KmL & KML3D : K- Means FOr Longitudinal Data
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KML & KML3D: K-MEANS FOR LONGITUDINAL DATA Christophe Genolini Bernard Desgraupes Bruno Falissard
description
KmL & KML3D : K- Means FOr Longitudinal Data. Christophe Genolini Bernard Desgraupes Bruno Falissard. Definition. Two trajectories. TEN trajectories. Two many trajectories. Solution : clusters. Cluster example. how cluster?. Parametric algorithms Non parametric algorithms. - PowerPoint PPT Presentation
Transcript of KmL & KML3D : K- Means FOr Longitudinal Data
KML & KML3D: K-MEANS FOR
LONGITUDINAL DATA
Christophe GenoliniBernard Desgraupes
Bruno Falissard
DEFINITION
TWO TRAJECTORIES
TEN TRAJECTORIES
TWO MANY TRAJECTORIES...
SOLUTION : CLUSTERS
CLUSTER EXAMPLE
HOW CLUSTER? Parametric algorithms
Non parametric algorithms
HOW CLUSTER? Parametric algorithms
Example : proc trajBase on likelihood
Non parametric algorithmsK means (KmL)
I ♥ Quebec…
LIKELIHOOD FOR SIZE
Size = 1,84
Small likelihood Big likelihood
BIG LIKELIHOOD?
PARAMETRIC ALGORITHMS
Number of clusters Trajectories shape (linear, polynomial,…) Distributions of variable (poisson, normal…)
Maximization of the likelihood
NON PARAMETRIC ALGORITHMS
Number of clusters
Maximization of some criteria
K-MEANSKML
K MEANS LONGITUDINAL
K MEANS LONGITUDINAL∆ +
3.4 4.2
1.7 2.3
0.65 1.2
3.1 2.3
3.9 3.2
K MEANS LONGITUDINAL∆ +
1.6 6.8
0.36 5.1
1.3 4
4.9 0.6
5.7 0.6
K MEANS LONGITUDINAL
EXAMPLE
> kml(cld3,4,1,print.traj=TRUE)
STRENGTH: MISSING VALUES
WEAKNESS: LOCAL MAXIMUM
SOLUTION: RE-RUNNING
PROBLEM: NUMBER OF CLUSTERS
EXAMPLE longData <- as.cld(gald())
kml(longData,2:5,10,print.traj=TRUE)
choice(longData)
KML3D
JOINT TRAJECTORIES
JOINT TRAJECTORIES
SOLUTION: CLUSTER 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}
PROBLEM
PROBLEM
PROBLEM
PROBLEM
PROBLEM
PROBLEM
PROBLEM
SOLUTION: THIRD DIMENSION
SOLUTION: THIRD DIMENSION
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)
CLUSTER IN 3D
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"))
PERSPECTIVES
AWARD: BEST “NUMBER OF CLUSTERS” FINDER…
The nominees are:Calinsky & HarabatzRay & TurieDavies & Bouldin ...
The winner is…
AWARD: BEST “NUMBER OF CLUSTERS” FINDER…
The nominees are:Calinsky & HarabatzRay & TurieDavies & Bouldin ...
The winner is…Falissard & Genolini (or G & F ?)
PERSPECTIVE : SHAPE DISTANCE
PERSPECTIVE : CLUSTER ACCORDING TO SHAPE« classic » distance
« shape » distance
IMPUTATION
IMPUTATION
IMPUTATION
IMPUTATION
THANK YOU!
