kml3d (version 0.6)

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 function needs to know the matrix of the distance between each individual.

Value

• Object of class Partition.

Author(s)

Christophe Genolini INSERM U669 / PSIGIAM: Paris Sud Innovation Group in Adolescent Mental Health Modal'X / Universite Paris Ouest-Nanterre- La Defense Contact author : [e-mail]

Details

Before alternating the phase Esperance and Maximisation, the EM algorithm needs to initialize a starting configuration. This initial partition has been proven to have an important impact on the final result and the convergence time. This function provides different ways of setting the initial partition.

• randomAll: all the individual are randomly assigned to a cluster with at least one individual in each clusters.
• randomK: K individuals are randomly assigned to a cluster, all the other are not assigned (each cluster has only one individual).
• maxDist: K indivuals are chosen. The two formers are the individual separated by the highest distance. The latter are added one by one, they are the "farthest" individual among those that are already been selected. "farthest" 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))) )

References

Article "KmL: K-means for Longitudinal Data", in Computational Statistics, Volume 25, Issue 2 (2010), Page 317. Web site: http://christophe.genolini.free.fr/kml

Examples

par(ask=TRUE)
###################
### Constrution of some longitudinal data
myCld <- gald()
plot(myCld)

###################
### partition using randamAll
pa1a <- partitionInitialise(3,lengthPart=150,method="randomAll")
plot(myCld,pa1a)
pa1b <- partitionInitialise(3,lengthPart=150,method="randomAll")
plot(myCld,pa1b)

###################
### partition using randamAll
pa2a <- partitionInitialise(3,lengthPart=150,method="randomK")
plot(myCld,pa2a)
pa2b <- partitionInitialise(3,lengthPart=150,method="randomK")
plot(myCld,pa2b)

###################
### partition using maxDist
pa3 <- partitionInitialise(3,lengthPart=150,method="maxDist",
    matrixDist=matDist3d(myCld["traj"]))
plot(myCld,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)