Calculate ELSA statistic for a hard partition. This local indicator of spatial autocorrelation can be used to determine where observations belong to different clusters.
calcELSA(object, nblistw = NULL, window = NULL, matdist = NULL)A FCMres object, typically obtained from functions CMeans, GCMeans, SFCMeans, SGFCMeans. Can also be a vector of categories. This vector must be filled with integers starting from 1. -1 can be used to indicate missing categories.
A list.w object describing the neighbours typically produced by the spdep package. Required if data is a dataframe, see the parameter window if you use a list of rasters as input.
A binary (0,1) matrix representing the neighbours spatial weights when working with rasters. The matrix must have odd dimensions.
A matrix representing the dissimilarity between the clusters. The matrix must be squared and the diagonal must be filled with zeros.
A depending of the input, a vector of ELSA values or a raster with the ELSA values.
The ELSA index (Naimi et al. 2019) can be used to measure local autocorrelation for a categorical variable. It varies between 0 and 1, 0 indicating a perfect positive spatial autocorrelation and 1 a perfect heterogeneity. It is based on the Shanon entropy index, and uses a measure of difference between categories. Thus it can reflect that proximity of two similar categories is still a form of positive autocorelation. The authors suggest to calculate the mean of the index at several lag distance to create an entrogram which quantifies global spatial structure and can be represented as a variogram-like graph.
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)
elsa_valus <- calcELSA(result)