wback of the K-means algorithm by introducing the soft

hip function to a clustering process [Dunn, 1973; Bezdek, 1981].

re of a cluster is defined as below, where ݂௞ሺܠ௡ሻ∈ሾ0,1ሿ is a soft

hip function measuring the degree by which the n^th data point ܠ௡

o the k^th cluster whose centre is ࢛௞,

࢛௞ൌ

∑

ሾ݂௞ሺܠ௡ሻሿ^௠ܠ௡

ே

௡ୀଵ

∑

ሾ݂௞ሺܠ௡ሻሿ^௠

ே

௡ୀଵ

(2.24)

e above definition, m is a positive parameter to weight the

hip. The membership ݂௥ሺܠ௡ሻ (for the n^th data point ܠ௡ to belong

cluster) is defined as below,

݂௥ሺܠ௡ሻൌ෍ቆ

‖ܠ௡െ࢛௥‖

‖ܠ௡െ࢛௞‖^ቇ

ଶ

௠ିଵ

௄

௞ୀଵ

(2.25)

ame as the K-means algorithm, the fuzzy C-means algorithm also

s model parameters (cluster centres ࢛௞) using random values.

n the initialised cluster centres, the algorithm estimates the

hips for each data point, i.e., ݂௥ሺܠ௡ሻ. Afterwards, the centres are

These two calculations are repeated until the maximum cycles

ed or the cluster centres stop to change.

use of the use of the soft membership function, the fuzzy C-means

m benefits from a slightly higher accuracy for dealing with a more

ted cluster model. In biological/medical pattern analysis, the

means algorithm has been integrated into a linear model which

o a significant improvement of the discovery accuracy of Type 1

based on blood glucose data [Montaser, et al., 2020]. It has also

d to cluster tissues in a computer-aided diagnosis of Alzheimer's

Lazli, et al., 2020].

R package for the fuzzy C-means algorithm is ppclust. The

unction for constructing a fuzzy C-means model is fcm, which is

s

fcm(x,centers, ⋯)