~ Package overview: longitudinalData ~

Description

longitudinalData package provide some tools to deal with the clusterization of longitudinal data.

Details

Overview

longitudinalData provide some tools to deal with the clustering of longitudinal data, mainly:

1. plotTrajMeans

2. imputation

3. qualityCriterion

Author

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

References

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

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

See Also

Classes: LongData, Partition
Methods: longData, partition, ordered
Plot: plotTrajMeans, plotTrajMeans3d
Imputation: imputation
Criterion: qualityCriterion

Examples

### Generation of artificial longData
data(artificialJointLongData)
myData <- longData3d(artificialJointLongData,timeInData=list(var1=2:12,var2=13:23,var3=24:34))

part <- partition(rep(1:3,each=50))
plotTrajMeans3d(myData,part)

### Quality criterion
qualityCriterion(myData,part)

~ Constants ~

Description

Constants define in the package ~

Usage

MAX_CLUSTERS
CRITERION_NAMES
DISTANCE_METHODS
CHOICE_STYLE

Value

MAX_CLUSTERS = 26

CLUSTER_NAMES = paste("c",2:MAX_CLUSTERS,sep="")

CRITERION_NAMES <- c(
"Calinski.Harabatz","Kryszczuk.Calinski","Genolini.Calinski","Ray.Turi","Davies.Bouldin",
"BIC","BIC2","AIC","AICc","AICc2","postProbaGlobal","random"
)

DISTANCE_METHODS = c("manhattan", "euclidean", "minkowski", "maximum", "canberra", "binary")

CHOICE_STYLE = list(
typeTraj=c("l","l","n"),
colTraj=c("clusters","black","black"),
typeMean=c("b","b","b","b","l","l","n"),
colMean=c("clusters","black","clusters","black","clusters","black","black"),
pchMean=c("letters","letters","symbols","symbols","letters","letters","letters")
)

Examples

### Maximum number of clusters that kml can deal with
MAX_CLUSTERS

### Names of the field that save clusters in object 'ClusterLongData'
cat(CLUSTER_NAMES,"\n")

### List of the available criterion
CRITERION_NAMES

### Distance available
DISTANCE_METHODS[2]

### Define the style use by choice
CHOICE_STYLE[['typeTraj']][2]

~ Class: ListPartition ~

Description

An object of class ListPartition contain several liste of Partition sorted by cluster numbers.

Objects from the Class

Objects are mainly design to store the numerous Partition found by kml or kml3d.

Slots

criterionActif

[character]: Store the criterion name that will be used by fonctions that need a single criterion (like plotCriterion or ordered).

initializationMethod

[vector(chararcter)]: list all the initialization method that has allready been used to find some Partition (usefull to not run several time a deterministic method).

sorted

[logical]: are the Partition curently hold in the object sorted in decreasing (or increasing, according to criterionActif) order ?

c1

[list(Partition)]: list of Partition with 1 clusters.

c2

[list(Partition)]: list of Partition with 2 clusters.

c3

[list(Partition)]: list of Partition with 3 clusters.

c4

[list(Partition)]: list of Partition with 4 clusters.

c5

[list(Partition)]: list of Partition with 5 clusters.

c6

[list(Partition)]: list of Partition with 6 clusters.

c7

[list(Partition)]: list of Partition with 7 clusters.

c8

[list(Partition)]: list of Partition with 8 clusters.

c9

[list(Partition)]: list of Partition with 9 clusters.

c10

[list(Partition)]: list of Partition with 10 clusters.

c11

[list(Partition)]: list of Partition with 11 clusters.

c12

[list(Partition)]: list of Partition with 12 clusters.

c13

[list(Partition)]: list of Partition with 13 clusters.

c14

[list(Partition)]: list of Partition with 14 clusters.

c15

[list(Partition)]: list of Partition with 15 clusters.

c16

[list(Partition)]: list of Partition with 16 clusters.

c17

[list(Partition)]: list of Partition with 17 clusters.

c18

[list(Partition)]: list of Partition with 18 clusters.

c19

[list(Partition)]: list of Partition with 19 clusters.

c20

[list(Partition)]: list of Partition with 20 clusters.

c21

[list(Partition)]: list of Partition with 21 clusters.

c22

[list(Partition)]: list of Partition with 22 clusters.

c23

[list(Partition)]: list of Partition with 23 clusters.

c24

[list(Partition)]: list of Partition with 24 clusters.

c25

[list(Partition)]: list of Partition with 25 clusters.

c26

[list(Partition)]: list of Partition with 26 clusters.

Construction

Class ListPartition objects are mainly constructed by kml. Neverdeless, it is also possible to construct them from scratch using the fonction listPartition that does create an empty object.

Methods

object['xxx']

If 'xxx' is 'cX', 'initializationMethod', 'sorted' or 'criterionActif', get the value of the field xxx.

object['criterionValues',j]

Give the values of the criterion 'j' for all the Partitions. The result is return as a list. If 'j' is missing, the criterion actif is used.

object['criterionValuesAsMatrix',j]

Give the values of the criterion 'j' for all the Partitions. The result is return as a matrix. If 'j' is missing, the criterion actif is used.

object['xxx']

If 'xxx' is a criterion, this is equivalent to object['criterionValuesAsMatrix','xxx']

object['initializationMethod']<-value

Set the field to value

object['criterionActif']<-value

If 'value' is one of CRITERION_NAMES, it sets the field to the criterion 'value'.

object['add']<-value

If 'value' is an object of class 'Partition', then value is added to the Partition already hold in the field 'cX'. Note that a Partition with 'X' clusters is automatiquely added to the correct list 'cX' according to its number of clusters.

object['clear']<-'cX'

Clear the list 'cX'.

listPartition

Constructor. Build an empty object.

ordered

Order the Partition according to the criterion actif.

regroup

Order then merge identical Partition (usefull to reduce the size of the ListPartition)

Author

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

References

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

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

See Also

Classes: LongData
Methods: Partition

Examples

##############
### Preparing data
data(artificialLongData)
traj <- as.matrix(artificialLongData[,-1])

### Some clustering
part2 <- partition(rep(c("A","B"),time=100),traj)
part3 <- partition(rep(c("A","B","C","A"),time=50),traj)
part3b <- partition(rep(c("A","B","C","B","C"),time=40),traj)
part4 <- partition(rep(c("A","B","A","C","D"),time=40),traj)


################
### ListPartition
listPart <- listPartition()
plotCriterion(listPart)

listPart["add"] <- part2
listPart["add"] <- part3
listPart["add"] <- part3b
listPart["add"] <- part4
listPart["add"] <- part4
listPart["add"] <- part3
listPart["add"] <- part3b

plotCriterion(listPart)
ordered(listPart)
plotCriterion(listPart)
regroup(listPart)
plotCriterion(listPart)
plotAllCriterion(listPart)

~ Class: LongData ~

Description

LongData is an objet containing the longitudinal data (the individual trajectories) and some associate value (like time, individual identifiant,...). It can be used either for a single variable-trajectory or for joint variable-trajectories.

Objects from the Class

Object LongData for single variable-trajectory can be created using the fonction longData on a data.frame or on a matrix.

LongData for joint trajectories can be created by calling the fonction longData3d on a data.frame or on an array.

Slots

idAll

[vector(character)]: Single identifier for each of the longData (each individual). Usefull to export clusters.

idFewNA

[vector(character)]: Restriction of idAll to the trajectories that does not have 'too many' missing value. See maxNA for 'too many' definition.

time

[numeric]: Time at which measures are made.

varNames

[character]: Name of the variable measured.

traj

[matrix(numeric)]: Contains the longitudianl data. Each lines is the trajectories of an individual. Each column is the time at which measures are made.

dimTraj

[vector3(numeric)]: size of the matrix traj (ie dimTraj=c(length(idFewNA),length(time))).

maxNA

[numeric] or [vector(numeric)]: Individual whose trajectories contain 'too many' missing value are exclude from traj and will no be use in the analysis. Their identifier is preserved in idAll but not in idFewNA. 'too many' is define by maxNA: a trajectory with more missing than maxNA is exclude.

reverse

[matrix(numeric)]: if the trajectories are scale using the function scale, the 'scaling parameters' (probably mean and standard deviation) are saved in reverse. This is usefull to restore the original data after a scaling operation.

Construction

Object LongData for single variable-trajectory can be created by calling the fonction longData on a data.frame or on a matrix.

LongData for joint trajectories can be created by calling the fonction longData3d on a data.frame or on an array.

Get [

Object["idAll"]

[vecteur(character)]: Gets the full list of individual identifiant (the value of the slot idAll)

Object["idFewNA"]

[vecteur(character)]: Gets the list of individual identifiant with not too many missing values (the value of the slot idFewNA)

Object["varNames"]

[character]: Gets the name(s) of the variable (the value of the slot varNames)

Object["time"]

[vecteur(numeric)]: Gets the times (the value of the slot time)

Object["traj"]

[array(numeric)]: Gets all the longData' values (the value of the slot traj)

Object["dimTraj"]

[vector3(numeric)]: Gets the dimension of traj.

Object["nbIdFewNA"]

[numeric]: Gets the first dimension of traj (ie the number of individual include in the analysis).

Object["nbTime"]

[numeric]: Gets the second dimension of traj (ie the number of time measurement).

Object["nbVar"]

[numeric]: Gets the third dimension of traj (ie the number of variables).

Object["maxNA"]

[vecteur(numeric)]: Gets maxNA.

Object["reverse"]

[matrix(numeric)]: Gets the matrix of the scaling parameters.

Methods

scale

scale the trajectories. Usefull to normalize variable trajectories measured with different units.

restoreRealData

restore original data that have been modified after a scaling operation.

longDataFrom3d

Extract a variable trajectory form a dataset of joint trajectories.

plotTrajMeans

plot all the variables of the LongData, optionnaly according to a Partition.

plotTrajMeans3d

plot two variables of the LongData in 3 dimensions, optionnaly according to a Partition.

plot3dPdf

create 'Triangle objects' representing in 3D the cluster's center according to a Partition. 'Triangle object' can latter be include in a LaTeX file to get a dynamique (rotationg) pdf figure.

imputation

Impute the missing values of the trajectories.

qualityCriterion

Compute some quality criterion that can be use to compare the quality of differents Partition.

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

See Also

Overview: longitudinalData-package
Methods: longData, longData3d, imputation, qualityCriterion
Plot: plotTrajMeans, plotTrajMeans3d, plot3dPdf

Examples

#################
### building trajectory (longData)
mat <- matrix(c(NA,2,3,4,1,6,2,5,1,3,8,10),4)
ld <- longData(mat,idAll=c("I1","I2","I3","I4"),time=c(2,4,8),varNames="Age")

### '[' and '[<-'
ld["idAll"]
ld["idFewNA"]
ld["varNames"]
ld["traj"]
(ld)

### Plot
plotTrajMeans(ld,parMean=parMEAN(type="n"))

~ Class: LongData3d ~

Description

LongData3d is an objet containing joint longitudinal data and some associate value (like time, individual identifiant,...).

Objects from the Class

Object LongData3d can be created using the fonction longData3d on a data.frame or on an array.

Slots

idAll

[vector(character)]: Single identifier for each of the longData3d (each individual). Usefull to export clusters.

idFewNA

[vector(character)]: Restriction of idAll to the trajectories that does not have 'too many' missing value. See maxNA for 'too many' definition.

time

[numeric]: Time at which measures are made.

varNames

[vector(character)]: Names of the variable measured.

traj

[array(numeric)]: Contains the joint variable-trajectories. Each horizontal plan (first dimension) corresponds to the joint-trajectories of an individual. Vertical plans (second dimension) refer to the time at which measures are made. Transversal plans (the third dimension) are for variables.

dimTraj

[vector3(numeric)]: size of the array traj (ie dimTraj=c(length(idFewNA),length(time),length(varNames))).

maxNA

[numeric] or [vector(numeric)]: Individual whose trajectories contain 'too many' missing value are exclude from traj and will no be use in the analysis. Their identifier is preserved in idAll but not in idFewNA. 'too many' is define by maxNA: a trajectory with more missing than maxNA is exclude. When maxNA is a single number, it is recycled for all the variables.

reverse

[matrix(numeric)]: if the trajectories are scale using the function scale, the 'scaling parameters' (probably mean and standard deviation) are saved in reverse. This is usefull to restore the original data after a scaling operation.

Construction

LongData3d can be created by calling the fonction longData3d on a data.frame or on an array.

Get [

Object["idAll"]

[vecteur(character)]: Gets the full list of individual identifiant (the value of the slot idAll)

Object["idFewNA"]

[vecteur(character)]: Gets the list of individual identifiant with not too many missing values (the value of the slot idFewNA)

Object["varNames"]

[character]: Gets the name(s) of the variable (the value of the slot varNames)

Object["time"]

[vecteur(numeric)]: Gets the times (the value of the slot time)

Object["traj"]

[array(numeric)]: Gets all the joint trajectories (the value of the slot traj)

Object["dimTraj"]

[vector3(numeric)]: Gets the dimension of traj.

Object["nbIdFewNA"]

[numeric]: Gets the first dimension of traj (ie the number of individual include in the analysis).

Object["nbTime"]

[numeric]: Gets the second dimension of traj (ie the number of time measurement).

Object["nbVar"]

[numeric]: Gets the third dimension of traj (ie the number of variables).

Object["maxNA"]

[vecteur(numeric)]: Gets maxNA.

Object["reverse"]

[matrix(numeric)]: Gets the matrix of the scaling parameters.

Methods

scale

scale the trajectories. Usefull to normalize variable trajectories measured with different units.

restoreRealData

restore original data that have been modified after a scaling operation.

longDataFrom3d

Create a LongData by extracting a single variable trajectory form a dataset of joint variable-trajectories.

plotTrajMeans

plot all the variable of the LongData3d, optionnaly according to a Partition.

plotTrajMeans3d

plot two variables of the LongData3d in a 3 dimensions graph, optionnaly according to a Partition.

plot3dPdf

create 'Triangle objects' representing in 3D the cluster's center according to a Partition. 'Triangle object' can latter be include in a LaTeX file to get a dynamique (rotationg) pdf figure.

imputation

Impute the missing values of the trajectories.

qualityCriterion

Compute some quality criterion that can be use to compare the quality of differents Partition.

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

See Also

Overview: longitudinalData-package
Methods: LongData, longData3d, imputation, qualityCriterion
Plot: plotTrajMeans, plotTrajMeans3d, plot3dPdf

Examples

#################
### building joint trajectories

dn <- data.frame(id=1:3,v1=c(11,14,16),t1=c(1,5,7),v2=c(12,10,13),t2=c(2,5,0),t3=c(3,6,8))
(ld <- longData3d(dn,timeInData=list(Vir=c(2,4,NA),Tes=c(3,5,6))))

### Scaling
scale(ld)
(ld)

### Plotting
plotTrajMeans3d(ld)
restoreRealData(ld)

~ Class: ParLongData ~

Description

ParLongData is an objet containing some graphical parameter used to plot LongData object and / or mean trajectories. They work as define in par.

Slots

type

[character]: Type of the plot that should be drawn ('p' for point, 'l' for line, 'b' for both, 'c' line appart, 'o' for overplot, 'h' for histogram, 's' and 'S' for steps, 'n' for no ploting)

col

[character]: A specification for the default plotting color. Can be either a single value or a vector.

pch

[numeric] or [character]: Either an integer specifying a symbol or a single character to be used as the default in plotting points. See example in points for possible values and their interpretation.

pchPeriod

[numeric]: Fix the number of point that should be plot. Usefull to plot points on trajectories with a lot of mesurement (see examples in plotTrajMeans for LongData for details).

cex

[numeric]: A numerical value giving the amount by which plotting text and symbols should be magnified relative to the default.

xlab

[character]: A title for the x axis.

ylab

[character]: A title for the y axis.

Construction

Object ParLongData can be created by three functions:

1. parLongData create an object from scratch ;

2. parTraj create an object containing default value to plot individutal trajectories;

3. parMean create an object containing default value to plot mean trajectories.

Methods

object['xxx']

Get the value of the field xxx.

object['xxx']<-value

Set the field xxx to value.

Author(s)

Christophe Genolini
PSIGIAM: Paris Sud Innovation Group in Adolescent Mental Health
INSERM U669 / Maison de Solenn / Paris

Contact author : <genolini@u-paris10.fr>

English translation

Raphaël Ricaud
Laboratoire "Sport & Culture" / "Sports & Culture" Laboratory
University of Paris 10 / Nanterre

Examples

   ### Building ParLongData
   parMyData <- parLongData(type="n",col=3,pch="1",pchPeriod=20,cex=1,xlab="Time",ylab="Size")

   ### Get
   parMyData['col']

   ### Set
   parMyData['cex'] <- 3
   (parMyData)

~ Class: ParWindows ~

Description

ParWindows is an objet containing graphical parameter used to set the screen display.

Slots

nbCol

[numeric]: Number of column of the screen matrix.

nbRow

[numeric]: Number of row of the screen matrix.

addLegend

[logical]: Shall a legend be added on the graph?

closeScreen

[logical]: On exit, high level plot function can either close the screen that they open and return nothing ; or not close it and return the list of the screen number.

screenMatrix

[matrix(numeric)]: Matrix with 4 column defining the screen region, like the figs argument of the function screen. The screenMatrix can be specified by the user (bad idea) or can be compute automaticaly according to nbCol, nbRow and addLegend. For that, use windowsCut.

Construction

Object ParWindows can be created by the constructor parWindows or by the function windowsCut.

Methods

object['xxx']

Get the value of the field xxx.

object['xxx']<-value

Set the field xxx to value.

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

Examples

### Building ParWindows
(paramWin <- parWindows(3,2,FALSE,TRUE))

### Get
figsScreen <- paramWin['screenMatrix']

### Usage
listScreen <- split.screen(figsScreen)
screen(listScreen[1])
plot(-5:5/10,2.5-(-5:5)^2/20,ylim=c(0,6),axes=FALSE,xlab="",ylab="",type="l",lwd=3)
lines(-5:5/10,(-5:5)^2/20,ylim=c(0,6),type="l",lwd=3)

screen(listScreen[3])
plot(-5:5/10,2.5-(-5:5)^2/20,ylim=c(0,6),axes=FALSE,xlab="",ylab="",type="l",lwd=3)
lines(-5:5/10,(-5:5)^2/20,ylim=c(0,6),type="l",lwd=3)

screen(listScreen[5])
plot(-5:5/10,(-5:5)^2/10,ylim=c(0,6),axes=FALSE,xlab="",ylab="",type="l",lwd=3)
lines(-5:5/10,(-5:5)^2/20+1.25,ylim=c(0,6),type="l",lwd=3)
close.screen(all.screens=TRUE)

### Sorry for that...

~ Class: Partition ~

Description

An object of class Partition is a partition of a population into subgroups. The object also contains some information like the percentage of trajectories in each group or some qualities criterion.

Objects from the Class

Objects are mainly intend to be created by some clustering methods (like k-means, fuzzy k-means, mixture modeling, latent class analysis,...)

Slots

nbClusters

[numeric]: number of groups, between 1 and 26

clusters

[vector(factor)]: vector containing the groups of each individual. Groups are in upper-case letters.

percentEachCluster

[vector(numeric)]: percentage of trajectories contained in each group.

postProba

[matrix(numeric)]: assuming that in each clusters C and for each time T, variable follow a normal law (mean and standard deviation of the variable at time T restricted to clusters C), then it is possible to compute the postterior probabilities of each individual (that is the probabilities that an individual has to belong to each clusters). These probabilities are hold in postProba.

postProbaEachCluster

[vector(numeric)]: for each clusters C, mean of the post probabilities to belong to C of the individual that effectively belong to C. A high percent means that the individual that are in this cluter realy meant to be here.

criterionValues

[vector(numeric)]: Value of the quality criterions used to evaluate the quality of the Clustering. See qualityCriterion for details.

details

[vector(character)]: hold different optionnal informations like the algorithm (if any) used to find the partition, the convergence time, the imputation methods, the starting condition. Examples: details=c(algorithm="kmeans",convergenceTime="3").

validation rules

A class Partition object must follow some rules to be valid:

• Slots should be either all empty, or all non empty.

• nbClusters has to be lower or equal to 26.

• clusters is a factor in LETTERS[1:nbCluster].

Construction

Class Partition objects are mainly constructed by some clustering methods (like k-means, fuzzy k-means, mixture modeling, latent class analysis,...). Neverdeless, it is also possible to construct them from scratch using the fonction partition.

Get [

Object["nbClusters"]

[numeric]: Gets the number of clusters (the value of the slot nbClusters)

Object["clusters"]

[vector(factor)]: Gets the cluster of each individual (the value of the slot clusters)

Object["clustersAsInteger"]

[vector(integer)]: Gets the cluster of each individual and turn them into integer

Object["percentEachClusters"]

[vector(numeric)]: Get the percent of individual in each clusters (the value of the slot nbClusters)

Object["postProbaEachClusters"]

[vector(numeric)]: Get the post probabilities for each clusters.

Object["postProba"]

[matrix(numeric)]: Get the post probabilities for each individual and each clusters.

Object["criterionValues"]

[vector(numeric)]: gives the values of all the criterion values (the value of the slot criterionValues)

Object["details"]

[vector(character)]: Get the values of the slot details.

Object["XcriterionX"]

[numeric]: Get the value of the criterion XcriterionX. It can be one of Calinski.Harabatz, Krzysztof.Calinski, Genolini.Calinski, Ray.Turi, Davies.Bouldin, BIC, AIC, AICc or random.

Object["XspecialX"]

[character]: Get the value named XspecialX in the slot details (probably one of multiplicity, convergenceTime, imputationMethod or algorithm.)

Setteur [<-

Object["multiplicity"]<-value

[numeric]: In the slot details, sets the values names multiplicity to value.

Object["convergenceTime"]<-value

[numeric]: In the slot details, sets the values names convergenceTime to value.

The others slot can not be change after the object creation.

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

See Also

Overview: longitudinalData-package
Classes: LongData
Methods: partition

Examples

############
### Building Partition

### number
part <- partition(rep(c(1,2,1,3),time=3))

### LETTERS
part <- partition(rep(c("A","B","D"),time=4),details=c(convergenceTime="3",multiplicity="1"))

### Others don't work
try(partition(rep(c("A","Bb","C"),time=3)))

#############
### Setteur and Getteur

### '['
part["clusters"]
part["clustersAsInteger"]
part["nbClusters"]

### '[<-'
part["multiplicity"] <- 2
(part)

~ Data: artificialJointLongData ~

Description

Some artificial joint longitudinal data.

Usage

data(artificialJointLongData)

Format

Some joint longitudinal data in wide format. It includes 90 trajectories divided in 3 groups.

id

unique idenfier for each patient.

v0

Measurment of variable 'V' at time t0

v1

Measurment of variable 'V' at time t1

...

...

v10

Measurment of variable 'V' at time t0

w0

Measurment of variable 'W' at time t0

w1

Measurment of variable 'W' at time t1

...

...

w10

Measurment of variable 'W' at time t0

x0

Measurment of variable 'X' at time t0

x1

Measurment of variable 'X' at time t1

...

...

x10

Measurment of variable 'X' at time t0

Details

Some joint longitudinal data in wide format. It includes 90 trajectories divided in 3 groups.

Author(s)

Christophe Genolini

Examples

data(artificialJointLongData)
str(artificialJointLongData)

~ Data: artificialLongData ~

Description

Some artificial longitudinal data.

Usage

data(artificialLongData)

Format

Some longitudinal data in wide format. It includes 120 trajectories divided in 4 groups.

id

unique idenfier for each patient.

t0

Measurment at time t0

t1

Measurment at time t1

...

...

t10

Measurment at time t10

Details

Some artificial longitudinal data in wide format. It includes 120 trajectories divided in 4 groups.

Author(s)

Christophe Genolini

Examples

data(artificialLongData)
str(artificialLongData)

~ Function: Frechet distance ~

Description

Compute Frechet distance between two trajectories.

Usage

distFrechet(Px,Py,Qx, Qy, timeScale=0.1, FrechetSumOrMax = "max")

Arguments

Details

Given two curve P and Q, Frechet distance between P and Q is define as inf_{a,b} max_{t} d(P(a(t)),Q(b(t))). It's computation is a NP-complex problem. When P and Q are trajectories (discrete curve), the problem is polynomial.

The Frechet distance can also be define using a sum instead of a max: inf_{a,b} sum_{t} d(P(a(t)),Q(b(t)))

The function distFrechet is C compiled, the function distFrechetR is in R, the function distFrechetRec is in recursive (the slowest) in R.

Value

A numeric value.

Author

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

References

[1] Thomas Eiter & Heikki Mannila:
"Computing Discrete Fr´echet Distance"

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

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

See Also

distTraj

Examples

   Px <- 1:20
   Py <- dnorm(1:20,12,2)
   Qx <- 1:20
   Qy <- dnorm(1:20,8,2)

   distFrechet(Px,Py,Qx,Qy)

   ### Frechet using sum instead of max.
   distFrechet(Px,Py,Qx,Qy,FrechetSumOrMax="sum")

~ Function: expandParLongData ~

Description

Prepare the values of an object ParLongData to make them being usable by a plotting function.

Usage

expandParLongData(xParLongData, y)

Arguments

Details

ParLongData object can hold values that are easy to specify (like col="clusters" or pch="symbol") but that can not be directly used by graphical functions plotTrajMeans and plotTrajMeans3d. This function modify theses values to make them fit with plotTrajMeans and plotTrajMeans3d expectations.

The field col and pch are the ones concern by this function.

If y is a Partition, col and pch are extanded to fit with the number of individual. If y is a number of clusters, col and pch are extanded to fit with the number of clusters.

If col='clusters', a color is affected to each clusters. Then the field col receive a vector of color such that each individual (if y is a Partition) or each clusters (if y is a number of clusters) get its corresponding color.

If pch='letters', a letters is affected to each clusters. Then the field pch receive a vector of letters such that each individual (if y is a Partition) or each clusters (if y is a number of clusters) get its corresponding letters.

Same if pch='symbols'.

Value

An object of class ParLongData

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

Examples

###################
### Some parameters for trajectories
(paramTraj <- parTRAJ(col="clusters"))

### Expand to a small partition with 3 clusters
part <- partition(LETTERS[rep(1:3,4)])
expandParLongData(paramTraj,part)


###################
### Some parameters for the mean trajectories
paramMean <- parMEAN()

### If there is 3 clusters :
expandParLongData(paramMean,3)

### If there is 5 clusters :
expandParLongData(paramMean,5)

~ Function: imputation ~

Description

imputation is a function that offer different methods to impute missing value of a LongData (or a matrix).

Usage

imputation(traj,method="copyMean",lowerBound="globalMin",upperBound="globalMax")

Arguments

Details

imputation is a function that impute missing value of a LongData or a matrix. Several imputation methods are available. A brief description follows. For a fully detailled description, see [3]. Illustrating examples showing strenghs and weakness of methods are presented section "examples".

For each method, the imputation has to deal with monotone missing value (at start and at end of the trajectories) and intermitant (in the middle). Here is a brief description of each methods.

'linearInterpol.locf' (linear interpolation, locf)

Intermitant:

values imediatly surounding the missing are join by a line.

Monotone:

imputed by 'locf' or 'nocb'.

'linearInterpol.global' (linear interpolation, global slope)

Intermitant:

values imediatly surounding the missing are join by a line.

Monotone:

the line joining the first and last non-missing value is considered (this line is the everage progression of the actual individual trajectoire). Missing-value at start and at end are chosen on this line.

'linearInterpol.local' (linear interpolation, global slope)

Intermitant:

values imediatly surounding the missing are join by a line.

Monotone at start:

the line joining the first and second non-missing value is considered. Missing-value at start are chose on this line.

Monotone at end:

the line joining the last and penultimate non-missing value is considered. Missing-value at end are chosen on this line.

'linearInterpol.bisector' (linear interpolation, bisector)

Intermitant:

values imediatly surounding the missing are join by a line.

Monotone:

linearInterpol.global is not sensitive to local variation, linearInterpol.local might be too much sensitive to abnormal value. linearInterpol.bisector offer a medium solution by considering the bissectrice of Global and Local solution. Point are chosen on the bissectrices.

'copyMean.locf' (copy mean, locf)

this method impute in two stages. First, it use 'linearInterpol.locf'. Then it add to each imputed value a variation that make the imputed value follow the shape of the average trajectory. For more details, see [3] and examples' section.

'copyMean.global' (copy mean, global slope)

this method impute in two stages. First, it use 'linearInterpol.global'. Then it add to each imputed value a variation that make the imputed value follow the shape of the average trajectory. For more details, see [3] and examples' section.

'copyMean.local' (copy mean, local slope)

this method impute in two stages. First, it use 'linearInterpol.local'. Then it add to each imputed value a variation that make the imputed value follow the shape of the average trajectory. For more details, see [3] and examples' section.

'copyMean.bisector' (copy mean, bisector)

this method impute in two stages. First, it use 'linearInterpol.bisector'. Then it add to each imputed value a variation that make the imputed value follow the shape of the average trajectory. For more details, see [3] and examples' section.

locf (Last Occurence Carried Forward)

THIS METHOD HAS BEEN PROUVEN TO NOT BE EFFICIANT SEVERAL TIME BY VARIOUS AUTHOR, we strongly recommand to not use it !

Intermitant and monotone at end:

the previous non-missing value is dipplicated forward.

Monotone at start:

the first non-missing value is dupplicated backward (nocb).

nocb (Next Occurence Carried Backward)

THIS METHOD HAS BEEN PROUVEN TO NOT BE EFFICIANT SEVERAL TIME BY VARIOUS AUTHOR, we strongly recommand to not use it !

Intermitant and monotone at start:

the next non-missing value is dipplicated backward.

Monotone at end:

the last non-missing value is dupplicated forward (locf).

trajMean

missing are imputed by the mean of the trajectory.

trajMedian

missing are imputed by the median of the trajectory.

trajHotDeck

each missing is imputed by one non-missing (randomly choosen) value of the trajectory.

crossMean

missing value at time t are imputed by the mean of all value present at time t.

crossMedian

missing value at time t are imputed by the median of all value present at time t.

crossHotDeck

each missing value at time t is imputed by one non-missing (randomly choosen) value present at time t.

Value

A LongData or a matrix with no missing values.

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] Christophe Genolini, René Écochard and Hélène Jacqmin-Gadda
"Copy Mean: A New Method to Impute Intermittent Missing Values in Longitudinal Studies"
Open Journal of Statistics, vol 3(26),2013

See Also

LongData, Partition, qualityCriterion

Examples

##################
### Preparation of the data
par(ask=TRUE)
timeV <- 1:14

matMissing <- matrix(
    c(NA  ,NA  ,NA  ,18  ,22  ,NA  ,NA  ,NA  ,NA  , 24  , 22  , NA  , NA  , NA,
      24  ,21  ,24  ,26  ,27  ,32  ,30  ,22  ,26  , 26  , 28  , 24  , 23  , 21,
      14  ,13  , 10 , 8  , 7  ,18  ,16  , 8  ,12  ,  6  ,  10 ,  10 ,  9  ,  7,
       3  ,1   , 1  , 1  ,  3,9   , 7  , -1 , 3   ,  2   ,  4 ,  1  ,  0  , -2
   ),4,byrow=TRUE
)


matplot(t(matMissing),col=c(2,1,1,1),lty=1,type="l",lwd=c(3,1,1,1),pch=16,
   xlab="Black=trajectories; Green=mean trajectory\nRed=trajectory to impute",
   ylab="",main="Four trajectories")
moy <- apply(matMissing,2,mean,na.rm=TRUE)
lines(moy,col=3,lwd=3)

 # # # # # # # # # # # # # # # # # # # # # # # # # #
#   Illustration of the different imputing method   #
 #           The best are at end  !!!              #
  # # # # # # # # # # # # # # # # # # # # # # # # #



##################
### Methods using cross sectionnal information (cross-methods)

par(mfrow=c(1,3))
mat2 <- matrix(c(
  NA, 9, 8, 8, 7, 6,NA,
   7, 6,NA,NA,NA, 4,5,
   3, 4, 3,NA,NA, 2,3,
  NA,NA, 1,NA,NA, 1,1),4,7,byrow=TRUE)

### crossMean
matplot(t(imputation(mat2,"crossMean")),type="l",ylim=c(0,10),
   lty=1,col=1,main="crossMean")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### crossMedian
matplot(t(imputation(mat2,"crossMedian")),type="l",ylim=c(0,10),
   lty=1,col=1,main="crossMedian")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### crossHotDeck
matplot(t(imputation(mat2,"crossHotDeck")),type="l",ylim=c(0,10),
   lty=1,col=1,main="crossHotDeck")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)



##################
### Methods using trajectory information (traj-methods)

par(mfrow=c(2,3))
mat1 <- matrix(c(NA,NA,3,8,NA,NA,2,2,1,NA,NA),1,11)

### locf
matplot(t(imputation(mat1,"locf")),type="l",ylim=c(0,10),
   main="locf\n DO NOT USE, BAD METHOD !!!")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### nocb
matplot(t(imputation(mat1,"nocb")),type="l",ylim=c(0,10),
   main="nocb\n DO NOT USE, BAD METHOD !!!")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### trajMean
matplot(t(imputation(mat1,"trajMean")),type="l",ylim=c(0,10),
   main="trajMean")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### trajMedian
matplot(t(imputation(mat1,"trajMedian")),type="l",ylim=c(0,10),
   main="trajMedian")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### trajHotDeck
matplot(t(imputation(mat1,"trajHotDeck")),type="l",ylim=c(0,10),
   main="trajHotDeck 1")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)

### spline
matplot(t(imputation(mat1,"spline",lowerBound=NA,upperBound=NA)),
   type="l",ylim=c(-10,10),main="spline")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16)





##################
### Different linear interpolation

par(mfrow=c(2,2))

### linearInterpol.locf
matplot(t(imputation(mat1,"linearInterpol.locf",NA,NA)),type="l",
   ylim=c(-5,10),lty=1,col=1,main="linearInterpol.locf")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16,lty=1)

### linearInterpol.global
matplot(t(imputation(mat1,"linearInterpol.global",NA,NA)),type="l",
   ylim=c(-5,10),lty=1,col=1,main="linearInterpol.global")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16,lty=1)

### linearInterpol.local
matplot(t(imputation(mat1,"linearInterpol.local",NA,NA)),type="l",
   ylim=c(-5,10),lty=1,col=1,main="linearInterpol.local")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16,lty=1)

### linearInterpol.bisector
matplot(t(imputation(mat1,"linearInterpol.bisector",NA,NA)),type="l",
   ylim=c(-5,10),lty=1,col=1,main="linearInterpol.bisector")
matlines(t(mat1),type="o",col=2,lwd=3,pch=16,lty=1)



##################
### Copy mean

mat3 <- matrix(c(
  NA, 9, 8, 8, 7, 6,NA,
   7, 6,NA,NA,NA, 4,5,
   3, 4, 3,NA,NA, 2,3,
  NA,NA, 1,NA,NA, 1,1),4,7,byrow=TRUE)


par(mfrow=c(2,2))

### copyMean.locf
matplot(t(imputation(mat2,"copyMean.locf",NA,NA)),type="l",
   ylim=c(-5,10),lty=1,col=1,main="copyMean.locf")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### copyMean.global
matplot(t(imputation(mat2,"copyMean.global",NA,NA)),type="l",
   ylim=c(-5,10),lty=1,col=1,main="copyMean.global")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### copyMean.local
matplot(t(imputation(mat2,"copyMean.local",NA,NA)),type="l",
   ylim=c(-5,10),lty=1,col=1,main="copyMean.local")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)

### copyMean.bisector
matplot(t(imputation(mat2,"copyMean.bisector",NA,NA)),type="l",
   ylim=c(-5,10),lty=1,col=1,main="copyMean.bisector")
matlines(t(mat2),type="o",col=2,lwd=3,pch=16,lty=1)




### crossMean
matImp <- imputation(matMissing,method="crossMean")
matplot(t(matImp),col=c(2,1,1,1),lty=c(2,1,1,1),type="l",lwd=c(2,1,1,1),pch=16,
   xlab="Dotted red=imputed trajectory\nFull red=trajectory to impute",
   ylab="",main="Method 'crossMean'")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)


### crossMedian
matImp <- imputation(matMissing,method="crossMedian")
matplot(t(matImp),col=c(2,1,1,1),lty=c(2,1,1,1),type="l",lwd=c(2,1,1,1),pch=16,
   xlab="Dotted red=imputed trajectory\nFull red=trajectory to impute",ylab="",
   main="Method 'crossMedian'")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### crossHotDeck
matImp <- imputation(matMissing,method="crossHotDeck")
matplot(t(matImp),col=c(2,1,1,1),lty=c(2,1,1,1),type="l",lwd=c(2,1,1,1),pch=16,
   xlab="Dotted red=imputed trajectory\nFull red=trajectory to impute",ylab="",
   main="Method 'crossHotDeck'")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)


##################
### Method using trajectory

par(mfrow=c(2,3))
### trajMean
matImp <- imputation(matMissing,method="trajMean")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="nocb")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### trajMedian
matImp <- imputation(matMissing,method="trajMedian")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="nocb")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### trajHotDeck
matImp <- imputation(matMissing,method="trajHotDeck")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="nocb")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### locf
matImp <- imputation(matMissing,method="locf")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="locf")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### nocb
matImp <- imputation(matMissing,method="nocb")
plot(timeV,matImp[1,],type="l",lwd=2,ylim=c(10,30),ylab="",xlab="nocb")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

par(mfrow=c(2,2))

### linearInterpol.locf
matImp <- imputation(matMissing,method="linearInterpol.locf")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### linearInterpol.local
matImp <- imputation(matMissing,method="linearInterpol.local")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### linearInterpol.global
matImp <- imputation(matMissing,method="linearInterpol.global")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)

### linearInterpol.bisector
matImp <- imputation(matMissing,method="linearInterpol.bisector")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)


par(mfrow=c(2,2))

### copyMean.locf
matImp <- imputation(matMissing,method="copyMean.locf")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)
lines(timeV,moy,col=3,type="o",lwd=3)

### copyMean.local
matImp <- imputation(matMissing,method="copyMean.local")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)
lines(timeV,moy,col=3,type="o",lwd=3)

### copyMean.global
matImp <- imputation(matMissing,method="copyMean.global")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)
lines(timeV,moy,col=3,type="o",lwd=3)

### copyMean.bisector
matImp <- imputation(matMissing,method="copyMean.bisector")
plot(timeV,matImp[1,],type="o",ylim=c(0,30),ylab="",xlab="LI-Global")
lines(timeV,matMissing[1,],col=2,type="o",lwd=3)
lines(timeV,moy,col=3,type="o",lwd=3)

par(ask=FALSE)

~ 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

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)

~ Function: longData ~

Description

longData is a constructor for the class LongData. It create object LongData containing a single variable-trajectory. For creating joint variable-trajectories, see longData3d.

Usage

longData(traj, idAll, time, timeInData,varNames,maxNA)

Arguments

Details

longData construct a object of class LongData. Two cases can be distinguised:

traj is an array:

lines are individual. Column are time of measurment.

If idAll is missing, the individuals are labelled i1, i2, i3,...

If timeInData is missing, all the column are used (timeInData=1:ncol(traj)).

If traj is a data.frame:

lines are individual. Column are time of measurement.

If idAll is missing, then the first column of the data.frame is used for idAll

If timeInData is missing and idAll is missing, then all the columns but the first are used for timeInData (the first is omited since it is already used for idAll): idAll=traj[,1],timeInData=2:ncol(traj).

If timeInData is missing but idAll is not missing, then all the column including the first are used for timeInData: timeInData=1:ncol(traj).

Value

An object of class LongData.

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

See Also

LongData

Examples

#####################
### From matrix

### Small data
mat <- matrix(c(1,NA,3,2,3,6,1,8,10),3,3,dimnames=list(c(101,102,104),c("T2","T4","T8")))
longData(mat)
(ld1 <- longData(traj=mat,idAll=as.character(c(101,102,104)),time=c(2,4,8),varNames="V"))
plotTrajMeans(ld1)

### Big data
mat <- matrix(runif(1051*325),1051,325)
(ld2 <- longData(traj=mat,idAll=paste("I-",1:1051,sep=""),time=(1:325)+0.5,varNames="Random"))

####################
### From data.frame

dn <- data.frame(id=1:3,v1=c(NA,2,1),v2=c(NA,1,0),v3=c(3,2,2),v4=c(4,2,NA))

### Basic
longData(dn)

### Selecting some times
(ld3 <- longData(dn,timeInData=c(1,2,4),varNames=c("Hyp")))

### Excluding trajectories with more than 1 NA
(ld3 <- longData(dn,maxNA=1))

~ longData: internal objects and methods ~

Description

longData: internal objects and methods

Details

These are not to be called by the user.

• medianNA : median with option na.rm=TRUE

• meaanNA : mean with option na.rm=TRUE

• sdNA : sandard deviation with option na.rm=TRUE

• sdcNA : standard deviation corrected (n-1)/n with option na.rm=TRUE

• varNA : var with option na.rm=TRUE

• rangeNA : range with option na.rm=TRUE

• which.minNA : which.min that return NA if it argument has only NA values.

• NAtrunc : function that remove only the NA value in the tail of its argument.

• showLongData : methods use to define the function 'show'

• METHODS : constant=c("manhattan", "euclidean", "minkowski", "maximum", "canberra", "binary")

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

~ Function: longData3d ~

Description

longData3d is a constructor of the class LongData. It create object LongData containing several joint trajectory (two or more variable-trajectories). For creating a single variable-trajectory, see longData.

Usage

longData3d(traj, idAll, time, timeInData,varNames,maxNA)

Arguments

Details

longData3d construct a object of class LongData. Two cases can be distinguised:

traj is an array:

the first dimension (line) are individual. The second dimension (column) are time at which the measurement are made. The third dimension are the differents variable-trajectories. For example, traj[,,2] is the second variable-trajectory.

If idAll is missing, the individuals are labelled i1, i2, i3,...

If timeInData is missing, all the column are used (1:ncol(traj)).

If traj is a data.frame:

lines are individual. Time of measurement and variables should be provide through timeInData. timeInData is a list. The label of the list are the variable-trajectories names. Elements of the list are the column containning the trajectories. For example, if timeInData=list(V=c(2,3,4),W=c(6,8,12)), then the first variable-trajectory is 'V', its measurement are in column 2,3 and 4. The second variable-trajectory is 'W', its measurement are in column 6,8 and 12.

If idAll is missing, the first column of the data.frame is used.

Value

An object of class LongData.

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

See Also

LongData

Examples

#################
### From array

mat <- array(c(1,NA,3,2,3,6,1,8,10,1,NA,1,2,NA,3,2,3,2),dim=c(3,3,2))
longData3d(mat)
(ld1 <- longData3d(mat,varNames=c("Hyp","Col"),idAll=c("i101","i104","i105")))
plotTrajMeans3d(ld1)

#################
### From data.frame

dn <- data.frame(id=1:3,v1=c(2,2,1),t1=c(20,21,22),v1=c(3,2,2),t2=c(23,20,28),t3=c(25,24,29))
longData3d(dn,timeInData=list(c(2,4),c(3,5)),varNames=c("V","T"))
(ld3 <- longData3d(dn,timeInData=list(V=c(2,4,NA),T=c(3,5,6))))
plotTrajMeans3d(ld3)

~ Function: longDataFrom3d ~

Description

Extract a single variable-trajectory from an object LongData that contain some joint-trajectories.

Usage

longDataFrom3d(xLongData3d,variable)

Arguments

Details

Extract a single variable-trajectory from an object LongData3d that contain some join-trajectories.

Value

An object of class LongData.

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

See Also

LongData

Examples

### Creation of joint-trajectories
mat <- array(c(1,NA,3,2,3,6,1,8,10,1,NA,1,2,NA,3,2,3,2),dim=c(3,3,2))
(ldJoint <- longData3d(mat,varNames=c("Hyp","Som")))

### Extraction of the first variable-trajectory
(ldHyp <- longDataFrom3d(ldJoint,variable="Hyp"))

### Extraction of the second variable-trajectory
(ldSom <- longDataFrom3d(ldJoint,variable="Som"))

### Extraction of the second variable-trajectory, using number
(ldSom <- longDataFrom3d(ldJoint,variable=2))

~ Function: longDataTo3d ~

Description

Build a object LongData3d from an object LongData. The resulting object has a single variable-trajectory stored in a array.

Usage

longDataTo3d(xLongData)

Arguments

Details

Build a object LongData3d from an object LongData. The resulting object has a single variable-trajectory stored in a array.

Value

An object of class LongData3d.

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

See Also

LongData

Examples

### Creation of single variable-trajectory
mat <- matrix(c(1,NA,3,2,3,6,1,8,10,1,NA,1,2,NA,3,2,3,2),6,3)
(ldSingle <- longData(mat))

### Extension to joint trajectories
(ldHyp <- longDataTo3d(ldSingle))

~ Function: makeLatexFile ~

Description

Create a LaTeX document that inclusde 3D objects into PDF documents.

Usage

makeLatexFile(filename = "main.tex", asyToInclude = "scene+0.prc")

Arguments

Details

Create a LaTeX document that inclusde 3D objects into PDF documents with PDF-1.5/1.6 compatibility.

Value

A LaTeX file, in the current directory.

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

See Also

makeTriangles,plot3dPdf, saveTrianglesAsASY.

Examples

  ### Move to tempdir
  wd <- getwd()
  setwd(tempdir()); getwd()
  
  ### Generating the data
  data(artificialJointLongData)
  myLd <- longData3d(artificialJointLongData,timeInData=list(var1=2:12,var2=13:23))
  part <- partition(rep(1:3,each=50))
  plotTrajMeans3d(myLd,part)

  ### Creation of the scene
  scene <- plot3dPdf(myLd,part)
  drawScene.rgl(scene)

  ### Export in '.asy' file
  saveTrianglesAsASY(scene)

  ### Creation of a '.prc' file
  # Open a console, then run:
  # 'asy -inlineimage -tex pdflatex scene.asy'

  ### Creation of the LaTeX main document
  makeLatexFile()

  ### Creation of the '.pdf'
  # Open a console window, then run
  # pdfLatex main.tex
  
  ### Go back to current dir
  setwd(wd)

~ Function: ordered(ListPartition) ~

Description

Sort the Partition of a ListPartition according to a quality criterion.

Usage

ordered(x,...)

Arguments

Details

Sort the Partition of a ListPartition for each list (sort the 'c2' list, the 'c3' list,...) according to a quality criterion. The criterion used to sort is the one in the field criterionActif.

Value

This function change internaly the order of the fields c2, c3, ... c26 of an object. In addition, it return the permutation matrix (the matrix use to re-ordered the ci).

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] Christophe M. Genolini and Bruno Falissard
"KmL: k-means for longitudinal data"
Computational Statistics, vol 25(2), pp 317-328, 2010

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

Examples

##############
### Preparing data
data(artificialLongData)
traj <- as.matrix(artificialLongData[,-1])

### Some clustering
part2 <- partition(rep(c("A","B"),time=100),traj)
part3 <- partition(rep(c("A","B","C","A"),time=50),traj)
part3b <- partition(rep(c("A","B","C","B"),time=50),traj)
part4 <- partition(rep(c("A","B","C","D"),time=50),traj)


################
### ListPartition
listPart <- listPartition()
listPart['criterionActif'] <-"Davies.Bouldin"
plotCriterion(listPart)

listPart["add"] <- part2
listPart["add"] <- part3
listPart["add"] <- part3b
listPart["add"] <- part4
listPart["add"] <- part4
listPart["add"] <- part3
listPart["add"] <- part3b

plotCriterion(listPart)
ordered(listPart)
plotCriterion(listPart)

listPart['criterionActif'] <-"Calinski.Harabatz"
plotCriterion(listPart)
ordered(listPart)
plotCriterion(listPart)

~ Function: parLongData, parTraj and parMean~

Description

parLongData, parTraj and parMean are constructors for the class ParLongData.

Usage

parLongData(type, col, pch, pchPeriod, cex, xlab, ylab)
parTRAJ(type = "l", col = "black", pch = "1",
   pchPeriod = 0, cex = 1, xlab = "Time", ylab = "")
parMEAN(type = "b", col = "clusters", pch = "letters",
   pchPeriod = 1, cex = 1.2, xlab = "Time", ylab = "")

Arguments

Details

parLongData is the basic constructor of the class ParLongData.

parTRAJ create an object with default values for ploting individual trajectories ;

parMEAN create an object with default values for ploting mean trajectories.

If col='clusters', pch='letters' or pch='symbol', the object can not be use directly, it should first be prepared using the function expandParLongData.

Value

An object of class ParLongData

Author(s)

Christophe Genolini
PSIGIAM: Paris Sud Innovation Group in Adolescent Mental Health
INSERM U669 / Maison de Solenn / Paris

Contact author : <genolini@u-paris10.fr>

English translation

Raphaël Ricaud
Laboratoire "Sport & Culture" / "Sports & Culture" Laboratory
University of Paris 10 / Nanterre

Examples

##################
### Construction of LongData

time=c(1,2,3,4,8,12,16,20)
id2=1:120
f <- function(id,t)((id-1)%%3-1) * t
g <- function(id,t)(id%%2+1)*t
ld2 <- longData3d(
   array(cbind(outer(id2,time,f),outer(id2,time,g))+rnorm(120*8*2,0,3),
   dim=c(120,8,2)))

### Example with default value
plotTrajMeans3d(ld2)
plotTrajMeans3d(ld2,parTraj=parTRAJ())

### Example with default value except for the color
plotTrajMeans3d(ld2,parTraj=parTRAJ(col="blue"))

~ Function: parWindows ~

Description

parWindows is the constructor of object ParWindows.

Usage

parWindows(nbRow, nbCol, addLegend,closeScreen)

Arguments

Details

parWindows is the constructor of object ParWindows. Given a number of rows and colonnes, it computes the screenMatrix that is use by split.screen for plot object LongData. If addLegend is true, an extra space is added on the top of the graphes to print the legend.

Value

An object of class ParWindows.

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

Examples

### Building ParWindows
(paramWin <- parWindows(3,2,FALSE,TRUE))

### Get
figsScreen <- paramWin['screenMatrix']

### Usage
listScreen <- split.screen(figsScreen)
screen(listScreen[1])
plot(-5:5/10,2.5-(-5:5)^2/20,ylim=c(0,6),axes=FALSE,xlab="",ylab="",type="l",lwd=3)
lines(-5:5/10,(-5:5)^2/20,ylim=c(0,6),type="l",lwd=3)

screen(listScreen[3])
plot(-5:5/10,2.5-(-5:5)^2/20,ylim=c(0,6),axes=FALSE,xlab="",ylab="",type="l",lwd=3)
lines(-5:5/10,(-5:5)^2/20,ylim=c(0,6),type="l",lwd=3)

screen(listScreen[5])
plot(-5:5/10,(-5:5)^2/10,ylim=c(0,6),axes=FALSE,xlab="",ylab="",type="l",lwd=3)
lines(-5:5/10,(-5:5)^2/20+1.25,ylim=c(0,6),type="l",lwd=3)
close.screen(all.screens=TRUE)

### :-)

~ Function: partition ~

Description

partition is the constructor of the class Partition. It can be build either alone or relatively to a object LongData.

Usage

partition(clusters, traj, details=character())

Arguments

Details

partition construct a object of class Partition. It does not provide any default values. yLongData and details are optional.

Value

An object of class Partition.

Author

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

References

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

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

See Also

Partition,ordered

Examples

### Empty partition
partition()

### Small partition
partition(clusters=c("A","B","A","C","C"))

### Random partition
partition(clusters=LETTERS[floor(runif(100,1,5))])

### Partition that clusters correctly some data
###   Quality criterion are high
data(artificialLongData)
traj <- as.matrix(artificialLongData[,-1])
partition(clusters=rep(1:4,each=50),traj)

### Partition that does not cluster correctly the data
###   Quality criterion are low
partition(clusters=rep(1:4,50),traj)

~ Function: plot3dPdf for LongData ~

Description

Given a LongData and a Partition, this function create 'Triangle objects' representing the 3D plot the clusters centers. Triangle object can latter be used to include dynamic rotating graph in a pdf file.

Usage

## S4 method for signature 'LongData3d,missing'
plot3dPdf(x,y,varY=1,varZ=2)
## S4 method for signature 'LongData3d,numeric'
plot3dPdf(x,y,varY=1,varZ=2)

Arguments

Details

Create Triangle objects representing the 3D plot of the main trajectories of a LongData.

The three functions plot3dPdf, saveTrianglesAsASY and makeLatexFile are design to export a 3D graph to a Pdf file. The process is the following:

1. plot3dPdf: Create a scene, that is a collection of Triangle object that represent a 3D images.

2. saveTrianglesAsASY: Export the scene in an '.asy' file.

3. '.asy' can not be include in LaTeX file. LaTeX can read only '.pre' file. So the next step is to use the software asymptote to convert '.asy' to '.pre'. This is done by the command asy -inlineimage -tex pdflatex scene.asy (not in R, in a console).

4. The previous step did produce a file scene+0.prc that can be include in a LaTeX file. makeLatexFile create a LaTeX file that is directly compilable (using pdfLatex). It produce a pdf file that contain the 3D object.

Value

A Triangle object.

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

See Also

saveTrianglesAsASY,makeLatexFile,makeTriangles

Examples

  ### Move to tempdir
  wd <- getwd()
  setwd(tempdir()); getwd()
  
  ### Generating the data
  data(artificialJointLongData)
  myLd <- longData3d(artificialJointLongData,timeInData=list(var1=2:12,var2=13:23))
  part <- partition(rep(1:3,each=50))
  plotTrajMeans3d(myLd,part)

  ### Creation of the scene
  scene <- plot3dPdf(myLd,part)
  drawScene.rgl(scene)

  ### Export in '.asy' file
  saveTrianglesAsASY(scene)

  ### Creation of a '.prc' file
  # Open a console, then run:
  # 'asy -inlineimage -tex pdflatex scene.asy'

  ### Creation of the LaTeX main document
  makeLatexFile()

  ### Creation of the '.pdf'
  # Open a console window, then run
  # pdfLatex main.tex
  
  ### Go back to current dir
  setwd(wd)

~ Function: plotAllCriterion ~

Description

This function graphically displays the quality criterion of all the Partition of a ListPartition object.

Usage

plotAllCriterion(x, criterion=CRITERION_NAMES[1:5],standardized = TRUE)

Arguments

Details

This function display graphically several quality criterion, probably to decide the best clusters' number.

Value

No value are return. A graph is printed.

Examples

###############
### Data generation
data(artificialLongData)
traj <- as.matrix(artificialLongData[,-1])

### Some clustering
listPart <- listPartition()
listPart["add"] <- partition(rep(c("A","B"),time=100),traj)
listPart["add"] <- partition(rep(c("A","B","B","B"),time=50),traj)
listPart["add"] <- partition(rep(c("A","B","C","A"),time=50),traj)
listPart["add"] <- partition(rep(c("A","B","C","D"),time=50),traj)
ordered(listPart)

################
### graphical display
plotAllCriterion(listPart)
plotAllCriterion(listPart,criterion=CRITERION_NAMES[1:5],TRUE)

~ Function: plotCriterion ~

Description

This function graphically displays the quality criterion of all the Partition of a ListPartition object.

Usage

plotCriterion(x, criterion=x["criterionActif"],nbCriterion=100)

Arguments

Details

This function display graphically the quality criterion (probably to decide the best clusters' number). It can either display all the criterion ; this is useful to see the consistency of the result : is the best clusterization obtain several time or only one ? It can also display only the best result for each clusters number : this helps to find the local maximum, which is classically used to chose the "correct" clusters' number.

Value

No value are return. A graph is printed.

Examples

###############
### Data generation
data(artificialLongData)
traj <- as.matrix(artificialLongData[,-1])

### Some clustering
listPart <- listPartition()
listPart["add"] <- partition(rep(c("A","B"),time=100),traj)
listPart["add"] <- partition(rep(c("A","B","B","B"),time=50),traj)
listPart["add"] <- partition(rep(c("A","B","C","A"),time=50),traj)
listPart["add"] <- partition(rep(c("A","B","C","D"),time=50),traj)
ordered(listPart)

################
### graphical display
plotCriterion(listPart)
plotAllCriterion(listPart,criterion=CRITERION_NAMES[1:5],TRUE)

~ Function: plotTrajMeans for LongData ~

Description

Plot the LongData or LongData3d optionnaly relatively to a Partition. For joint trajectories, one graphe for each variable trajectory is displayed.

Usage

plotTrajMeans(x, y, parTraj=parTRAJ(), parMean=parMEAN(),...)

Arguments

Details

Plot either a LongData, or each variable of a LongData3d optionnaly according to the Partition define by y.

Graphical option concerning the individual trajectory (col, type, pch and xlab) can be change using parTraj. Graphical option concerning the cluster mean trajectory (col, type, pch, pchPeriod and cex) can be change using parMean. For more detail on parTraj and parMean, see object of class ParLongData.

Author

Christophe Genolini
1. UMR U1027, INSERM, Université Paul Sabatier / Toulouse III / France
2. CeRSM, 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

See Also

LongData, LongData3d, plotTrajMeans3d.

Examples

##################
### Construction of the data
data(artificialLongData)
ld <- longData(artificialJointLongData)
part <- partition(rep(1:3,each=50))

### Basic plotting
plotTrajMeans(ld)
plotTrajMeans(ld,part,xlab="Time")


##################
### Changing graphical parameters 'par'

### No letters on the mean trajectories
plotTrajMeans(ld,part,parMean=parMEAN(type="l"))

### Only one letter on the mean trajectories
plotTrajMeans(ld,part,parMean=parMEAN(pchPeriod=Inf))

### Color individual according to its clusters (col="clusters")
plotTrajMeans(ld,part,parTraj=parTRAJ(col="clusters"))

### Mean without individual
plotTrajMeans(ld,part,parTraj=parTRAJ(type="n"))


### No mean trajectories (type="n")
### Color individual according to its clusters (col="clusters")
plotTrajMeans(ld,part,parTraj=parTRAJ(col="clusters"),parMean=parMEAN(type="n"))

### Only few trajectories
plotTrajMeans(ld,part,nbSample=10,parTraj=parTRAJ(col='clusters'),parMean=parMEAN(type="n"))


##################
### single variable trajectory

data(artificialLongData)
ld2 <- longData(artificialLongData)
part2 <- partition(rep(1:4,each=50))
plotTrajMeans(ld2)
plotTrajMeans(ld2,part2)

~ Function: plotTrajMeans3d for LongData3d ~

Description

Plot two variables of a LongData3d object in 3D, optionnaly relatively to a Partition.

Usage

plotTrajMeans3d(x,y,varY=1,varZ=2,
   parTraj=parTRAJ(),parMean=parMEAN(type="n"),...)

Arguments

Details

Plot two variables of a LongData3d object in 3D. It use the rgl library. The user can make the graphical representation turn using the mouse.

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

See Also

LongData3d

Examples

##################
### Construction of the data


time=c(1,2,3,4,8,12,16,20)
id2=1:120
f <- function(id,t)((id-1)%%3-1) * t
g <- function(id,t)(id%%2+1)*t
h <- function(id,t)(id%%4-0.5)*(20-t)
ld <- longData3d(array(cbind(outer(id2,time,f),outer(id2,time,g),outer(id2,time,h))+
   rnorm(120*8*3,0,3),dim=c(120,8,3)))
part <- partition(rep(1:6,20))

### Basic plotting
plotTrajMeans3d(ld)
plotTrajMeans3d(ld,part)

### Variable 1 and 3, then 2 and 3
plotTrajMeans3d(ld,part)
plotTrajMeans3d(ld,part,varY=3,varZ=2)
plotTrajMeans3d(ld,part,varY=1,varZ=3)

##################
### Changing graphical parameters 'par'

### Color individual according to its clusters (col="clusters")
plotTrajMeans3d(ld,part,parTraj=parTRAJ(col="clusters"))
plotTrajMeans3d(ld,part,parTraj=parTRAJ(col="clusters"),varY=1,varZ=3)

### No mean trajectories (type="n"), only few trajectories
### Color individual according to its clusters (col="clusters")
plotTrajMeans3d(ld,part,parTraj=parTRAJ(col="clusters"),parMean=parMEAN(type="n"),nbSample=10)

~ Function: qualityCriterion ~

Description

Given a LongData and a Partition, the fonction qualityCriterion calculate some qualities criterion.

Usage

qualityCriterion(traj,clusters,imputationMethod="copyMean")

Arguments

Details

Given a LongData and a Partition (or a matrix and a vector of integer), the fonction qualityCriterion calculate several quality criterion and return then as a list (see 'value' below).

If some individual have no clusters (ie if Partition has some missing values), the corresponding trajectories are exclude from the calculation.

Note that if there is an empty cluster or an empty trajectory, most of the criterions are anavailable.

Basicaly, 6 non-parametrics criterions are computed. In addition, ASSUMING THAT in each clusters C and for each time T, the variable follow a NORMAL LAW (mean and standard deviation of the variable at time T restricted to clusters C), it is possible to compute the the posterior probabilities of the individual trajectories and the likelihood. From there, we can also compute the BIC, the AIC and the global posterior probability. The function qualityCriterion also compute these criterion. But the user should alway keep in mind that these criterion are valid ONLY under the hypothesis of normality. If this hypothèsis is not respected, algorithm like k-means will converge but the BIC and AIC will have no meaning.

IMPORTANT NOTE: Some criterion should be maximized, some other should be minimized. This might be confusing for the non expert. In order to simplify the comparison of the criterion, qualityCriterion compute the OPPOSITE of the criterion that should be minimized (Ray & Bouldin, Davies & Turi, BIC and AIC). Thus, all the criterion computed by this function should be maximized.

Value

A list with three fields: the first is the list of the criterions. the second is the clusters post probabilities; the third is the matrix of the individual post probabilities.

Non-parametric criterion

Notations: k=number of clusters; n=number of individual; B=Between variance ; W=Within variance The criterion are:

Calinski.Harabatz

[numeric]: Calinski and Harabatz criterion: c(k)=Trace(B)/Trace(W)*(n-k)/(k-1).

Calinski.Harabatz2

[numeric]: Calinski and Harabatz criterion modified by Krysczuk: c(k)=Trace(B)/Trace(W)*(n-1)/(n-k).

Calinski.Harabatz3

[numeric]: Calinski and Harabatz criterion modified by Genolini: g(k)=Trace(B)/Trace(W)*(n-k)/sqrt(k-1).

Ray.Turi

[numeric]: Ray and Turi criterion: r(k)=-Vintra/Vinter with Vintra=Sum(dist(x,center(x))) and Vinter=min(dist(center_i,center_j)^2). (The "true" index of Ray and Turi is Vintra/Vinter and should me minimized. See IMPORTANT NOTE above.)

Davies.Bouldin

[numeric]: Davies and Bouldin criterion: d(k)=-mean(Proximite(cluster_i,cluster_j)) with Proximite(i,j)=(DistInterne(i)+DistInterne(j))/(DistExterne(i,j)). (The "true" index of Davies and Bouldin is mean(Proximite()) and should me minimized. See IMPORTANT NOTE above.)

random

[numeric]: random value following the normal law N(0,1).

Parametric criterion

All the parametric indices should be minimized. So the function qualityCriterion compute their opposite (see IMPORTANT NOTE above.)

Notation: L=likelihood; h=number of parameters; n=number of trajectories; t=number of time measurement; N=total number of measurement (N=t.n).

SECOND IMPORTANT NOTE: the formula of parametrics criterion ofen include the size of the population. In the specific case on longitudinal data, the definition of the "size of the population" is not obvious. It can be either the number of individual n, or the number of measurement N=n.t. So, the function qualityCriterion gives two version of all the non parametrics criterion, the first using n, the second using N.

BIC

[numeric]: Bayesian Information Criterion: BIC=2*log(L)-h*log(n). See IMPORTANT NOTE above.

BIC2

[numeric]: Bayesian Information Criterion: BIC=2*log(L)-h*log(N). See IMPORTANT NOTE above.

AIC

[numeric]: Akaike Information Criterion, bis: AIC=2*log(L)-2*h. See IMPORTANT NOTE above.

AICc

[numeric]: Akaike Information Criterion with correction: AIC=AIC+(2h(h+1))/(n-h-1). See IMPORTANT NOTE above.

AICc2

[numeric]: Akaike Information Criterion with correction, bis: AIC=AIC+(2h(h+1))/(n-h-1). See IMPORTANT NOTE above.

Author

Christophe Genolini
1. UMR U1027, INSERM, Université Paul Sabatier / Toulouse III / France
2. CeRSM, 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

See Also

LongData, Partition, imputation.

Examples

##################
### Preparation of some artificial data
par(ask=TRUE)
data(artificialLongData)
ld <- longData(artificialLongData)


### Correct partition
part1 <- partition(rep(1:4,each=50))
plotTrajMeans(ld,part1)
(cr1 <- qualityCriterion(ld,part1))

### Random partition
part2 <- partition(floor(runif(200,1,5)))
plotTrajMeans(ld,part2)
(cr2 <- qualityCriterion(ld,part2))

### Partition with 3 clusters instead of 4
part3 <- partition(rep(c(1,2,3,3),each=50))
plotTrajMeans(ld,part3)
(cr3 <- qualityCriterion(ld,part3))


### Comparisons of the Partition
plot(c(cr1[[1]],cr2[[1]],cr3[[1]]),main="The highest give the best partition
(according to Calinski & Harabatz criterion)")
par(ask=FALSE)

~ Function: regroup ~

Description

Remove duplicate Partition present in a ListPartition (or, by inheritance, in ClusterLongData and ClusterLongData3d objects.

Usage

regroup(object)

Arguments

Details

A clusterizing algorithm can find a Partition several time. It is store several time in object ListPartition(or in ClusterLongData or in ClusterLongData3d), encombering the memory. regroup remove the duplicate Partition. Note that if the ListPartition is not ordered, then regroup sort it unless toOrder=FALSE.

Value

None (this function change internaly the field of an object, it does not return any values.)

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] Christophe M. Genolini and Bruno Falissard
"KmL: k-means for longitudinal data"
Computational Statistics, vol 25(2), pp 317-328, 2010

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

Examples

### Some data
data(artificialLongData)
myLd <- as.matrix(artificialLongData[,-1])
### Some clustering
part2 <- partition(rep(c("A","B","A","C"),time=50),myLd)
part3 <- partition(rep(c("A","B","C","D"),time=50),myLd)

################
### ListPartition
listPart <- listPartition()

listPart["add"] <- part2
listPart["add"] <- part3
listPart["add"] <- part2
listPart["add"] <- part3

### Some clustering has been found several time
### regroup will suppress the duplicate one
regroup(listPart)
plotCriterion(listPart)

~ Function: longToWide (or reshapeWide) ~

Description

This function reshapes a data frame in 'long' format (repeated measurements in the same column) into a data frame in 'wide' format (repeated measurements in separate columns). It also correct a bug of reshape.

Usage

longToWide(trajLong)
reshapeLongToWide(trajLong)

Arguments

Details

This function reshapes a data frame in 'long' format (repeated measurements in the same column) into a data frame in 'wide' format (repeated measurements in separate columns).

Value

A data frame in 'wide' format (repeated measurements in separate columns).

Note

longToWide is just a 'friendly overlay' of the function reshape. It also corrects a reshape bug (modification of the order of some trajectories value when some times are missing).

Author(s)

Christophe Genolini

See Also

wideToLong, reshape.

Examples

summary(Indometh)
longToWide(Indometh)


df2 <- data.frame(id = rep(LETTERS[1:4], rep(2,4)),
                 visit = I(rep(c("3","6"), 4)),
                 x = rnorm(4), y = runif(4),
                 sex=rep(c("H","F","H"),time=c(4,2,2)))[1:7,]
longToWide(df2[,1:3])
longToWide(df2[,c(1,2,4)])

~ Function: wideToLong (or reshapeWideToLong) ~

Description

This function reshapes a data frame in 'wide' format (repeated measurements in separate column) into a data frame in 'long' format (repeated measurements in the same columns).

Usage

wideToLong(trajWide,times=1:(ncol(trajWide)-1))
reshapeWideToLong(trajWide,times=1:(ncol(trajWide)-1))

Arguments

Details

This function reshapes a data frame in 'wide' format (repeated measurements in separe column) into a data frame in 'long' format (repeated measurements in the same columns). The first column has to be the individual indentier. All the other column should be the trajectories. The missing values are removed in long format.

Value

A data frame in 'long' format.

Author(s)

Christophe Genolini

See Also

longToWide, reshape.

Examples

df3 <- data.frame(id = LETTERS[rep(1:4)], sex=c("H","F","H","F"),
    v1=rnorm(4),v2=rnorm(4),w1=rnorm(4),w2=rnorm(4))

wideToLong(df3[,c(1,3,4)])
wideToLong(df3[,c(1,5,6)])
wideToLong(df3[,c(1,3:6)])
wideToLong(df3[,c(1,3:6)],times=c(1,2,4,8))

~ Function: restoreRealData ~

Description

This function revert the effect of scale by restauring the initial values of trajectories.

Usage

restoreRealData(object)

Arguments

Details

This function revert the effect of scale by restauring the initial values of trajectories.

Value

None: this function change internaly the field of an object, it does not return any values.)

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

See Also

scale

Examples

##################
### Building LongData

time=c(1,2,3,4,8,12,16,20)
id2=1:12
f <- function(id,t)((id-1)%%3-1) * t
g <- function(id,t)(id%%2+1)*t
ld1 <- longData3d(array(cbind(outer(id2,time,f),outer(id2,time,g))+rnorm(12*8*2,0,1),dim=c(12,8,2)))
plotTrajMeans3d(ld1)

##################
### Scaling by 'mean' and 'standard deviation'
scale(ld1,scale=c(-1,-1))
plotTrajMeans3d(ld1)

##################
### Back to the first version of the data
restoreRealData(ld1)
plotTrajMeans3d(ld1)

~ Function: saveTrianglesAsASY ~

Description

Export a Triangle object to an '.asy' file.

Usage

saveTrianglesAsASY(scene, filename = "scene.asy")

Arguments

Details

Export a Triangle object to an '.asy' file. See plot3dPdf for a summary of the overall procedure.

Value

An '.asy' file, in the current directory.

Author(s)

Luke Tierney
Chair, Statistics and Actuarial Science
Ralph E. Wareham Professor of Mathematical Sciences
University of Iowa

References

https://homepage.divms.uiowa.edu/~luke/R/misc3d/misc3d-pdf/misc3d-pdf.pdf

See Also

plot3dPdf,makeLatexFile,makeTriangles

Examples

  ### Move to tempdir
  wd <- getwd()
  setwd(tempdir()); getwd()
  
  ### Generating the data
  data(artificialJointLongData)
  myLd <- longData3d(artificialJointLongData,timeInData=list(var1=2:12,var2=13:23))
  part <- partition(rep(1:3,each=50))
  plotTrajMeans3d(myLd,part)

  ### Creation of the scene
  scene <- plot3dPdf(myLd,part)
  drawScene.rgl(scene)

  ### Export in '.asy' file
  saveTrianglesAsASY(scene)

  ### Creation of a '.prc' file
  # Open a console, then run:
  # 'asy -inlineimage -tex pdflatex scene.asy'

  ### Creation of the LaTeX main document
  makeLatexFile()

  ### Creation of the '.pdf'
  # Open a console window, then run
  # pdfLatex main.tex
  
  ### Go back to current dir
  setwd(wd)

~ Function: scale for LongData ~

Description

scale the trajectories of the different variable of a LongData object.

Usage

scale(x, center = TRUE, scale = TRUE)

Arguments

Details

When variable with different unit are used jointly, it might be necessary to change their scale them in order to change their individual influance. This is what scale do.

More precisely, all the value x[i,j,k] of the variable k will be scale according to the classic formula (x[i,j,k]- m_k)/s_k where m_k and s_k are respectively the k-ieme value of the argument center and scale.

Note that center=TRUE is a special value that set m_k=mean(x[,,k],na.rm=TRUE). Similarly, scale=TRUE is a special value that set s_k=sd(x[,,k],na.rm=TRUE).

Value

scale directly modify the internal value of the LongData. No value is return.

Author

Christophe Genolini
1. UMR U1027, INSERM, Université Paul Sabatier / Toulouse III / France
2. CeRSM, 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

See Also

restoreRealData

Examples

##################
### Building LongData

time=c(1,2,3,4,8,12,16,20)
id2=1:12
f <- function(id,t)((id-1)%%3-1) * t
g <- function(id,t)(id%%2+1)*t
ld1 <- longData3d(array(cbind(outer(id2,time,f),outer(id2,time,g))+rnorm(12*8*2,0,1),dim=c(12,8,2)))
plotTrajMeans3d(ld1)

##################
### Scaling by 'mean' and 'standard deviation'
plotTrajMeans3d(ld1)
scale(ld1)
plotTrajMeans3d(ld1)

### Scaling by some parameters
scale(ld1,center=c(10,100),scale=c(3,-1))
plotTrajMeans3d(ld1)

##################
### To restore the data
restoreRealData(ld1)

~ Function: windowsCut ~

Description

windowsCut prepare an object ParWindows according to its arguments.

Usage

windowsCut(x, addLegend = TRUE,closeScreen=TRUE)

Arguments

Details

If x is a number of variable, the column and row number are estimate according to the formula nbCol <- ceiling(sqrt(x)) and nbRow <- ceiling(x/nbCol).

Value

An object of class ParWindows.

Author

Christophe Genolini
1. UMR U1027, INSERM, Université Paul Sabatier / Toulouse III / France
2. CeRSM, 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

Examples

  ### Simple cut with no space for legent
  windowsCut(3,FALSE)
  windowsCut(4,FALSE)
  windowsCut(5,FALSE)

  ### Simple cut with legend
  windowsCut(5)