entropy.capa.ident: Unsupervised identification of a capacity from profiles

Description

This function estimates a capacity using as argument a set of data under the form: datum=(score on attribute 1, ..., score on attribute n). The approach roughly consists in replacing the subjective notion of importance of a subset of attributes by that of information content of a subset of attributes, which is estimated from the data by means of a parametric entropy measure. For more details, see the references hereafter.

Usage

entropy.capa.ident(d, entropy = "renyi", parameter = 1)

Value

Returns an object of class capacity.

Arguments

d: An object of class data.frame containing the discretized data. Each column of the data.frame must be a factor. Each line corresponds to a datum.
entropy: An object of class character containg the name of the parametric entropy measure to be used for the estimation. The allowed values are "renyi" and "havrda.charvat".
parameter: An object of class numeric containing he value of the parameter of the choosen entropy. The parameter value must be a positive real number. If equal to 1, the Shannon entropy is used.

References

I. Kojadinovic (2004), Estimation of the weights of interacting criteria from the set of profiles by means of information-theoretic functionals, European Journal of Operational Research 155:3, pages 741-751.

I. Kojadinovic (2005), Unusupervised aggregation of commensurate correlated attributes by means of the Choquet integral and entropy functionals, International Journal of Intelligent Systems, in press.

Examples

Run this code

## a set of randomly generated data
## for instance, marks on a [0,20] scale
p <- data.frame(matrix(runif(500,0,20),100,5))
names(p) <- c("Stat","Prob","Alg","Cal","Eng")

## discretization
p[p <= 5] <- 1  
p[p > 5 & p <= 10] <- 2 
p[p > 10 & p <= 15] <- 3 
p[p > 15] <- 4

d <- data.frame(factor(p[[1]]),
                factor(p[[2]]),
                factor(p[[3]]),
                factor(p[[4]]),
                factor(p[[5]]))

## associated unsupervised capacity
mu <- entropy.capa.ident(d)
mu