mode="classic", rasterOut=TRUE,
  rescale=FALSE, na.tolerance=1.0, simplify=2, np=1, 
  cluster.type="SOCK", debugging=FALSE)

Arguments

x	input data may be a matrix, a Spatial Grid Data Frame, a RasterLayer or a list of these objects. In the latter case, if mode="classic" only the first element of the list will be considered.
window	the side of the square moving window, it must be a odd numeric value greater than 1 to ensure that the target pixel is in the centre of the moving window. Default value is 3.
mode	currently, there are two modes to calculate Cumulative Residual Entropy (CRE). If mode is "classic", then the monodimension CRE will be calculated on one single matrix. If mode is "multidimension" (experimental!) a list of matrices must be provided as input. In this latter case, the multidimensional cumulative residual probability will be calculated. Default value is "classic".
rasterOut	Boolean, if TRUE output will be in RasterLayer format with x as template.
rescale	a boolean variable set to FALSE by default. If TRUE, x will be scaled and centred to standardise different matrices if mode is "multidimension". Default value is FALSE.
na.tolerance	a numeric value (0.0-1.0) which indicates the proportion of NA values that will be tolerated to calculate CRE in each moving window over x. If the relative proportion of NA's in a moving window is bigger than na.tolerance, then the value of the window will be set as NA, otherwise CRE will be calculated considering the non-NA values. Default values is 1.0 (i.e., full tolerance for NA's).
simplify	Number of decimal places to be retained to calculate CRE. Only if x is floats.
np	the number of processes (cores) which will be spawned. Default value is 1.
cluster.type	the type of cluster which will be created. The options are "MPI" (which calls "makeMPIcluster"), "FORK" and "SOCK" (which call "makeCluster"). Default type is "SOCK".
debugging	a boolean variable set to FALSE by default. If TRUE, additional messages will be printed. For debugging only.

Details

Unidimension Cumulative Residual Entropy (CRE) is calculated on a numerical vector as CRE = CRE=-∑_{i=1}^{N}{P(X≥q x_i)\log{P(X≥q x_i)dx}} [1] where dx=(x_i -x_{i-1}) and P is a vector of probabilities that the vector of observations is larger or equal to each value of the vector. In the "multidimension" CRE, P becomes an array with as many dimensions as the one of the observations. In each cell of P the probability estimates with the frequency of the number of observation that as the same time satisfy the larger or equal requirement for the different combination of values along the dimension. dx becomes the products of the difference along each dimension.
The theoretical minimum of CRE is 0, when all values are identical in a window. The values of CRE increases with the range of observations, thus the more the observations are equally spread (even) across values the higher CRE will be.

Value

A matrix of dimension dim(x).

Author(s)

Saverio Vicario [e-mail]

References

[1] Rao M, Chen Y, Vemuri BC, Wang F (2004) Cumulative Residual Entropy: A New Measure of Information. IEEE Trans Inf Theory 50:1220–1228.

Examples

#Minimum example; compute CRE
a <- matrix(c(10,10,10,20,20,20,20,30,30),ncol=3,nrow=3)
out <- CRE(x=a,window=3,na.tolerance=0,mode="classic")

#Minimum example; compute CRE in paralllel
a <- matrix(c(10,10,10,20,20,20,20,30,30),ncol=3,nrow=3)
out <- CRE(x=a,window=3,na.tolerance=0,mode="classic",np=1)

#Compute multidimension Rao's index rescaling the input matrices
a <- matrix(c(10,10,10,20,20,20,20,30,30),ncol=3,nrow=3)
b <- matrix(c(0.5,0.5,0.1,0.1,0.3,0.3,0.3,0.3,0.3),ncol=3,nrow=3)
out <- CRE(x=list(a,b),window=3,na.tolerance=0,
  mode="multidimension",rescale=TRUE,debugging=TRUE)

rasterdiv documentation built on Nov. 24, 2022, 9:07 a.m.