# calcFukuyamaSugeno: Fukuyama and Sugeno index In geocmeans: Implementing Methods for Spatial Fuzzy Unsupervised Classification

 calcFukuyamaSugeno R Documentation

## 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)=∑_{k=1}^{n} ∑_{i=1}^{c}≤ft(U_{i k}\right)^{m}≤ft(≤ft\|x_{k}-v_{i}\right\|^{2}-≤ft\|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

\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 Oct. 16, 2022, 1:07 a.m.