calcGD43: Generalized Dunn’s index (43)

In geocmeans: Implementing Methods for Spatial Fuzzy Unsupervised Classification

Generalized Dunn’s index (43)

Description

Calculate the Generalized Dunn’s index (v43) of clustering quality.

Usage

calcGD43(data, belongmatrix, centers)

Arguments

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

Details

The Generalized Dunn’s index \insertCiteda2020incrementalgeocmeans is a ratio of the worst pair-wise separation of clusters and the worst compactness of clusters. A higher value indicates a better clustering. The formula is:

GD_{r s}=\frac{\min_{i \neq j}\left[\delta_{r}\left(\omega_{i}, \omega_{j}\right)\right]}{\max_{k}\left[\Delta_{s}\left(\omega_{k}\right)\right]}

The numerator is a measure of the minimal separation between all the clusters i and j given by the formula:

\delta_{r}\left(\omega_{i}, \omega_{j}\right)=\left\|\boldsymbol{c}_{i}-\boldsymbol{c}_{j}\right\|

which is basically the Euclidean distance between the centres of clusters c_{i} and c_{j}

The denominator is a measure of the maximal dispersion of all clusters, given by the formula:

\frac{2*\sum_{l=1}^{n}\left\|\boldsymbol{x}_{l}-\boldsymbol{c_{i}}\right\|^{\frac{1}{2}}}{\sum{u_{i}}}

Value

A float: the Generalized Dunn’s index (43)

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)
calcGD43(result$Data, result$Belongings, result$Centers)

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