kml (version 2.1.2)

partitionInitialise: ~ Function: partitionInitialise ~

Description

This function provide different way of setting the initial partition for an EM algoritm.

Usage

partitionInitialise(nbClusters, lengthPart, method = "randomK", matrixDist)

Arguments

nbClusters

[numeric]: number of clusters of that the initial partition should have.

lengthPart

[numeric]: number of individual in the partition.

method

[character]: one off "randomAll", "randomK" and "maxDist".

matrixDist

[matrix]: if the method "maxDist" is used, the fonction need to know the matrix of the distance between each individual.

Value

• Object of class Partition.

Details

Before alterning the phase Esperance and Maximisation, the EM algorithm need to initialise a starting configuration. This initial partition has been prooved to have an important impact on the final result and the convergence time. This function provide different way of setting the initial partition.

• randomAll: all the individual are randomly assign to a cluster with at least one individual in each clusters.
• randomK: K individuals are randomly assign to a cluster, all the other are not assign (each cluster has only one individual).
• maxDist: K indivuals are choose. The two formers are the individual separated by the highest distance. The latters are added one by one, they are the "farest" individual of those that are allready selected. "farest" is the individual with the highest distance (min) to the selected individuals (if "t" are the individual already selected, the next selected individual is "i" such that max_i(min_t(dist(IND_i,IND_t))) )

Examples

par(ask=TRUE)
###################
### Constrution of some longitudinal data
dn <- as.cld(gald())
plot(dn,type.mean="n",col=1)

###################
### partition using randamAll
pa1a <- partitionInitialise(3,lengthPart=200,method="randomAll")
plot(dn,pa1a)
pa1b <- partitionInitialise(3,lengthPart=200,method="randomAll")
plot(dn,pa1b)

###################
### partition using randamAll
pa2a <- partitionInitialise(3,lengthPart=200,method="randomK")
plot(dn,pa2a)
pa2b <- partitionInitialise(3,lengthPart=200,method="randomK")
plot(dn,pa2b)

###################
### partition using maxDist
pa3 <- partitionInitialise(3,lengthPart=200,method="maxDist",
    matrixDist=as.matrix(dist(dn["traj"])))
plot(dn,pa3)
### maxDist is deterministic, so no need for a second example

###################
### Example to illustrate "maxDist" method on classical clusters
point <- matrix(c(0,0, 0,1, -1,0, 0,-1, 1,0),5,byrow=TRUE)
points <- rbind(point,t(t(point)+c(10,0)),t(t(point)+c(5,6)))
points <- rbind(points,t(t(points)+c(30,0)),t(t(points)+c(15,20)),t(-t(point)+c(20,10)))
plot(points,main="Some points")

paInit <- partitionInitialise(2,nrow(points),as.matrix(dist(points)),method="maxDist")
plot(points,main="Two farest points")
lines(points[!is.na(paInit["clusters"]),],col=2,type="p",lwd=3)

paInit <- partitionInitialise(3,nrow(points),as.matrix(dist(points)),method="maxDist")
plot(points,main="Three farest points")
lines(points[!is.na(paInit["clusters"]),],col=2,type="p",lwd=3)

paInit <- partitionInitialise(4,nrow(points),as.matrix(dist(points)),method="maxDist")
plot(points, main="Four farest points")
lines(points[!is.na(paInit["clusters"]),],col=2,type="p",lwd=3)

par(ask=FALSE)