| calcDaviesBouldin {geocmeans} | R Documentation |
Davies-Bouldin index
Description
Calculate the Davies-Bouldin index of clustering quality.
Usage
calcDaviesBouldin(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 Davies-Bouldin index (Da Silva et al. 2020) can be seen as the ratio of the within cluster dispersion and the between cluster separation. A lower value indicates a higher cluster compacity or a higher cluster separation. The formula is:
DB = \frac{1}{k}\sum_{i=1}^k{R_{i}}
with:
R_{i} =\max_{i \neq j}\left(\frac{S_{i}+S_{j}}{M_{i, j}}\right)
S_{l} =\left[\frac{1}{n_{l}} \sum_{l=1}^{n}\left\|\boldsymbol{x_{l}}-\boldsymbol{c_{i}}\right\|*u_{i}\right]^{\frac{1}{2}}
M_{i, j} =\sum\left\|\boldsymbol{c}_{i}-\boldsymbol{c}_{j}\right\|
So, the value of the index is an average of R_{i} values. For each cluster, they represent
its worst comparison with all the other clusters, calculated
as the ratio between the compactness of the two clusters and the separation
of the two clusters.
Value
A float: the Davies-Bouldin index
References
Da Silva LEB, Melton NM, Wunsch DC (2020). “Incremental cluster validity indices for online learning of hard partitions: Extensions and comparative study.” IEEE Access, 8, 22025–22047.
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)
calcDaviesBouldin(result$Data, result$Belongings, result$Centers)