ClustGeo (version 2.1)

hclustgeo: Ward clustering with soft contiguity contraints

Description

Implements a Ward-like hierarchical clustering algorithm including soft contiguity constraints. The algorithm takes as input two dissimilarity matrices D0 and D1 and a mixing parameter alpha between 0 an 1. The dissimilarities can be non euclidean and the weights of the observations can be non uniform. The first matrix gives the dissimilarities in the "feature space". The second matrix gives the dissimilarities in the "constraint" space. For instance, D1 can be a matrix of geographical distances or a matrix build from a contiguity matrix. The mixing parameter alpha sets the importance of the constraint in the clustering process.

Usage

hclustgeo(D0, D1 = NULL, alpha = 0, scale = TRUE, wt = NULL)

Arguments

D0

an object of class dist with the dissimilarities between the n observations. The function as.dist can be used to transform an object of class matrix to object of class dist.

D1

an object of class "dist" with other dissimilarities between the same n observations.

alpha

a real value between 0 and 1. This mixing parameter gives the relative importance of D0 compared to D1. By default, this parameter is equal to 0 and D0 is used alone in the clustering process.

scale

if TRUE the two dissimilarity matric D0 and D1 are scaled i.e. divided by their max. If D1=NULL, this parameter is no used and D0 is not scaled.

wt

vector with the weights of the observations. By default, wt=NULL corresponds to the case where all observations are weighted by 1/n.

Value

Returns an object of class hclust.

Details

The criterion minimized at each stage is a convex combination of the homogeneity criterion calculated with D0 and the homogeneity criterion calculated with D1. The parameter alpha (the weight of this convex combination) controls the importance of the constraint in the quality of the solutions. When alpha increases, the homogeneity calculated with D0 decreases whereas the homogeneity calculated with D1 increases.

References

M. Chavent, V. Kuentz-Simonet, A. Labenne, J. Saracco. ClustGeo: an R package for hierarchical clustering with spatial constraints. Comput Stat (2018) 33: 1799-1822.

See Also

choicealpha

Examples

# NOT RUN {
data(estuary)
# with one dissimilarity matrix
w <- estuary$map@data$POPULATION # non uniform weights 
D <- dist(estuary$dat)
tree <- hclustgeo(D,wt=w)
sum(tree$height)
inertdiss(D,wt=w)
inert(estuary$dat,w=w)
plot(tree,labels=FALSE)
part <- cutree(tree,k=5)
sp::plot(estuary$map, border = "grey", col = part)

# with two dissimilarity matrix
D0 <- dist(estuary$dat) # the socio-demographic distances
D1 <- as.dist(estuary$D.geo) # the geographical distances
alpha <- 0.2 # the mixing parameter
tree <- hclustgeo(D0,D1,alpha=alpha,wt=w)
plot(tree,labels=FALSE)
part <- cutree(tree,k=5)
sp::plot(estuary$map, border = "grey", col = part)

# }