## Description

mixedClust is an R package to perform co-clustering on heterogeneous data. The kind of data that are taken into account are:

- Categorical
- Quantitative
- Integer
- Ordinal
- Functional

## Installation

    set.seed(5)

    library(mixedClust)

## Datasets

under construction

## Simulation of heterogeneous data

The following codes simulate a sample of heterogeneous data.

    M <- matrix(0, nrow=150,ncol=250)

### Simulation of categorical data

This snippet creates a sample of categorical data with 6 levels.

    multinomial6.block1 <- sample(1:6, 120*75, prob = c(0.4,0.25,0.1,0.1,0.05,0.1), replace = TRUE)
    multinomial6.block2 <- sample(1:6, 120*50, prob = c(0.1,0.1,0.05,0.6,0.1,0.05), replace = TRUE)
    multinomial6.block3 <- sample(1:6, 30*75, prob = c(0.2,0.1,0.2,0.1,0.1,0.3), replace = TRUE)
    multinomial6.block4 <- sample(1:6, 30*50, prob = c(0.05,0.2,0.1,0.2,0.4,0.05), replace = TRUE)

    M[1:120,1:75] <- multinomial6.block1
    M[1:120,76:125] <- multinomial6.block2
    M[121:150,1:75] <- multinomial6.block3
    M[121:150,76:125] <- multinomial6.block4

### Simulation of quantitative data

    gaussian.block1 <- rnorm(120*10)
    gaussian.block2 <- rnorm(120*40,mean=28,sd=7)
    gaussian.block3 <- rnorm(30*10,mean=-12,sd=1.5)
    gaussian.block4 <- rnorm(30*40,mean=2,sd=1.5)

    M[1:120,126:135] <-gaussian.block1
    M[1:120,136:175] <- gaussian.block2
    M[121:150,126:135] <- gaussian.block3
    M[121:150,136:175] <- gaussian.block4

### Simulation of ordinal data

The model Bos is used to simulate ordinal data. This snippet creates a sample of ordinal data with 5 levels.

    library(ordinalClust)

    m=5
    probaBOS=rep(0,m)
    for (im in 1:m) probaBOS[im]=pejSim(im,m,4,0.8)
    bos.block1 <- matrix(0,nrow = 120, ncol = 35)
    bos.block1 <- sample(1:m,120*35,prob = probaBOS, replace=TRUE)

    probaBOS=rep(0,m)
    for (im in 1:m) probaBOS[im]=pejSim(im,m,2,0.3)
    bos.block2 <- matrix(0,nrow = 120, ncol = 20)
    bos.block2 <- sample(1:m,120*20,prob = probaBOS, replace=TRUE)

    probaBOS=rep(0,m)
    for (im in 1:m) probaBOS[im]=pejSim(im,m,1,0.7)
    bos.block3 <- matrix(0,nrow = 120, ncol = 20)
    bos.block3 <- sample(1:m,120*20,prob = probaBOS, replace=TRUE)

    probaBOS=rep(0,m)
    for (im in 1:m) probaBOS[im]=pejSim(im,m,3,0.8)
    bos.block4 <- matrix(0,nrow = 30, ncol = 35)
    bos.block4 <- sample(1:m,30*35,prob = probaBOS, replace=TRUE)

    probaBOS=rep(0,m)
    for (im in 1:m) probaBOS[im]=pejSim(im,m,5,0.4)
    bos.block5 <- matrix(0,nrow = 30, ncol = 20)
    bos.block5 <- sample(1:m,30*20,prob = probaBOS, replace=TRUE)

    probaBOS=rep(0,m)
    for (im in 1:m) probaBOS[im]=pejSim(im,m,5,0.8)
    bos.block6 <- matrix(0,nrow = 30, ncol = 20)
    bos.block6 <- sample(1:m,30*20,prob = probaBOS, replace=TRUE)

    M[1:120,176:210] <-bos.block1
    M[1:120,211:230] <- bos.block2
    M[1:120,231:250] <- bos.block3
    M[121:150,176:210] <-bos.block4
    M[121:150,211:230] <- bos.block5
    M[121:150,231:250] <- bos.block6

### Shuffling lines and columns

    line.sample <- sample(1:150,150,replace = F)

    col.sample.cat <- sample(1:125,125,replace=F)
    col.sample.gaussian <- sample(126:175,50,replace=F)
    col.sample.bos <- sample(176:250,75,replace=F)

    M1 <- M[line.sample,c(col.sample.cat, col.sample.gaussian, col.sample.bos)]

## Setting parameters

    nbSEM=120
    nbSEMburn=100
    nbindmini=1
    init = "kmeans"

    kr=2
    kc=c(2,2,3)
    m=c(6,5)
    d.list <- c(1,126,176)
    distributions <- c("Multinomial","Gaussian","Bos")

## Perform co-clustering

In this section, a co-clustering is executed with the simulated dataset, thanks to the mixedCoclust function.

    res <- mixedCoclust(x = M1, myList = d.list,distrib_names = distributions,
                        kr = kr, kc = kc, m = m, init = init,nbSEM = nbSEM,
                        nbSEMburn = nbSEMburn, nbindmini = nbindmini)

## The particular case of functional data

Functional data is taken into account in this package. However, the way of introducing them is a bit different since they are not represented by a simple matrix. Functional data must be stored in a functionalData array with three dimensions:

- nrow = number of row that must be identical to the number of rows of the x data matrix.
- ncol = number of features of the functional type
- nslice = number of points for one function (all functions must have the same number of points) Then, functionalData is passed as an argument to the different functions (co-clustering, clustering, classification).

### Simulation of functional data

The fda.usc package is used to simulate functional data

    library(fda.usc)

    par(mfrow=c(1,2))
    lent<-50
    tt<-seq(0,1,len=lent)
    mu1<-fdata(0.5*cos(2.3*2*pi*tt)+5.4*sin(0.4*2*pi*tt),tt)
    mu2<-fdata(cos(2*pi*tt)+sin(2*pi*tt),tt)
    mu3<-fdata(2*cos(2*pi*tt)+sin(2*pi*tt*4),tt)
    mu4<-fdata(sin(2*pi*tt*5),tt)
    nb <- 100
    func.block.1 <- rproc2fdata(nb,mu=mu1,sigma="OU",par.list=list("scale"=1))
    func.block.2 <- rproc2fdata(nb,mu=mu2,sigma="OU",par.list=list("scale"=1))
    func.block.3 <- rproc2fdata(nb,mu=mu3,sigma="OU",par.list=list("scale"=1))
    func.block.4 <- rproc2fdata(nb,mu=mu4,sigma="OU",par.list=list("scale"=1))

The functionalData array is built:

    functionalData <- array(0,c(20,20,50))
    functionalData[1:10,1:10,]=func.block.1$data
    functionalData[1:10,11:20,]=func.block.2$data
    functionalData[11:20,1:10,]=func.block.3$data
    functionalData[11:20,11:20,]=func.block.4$data

    sample.lines <- sample(1:20,20,replace=F)
    sample.cols <- sample(1:20, 20, replace=F)
    functionalData <- functionalData[sample.lines, sample.cols,]

    line.labels <- c(rep(1,10),rep(2,10))[sample.lines]
    col.labels <- c(rep(1,10),rep(2,10))[sample.cols]

### Setting parameters

One of the limitation of functional data is that the kmeans algorithm cannot be used as initialization.

    nbSEM=120
    nbSEMburn=100
    nbindmini=1
    init = "random"
    kc = c(2)
    kr = 2
    distributions <- c("Functional")

### Performing co-clustering with functional data

    res <- mixedCoclust(distrib_names = distributions,kr = kr, kc = kc,
                        init = init, nbSEM = nbSEM, nbSEMburn = nbSEMburn,
                        nbindmini = nbindmini, functionalData = functionalData)

## References