Christophe Genolini Bernard Desgraupes Bruno Falissard

 Parametric algorithms  Non parametric algorithms

 Parametric algorithms  Example : proc traj  Base on likelihood  Non 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

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> 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 nominees are:  Calinsky & Harabatz  Ray & Turie  Davies & Bouldin ...  The winner is…  Falissard & Genolini  (or G & F ?)

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