initializePartition {longitudinalData}

~ Function: initializePartition ~

Description

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

Usage

initializePartition(nbClusters, lengthPart, method = "kmeans++", data)

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", "maxDist", "kmeans++", "kmeans+", "kmeans–" or "kmeans-".

data

[matrix]: data is the matrix of the individuals (usefull for the methods that need to compute distance between individual). If data is an array, the distance is computed using "maxDist" is used, the function needs to know the matrix of the distance between each individual.

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))) ). This method is efficient but time consuming.

• kmeans++: see [3]

• kmeans+, kmeans–, kmeans-: experimental methods derived from [3].

Value

vecteur of numeric.

Author

Christophe Genolini
1. UMR U1027, INSERM, Université Paul Sabatier / Toulouse III / France
2. CeRSME, EA 2931, UFR STAPS, Université de Paris Ouest-Nanterre-La Défense / Nanterre / France

References

[1] C. Genolini and B. Falissard
"KmL: k-means for longitudinal data"
Computational Statistics, vol 25(2), pp 317-328, 2010

[2] C. Genolini and B. Falissard
"KmL: A package to cluster longitudinal data"
Computer Methods and Programs in Biomedicine, 104, pp e112-121, 2011

[3] D. Arthur and S. Vassilvitskii
"k-means++: the advantages of careful seeding"
Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms. pp. 1027-1035, 2007.

Examples

par(ask=TRUE)
###################
### Constrution of some longitudinal data
data(artificialLongData)
dn <- longData(artificialLongData)
plotTrajMeans(dn)

###################
### partition using randamAll
pa1a <- initializePartition(3,lengthPart=200,method="randomAll")
plotTrajMeans(dn,partition(pa1a),parMean=parMEAN(type="n"),parTraj=parTRAJ(col="clusters"))
pa1b <- initializePartition(3,lengthPart=200,method="randomAll")
plotTrajMeans(dn,partition(pa1b),parMean=parMEAN(type="n"),parTraj=parTRAJ(col="clusters"))

###################
### partition using randamK
pa2a <- initializePartition(3,lengthPart=200,method="randomK")
plotTrajMeans(dn,partition(pa2a),parMean=parMEAN(type="n"),parTraj=parTRAJ(col="clusters"))
pa2b <- initializePartition(3,lengthPart=200,method="randomK")
plotTrajMeans(dn,partition(pa2b),parMean=parMEAN(type="n"),parTraj=parTRAJ(col="clusters"))

###################
### partition using maxDist
pa3 <- initializePartition(3,lengthPart=200,method="maxDist",data=dn["traj"])
plotTrajMeans(dn,partition(pa3),parMean=parMEAN(type="n"),parTraj=parTRAJ(col="clusters"))
### 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 <- initializePartition(2,nrow(points),method="maxDist",points)
plot(points,main="Two farest points")
lines(points[!is.na(paInit),],col=2,type="p",pch=16)

paInit <- initializePartition(3,nrow(points),method="maxDist",points)
plot(points,main="Three farest points")
lines(points[!is.na(paInit),],col=2,type="p",pch=16)

paInit <- initializePartition(4,nrow(points),method="maxDist",points)
plot(points, main="Four farest points")
lines(points[!is.na(paInit),],col=2,type="p",pch=16)

par(ask=FALSE)