K Means FOr Longitudinal Data Christophe Genolini Bernard Desgraupes Bruno Falissard Definition Two trajectories TEN trajectories Two many trajectories Solution clusters ID: 334140
Download Presentation The PPT/PDF document "KmL & KML3D" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
KmL & KML3D: K-Means FOr Longitudinal Data
Christophe GenoliniBernard DesgraupesBruno FalissardSlide2
DefinitionSlide3
Two trajectoriesSlide4
TEN trajectoriesSlide5
Two many trajectories...Slide6
Solution : clustersSlide7
Cluster exampleSlide8
how cluster?Parametric algorithmsNon parametric algorithmsSlide9
how cluster?Parametric algorithmsExample : proc traj
Base on likelihoodNon parametric algorithmsK means (KmL)Slide10
I
♥
Quebec…Slide11
Likelihood for size
Size = 1,84
Small likelihood
Big likelihoodSlide12
Big likelihood?Slide13
Parametric AlgorithmsNumber of clustersTrajectories shape (linear, polynomial,…)Distributions of variable (
poisson, normal…)Maximization of the likelihoodSlide14
Non Parametric algorithmsNumber of clusters
Maximization of some criteriaSlide15
K-meanskmlSlide16
K Means LongitudinalSlide17
K Means Longitudinal
∆
+
3.4
4.2
1.7
2.3
0.65
1.2
3.1
2.3
3.9
3.2Slide18
K Means Longitudinal
∆
+
1.6
6.8
0.36
5.1
1.3
4
4.9
0.6
5.7
0.6Slide19
K Means LongitudinalSlide20
Example
> kml(cld3,4,1,print.traj=TRUE)Slide21
Strength: Missing valuesSlide22
weakness:
local maximumSlide23
Solution:
re-runningSlide24
Problem: number of clustersSlide25
examplelongData
<- as.cld(gald())kml(
longData,2:5,10,print.traj
=TRUE)
choice
(
longData
)Slide26
kml3DSlide27
Joint trajectoriesSlide28
Joint trajectoriesSlide29
Solution: clusterC1: partition for V1C2: partition for V2C1xC2: partition for joint trajectories?C1 = {
small,medium,big}C2 = {blue,red}C1xC2 = {small blue, small red, medium blue, medium red, big blue, big red}Slide30
ProblemSlide31
ProblemSlide32
ProblemSlide33
ProblemSlide34
ProblemSlide35
ProblemSlide36
ProblemSlide37
Solution: third dimension Slide38
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)Slide39
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"))Slide40
PerspectivesSlide41
Award: best “number of clusters” finder…
The nominees are:Calinsky & HarabatzRay & TurieDavies & Bouldin...
The winner is…Slide42
Award: best “number of clusters” finder…
The nominees are:Calinsky & HarabatzRay & TurieDavies & Bouldin...
The winner is…Falissard & Genolini
(or G & F ?)Slide43
Perspective : shape distanceSlide44
Perspective : Cluster according to shape
«
classic
»
distance
«
shape
» distanceSlide45
ImputationSlide46
ImputationSlide47
ImputationSlide48
ImputationSlide49
Thank you!