calcFukuyamaSugeno: Fukuyama and Sugeno index

In geocmeans: Implementing Methods for Spatial Fuzzy Unsupervised Classification

Fukuyama and Sugeno index

Description

Calculate Fukuyama and Sugeno index of clustering quality

Usage

calcFukuyamaSugeno(data, belongmatrix, centers, m)

Arguments

data	The original dataframe used for the clustering (n*p)
belongmatrix	A membership matrix (n*k)
centers	The centres of the clusters
m	The fuzziness parameter

Details

The Fukuyama and Sugeno index \insertCitefukuyama1989newgeocmeans is the difference between the compacity of clusters and the separation of clusters. A smaller value indicates a better clustering. The formula is:

S(c)=\sum_{k=1}^{n} \sum_{i=1}^{c}\left(U_{i k}\right)^{m}\left(\left\|x_{k}-v_{i}\right\|^{2}-\left\|v_{i}-\bar{x}\right\|^{2}\right) 2

with n the number of observations, k the number of clusters and \bar{x} the mean of the dataset.

Value

A float: the Fukuyama and Sugeno index

References

\insertAllCited

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcFukuyamaSugeno(result$Data,result$Belongings, result$Centers, 1.5)

geocmeans documentation built on Sept. 12, 2023, 9:06 a.m.