R/entropy.capa.ident.R

In kappalab: Non-Additive Measure and Integral Manipulation Functions

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#
# Copyright © 2005 Michel Grabisch and Ivan Kojadinovic    
#
# Ivan.Kojadinovic@polytech.univ-nantes.fr
#
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## Unsupervised capacity identification from data based on entropy measures

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## Internal functions

## Converts a subset represented as an integer (binary notation) 
## to a numeric
binary2subset <- function(n,b) {
    
    result <- .C("binary2subsetR", 
                 as.integer(n),
                 as.integer(b),
                 subset = integer(n), 
                 len = integer(1),
                 PACKAGE="kappalab")
    
    result$subset[1:result$len]
}

shannon.function <- function(x) {
    if (x > 0)
        return(-x * log(x))
    else
        return(0)
}

shannon.entropy <- function(f,...) {
    
    sum(sapply(f,shannon.function))
}

renyi.entropy <- function(f,alpha) {
    
    1/(1-alpha)*log(sum(f^alpha))
}

havrda.charvat.entropy <- function(f,beta) {
    
    1/(1-beta)*(sum(f^beta)-1)
}

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##Constructs a capacity from discretized profiles
## and using parametric entropy measures  

entropy.capa.ident <- function(d,entropy = "renyi",parameter = 1)
{
    if (!is.data.frame(d))
        stop("wrong arguments")
    
    n <- length(d)

    for(i in 1:n)
        if (!is.factor(d[[i]]))
            stop("wrong arguments")

    if (!(entropy %in% c("renyi","havrda.charvat")))
        stop("wrong arguments")	

    if (!(as.double(parameter) && length(parameter) == 1))
        stop("wrong arguments")	

    if (parameter == 1)
        entropy.measure <- shannon.entropy
    else if (entropy == "renyi")
        entropy.measure <- renyi.entropy
    else 
        entropy.measure <- havrda.charvat.entropy

    ## multidimensional contingency table
    t <- table(d)
    
    ## frequency table
    f <- t/sum(t)

    ## unsupervised capacity identification

    mu <- numeric(2^n)
    
    for (i in 2:2^n)
        mu[i] <- entropy.measure(margin.table(f,binary2subset(n,i-1)),
                                 parameter)

    subsets <-  .C("k_power_set", 
                   as.integer(n),
                   as.integer(n),
                   subsets = integer(2^n),
                   PACKAGE="kappalab")$subsets

    new("capacity", data = mu/mu[2^n], subsets = subsets, n = n)
}

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