calcNegentropyI: Negentropy Increment index

In geocmeans: Implementing Methods for Spatial Fuzzy Unsupervised Classification

Negentropy Increment index

Description

Calculate the Negentropy Increment index of clustering quality.

Usage

calcNegentropyI(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 Negentropy Increment index \insertCiteda2020incrementalgeocmeans is based on the assumption that a normally shaped cluster is more desirable. It uses the difference between the average negentropy of all the clusters in the partition, and that of the whole partition. A smaller value indicates a better partition. The formula is:

NI=\frac{1}{2} \sum_{j=1}^{k} p_{i} \ln \left|{\boldsymbol{\Sigma}}_{j}\right|-\frac{1}{2} \ln \left|\boldsymbol{\Sigma}_{d a t a}\right|-\sum_{j=1}^{k} p_{j} \ln p_{j}

with a cluster, |.| the determinant of a matrix,

• j a cluster

• |.| the determinant of a matrix

• \left|{\boldsymbol{\Sigma}}_{j}\right| the covariance matrix of the dataset weighted by the membership values to cluster j

• \left|\boldsymbol{\Sigma}_{d a t a}\right| the covariance matrix of the dataset

• p_{j} the sum of the membership values to cluster j divided by the number of observations.

Value

A float: the Negentropy Increment 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)
calcNegentropyI(result$Data, result$Belongings, result$Centers)

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