cl_fuzziness: Partition Fuzziness

In clue: Cluster Ensembles

Partition Fuzziness

Description

Compute the fuzziness of partitions.

Usage

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

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).

Value

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

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"))
}

clue documentation built on Sept. 23, 2023, 5:06 p.m.