spConsistency {geocmeans}R Documentation

Spatial consistency index

Description

Calculate a spatial consistency index

Usage

spConsistency(belongmatrix, nblistw, nrep = 999)

Arguments

belongmatrix

A membership matrix

nblistw

A list.w object describing the neighbours (spdep package) observation must get in the membership matrix to not be considered as uncertain (default = NULL)

nrep

An integer indicating the number of permutation to do to simulate

Details

This index is experimental, it aims to measure how much a clustering solution is spatially consistent. A classification is spatially inconsistent if neighbouring observation do not belong to the same group. See detail for a description of its calculation

The total spatial inconsistency (*Scr*) is calculated as follow

isp = ∑_{i}∑_{j}∑_{k} (u_{ik} - u_{jk})^{2} * W_{ij}

With U the membership matrix, i an observation, k the neighbours of i and W the spatial weight matrix This represents the total spatial inconsistency of the solution (true inconsistency) We propose to compare this total with simulated values obtained by permutations (simulated inconsistency). The values obtained by permutation are an approximation of the spatial inconsistency obtained in a random context Ratios between the true inconsistency and simulated inconsistencies are calculated A value of 0 depict a situation where all observations are identical to their neighbours A value of 1 depict a situation where all observations are as much different as their neighbours that what randomness can produce A classification solution able to reduce this index has a better spatial consistency

Value

A named list with

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- LyonIris@data[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)
spConsistency(result$Belongings, Wqueen, nrep=50)

[Package geocmeans version 0.1.1 Index]