### KmL: K-Means Longitudinal Data

```Christophe Genolini
Bernard Desgraupes
Bruno Falissard
 Parametric
 Non
algorithms
parametric algorithms
 Parametric


Example : proc traj
Base on likelihood
 Non

algorithms
parametric algorithms
K means (KmL)
I ♥ Quebec…
Size = 1,84
Small likelihood
Big likelihood
 Number
of clusters
 Trajectories shape (linear, polynomial,…)
 Distributions of variable (poisson, normal…)
Maximization of the likelihood
 Number
of clusters
Maximization of some criteria
∆
+
3.4
4.2
1.7
2.3
0.65
1.2
3.1
2.3
3.9
3.2
∆
+
1.6
6.8
0.36
5.1
1.3
4
4.9
0.6
5.7
0.6
> kml(cld3,4,1,print.traj=TRUE)
longData <- as.cld(gald())
kml(longData,2:5,10,print.traj=TRUE)
choice(longData)
 C1:
partition for V1
 C2: partition for V2
 C1xC2:



partition for joint trajectories?
C1 = {small,medium,big}
C2 = {blue,red}
C1xC2 = {small blue, small red, medium blue,
medium red, big blue, big red}
par(mfrow=c(1,2))
a <- c(1,2,1,3,2,3,3,4,5,3,5)
b <- c(6,6,6,5,6,6,5,5,4,3,3)
plot(a,type="l",ylim=c(0,10),xlab="First variable",ylab="")
plot(b,type="l",ylim=c(0,10),xlab="Second variable",ylab="")
points3d(1:11,a,b)
axes3d(c("x", "y", "z"))
title3d(, , "Time","First variable","Second variable")
box3d()
aspect3d(c(2, 1, 1))
rgl.viewpoint(0, -90, zoom = 1.2)
cl <- gald(functionClusters=list(function(t){c(-4,-4)},function(t){c(5,0)},function(t){c(0,5)}),functionNoise = function(t){c(rnorm(1,0,2),rnorm(1,0,2))})
plot3d(cl)
kml(cl,3,1,paramKml=parKml(startingCond="randomAll"))
plot3d(cl,paramTraj=parTraj(col="clusters"))
 The




nominees are:
Calinsky & Harabatz
Ray & Turie
Davies & Bouldin
...
 The
winner is…
 The




Calinsky & Harabatz
Ray & Turie
Davies & Bouldin
...
 The


nominees are:
winner is…
Falissard & Genolini
(or G & F ?)
« classic » distance
« shape » distance
```