clue (version 0.3-65)

cl_fuzziness: Partition Fuzziness

Description

Compute the fuzziness of partitions.

Usage

cl_fuzziness(x, method = NULL, normalize = TRUE)

Value

An object of class "cl_fuzziness" giving the fuzziness values.

Arguments

x

a cluster ensemble of partitions, or an R object coercible to such.

method

a character string indicating the fuzziness measure to be employed, or NULL (default), or a function to be taken as a user-defined method. Currently available built-in methods are "PC" (Partition Coefficient) and "PE" (Partition Entropy), with the default corresponding to the first one. If method is a character string, its lower-cased version is matched against the lower-cased names of the available built-in methods using pmatch.

normalize

a logical indicating whether the fuzziness measure should be normalized in a way that hard partitions have value 0, and “completely fuzzy” partitions (where for all objects, all classes get the same membership) have value 1.

Details

If \(m\) contains the membership values of a partition, the (unnormalized) Partition Coefficient and Partition Entropy are given by \(\sum_{n,i} m_{n,i}^2\) and \(\sum_{n,i} H(m_{n,i})\), respectively, where \(H(u) = u \log u - (1-u) \log(1-u)\).

Note that the normalization used here is different from the normalizations typically found in the literature.

If a user-defined fuzziness method is to be employed, is must be a function taking a matrix of membership values and a logical to indicate whether normalization is to be performed as its arguments (in that order; argument names are not used).

References

J. C. Bezdek (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum.

See Also

Function fclustIndex in package e1071, which also computes several other “fuzzy cluster indexes” (typically based on more information than just the membership values).

Examples

if(require("e1071", quietly = TRUE)) {
    ## Use an on-line version of fuzzy c-means from package e1071 if
    ## available.
    data("Cassini")
    pens <- cl_boot(Cassini$x, B = 15, k = 3, algorithm = "cmeans",
                    parameters = list(method = "ufcl"))
    pens
    summary(cl_fuzziness(pens, "PC"))
    summary(cl_fuzziness(pens, "PE"))
}