UniversalCVI (version 1.2.0)

GC.IDX: The generalized C index

Description

Computes the GC1 GC2 GC3 and GC4 (J. C. Bezdek et al., 2016) indexes for a result of either FCM or EM clustering from user specified cmin to cmax.

Usage

GC.IDX(x, cmax, cmin = 2, indexlist = "all", method = 'FCM', fzm = 2,
  iter = 100, nstart = 20)

Value

Each of the followings shows the values of each index for c from cmin to cmax in a data frame.

GC1

the generalized C index (\(\sum\cdot \sim\) Sum-Product).

GC2

the generalized C index (\(\sum\wedge \sim\) Sum-Min).

GC3

the generalized C index (\(\vee\cdot \sim\) Max-Product).

GC4

the generalized C index (\(\vee\wedge \sim\) Max-Min).

Arguments

x

a numeric data frame or matrix where each column is a variable to be used for cluster analysis and each row is a data point.

cmax

a maximum number of clusters to be considered.

cmin

a minimum number of clusters to be considered. The default is 2.

indexlist

a character string indicating which The generalized C index be computed ("all","GC1","GC2","GC3","GC4"). More than one indexes can be selected.

method

a character string indicating which clustering method to be used ("FCM" or "EM"). The default is "FCM".

fzm

a number greater than 1 giving the degree of fuzzification for method = "FCM". The default is 2.

iter

a maximum number of iterations for method = "FCM". The default is 100.

nstart

a maximum number of initial random sets for FCM for method = "FCM". The default is 20.

Author

Nathakhun Wiroonsri and Onthada Preedasawakul

Details

The GC index is a soft version of the C-index, formulated based on relational transformations of the membership degree matrix \(\mu\). It comprises four distinct variants, each with its own definition.
The smallest value of \(GC(c)\) indicates a valid optimal partition.

References

J. C. Bezdek, M. Moshtaghi, T. Runkler, and C. Leckie, “The generalized c index for internal fuzzy cluster validity,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 6, pp. 1500–1512, 2016. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7429723&isnumber=7797168

See Also

R1_data, TANG.IDX, FzzyCVIs, WP.IDX, Hvalid

Examples

library(UniversalCVI)

# Iris data
x = iris[,1:4]

# ---- FCM algorithm ----

# Compute all the indices by GC.IDX
FCM.all.GC = GC.IDX(scale(x), cmax = 10, cmin = 2, indexlist = "all",
  method =  'FCM', fzm = 2, iter = 100, nstart = 5)
print(FCM.all.GC)

# Compute GC2 index
FCM.GC2 = GC.IDX(scale(x), cmax = 10, cmin = 2, indexlist = "GC2",
  method = 'FCM', fzm = 2, iter = 100, nstart = 5)
print(FCM.GC2)

# ---- EM algorithm ----

# Compute all the indices by GC.IDX
EM.all.GC = GC.IDX(scale(x), cmax = 10, cmin = 2, indexlist = "all",
  method =  'EM', iter = 100, nstart = 5)
print(EM.all.GC)

# Compute GC2 index
EM.GC2 = GC.IDX(scale(x), cmax = 10, cmin = 2, indexlist = "GC2",
  method =  'EM', iter = 100, nstart = 5)
print(EM.GC2)