HF.IDX {UniversalCVI}

HF index

Description

Computes the HF (F. Haouas et al., 2017) index for a result of either FCM or EM clustering from user specified cmin to cmax.

Usage

HF.IDX(x, cmax, cmin = 2, method = "FCM", fzm = 2, nstart = 20, iter = 100)

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.

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.

nstart

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

iter

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

Details

The HF index is defined as

HF(c) = \frac{\sum_{j=1}^c \sum_{i=1}^n\mu_{ij}^m\| {x}_i-{v}_j\|^2 + \frac{1}{c(c-1)}\sum_{j\neq k}\| {v}_j-{v}_k\|^2}{\frac{n}{2c}\left(\min_{j \neq k}\{\| {v}_j-{v}_k\|^2\} +\text{median}_{j \neq k }\{\| {v}_j-{v}_k\|^2\}\right)}.

The smallest value of HF(c) indicates a valid optimal partition.

Value

HF

the HF index for c from cmin to cmax shown in a data frame where the first and the second columns are c and the HF index, respectively.

Author(s)

Nathakhun Wiroonsri and Onthada Preedasawakul

References

F. Haouas, Z. Ben Dhiaf, A. Hammouda and B. Solaiman, "A new efficient fuzzy cluster validity index: Application to images clustering," 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Naples, Italy, 2017, pp. 1-6. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8015651&isnumber=8015374

See Also

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

Examples

library(UniversalCVI)

# The data is from Wiroonsri (2024).
x = R1_data[,1:2]

# ---- FCM algorithm ----

# Compute the HF index
FCM.HF = HF.IDX(scale(x), cmax = 15, cmin = 2, method = "FCM",
  fzm = 2, nstart = 20, iter = 100)
print(FCM.HF)

# The optimal number of cluster
FCM.HF[which.min(FCM.HF$HF),]

# ---- EM algorithm ----

# Compute the HF index
EM.HF = HF.IDX(scale(x), cmax = 15, cmin = 2, method = "EM",
  nstart = 20, iter = 100)
print(EM.HF)

# The optimal number of cluster
EM.HF[which.min(EM.HF$HF),]