ordinalClust is an R package to perform classification, clustering and co-clustering of ordinal data. Furthermore, it can handle different numbers of levels and missing values. The ordinal data is considered to follow a BOS distribution [@biernacki16], which is specific to this kind of data. The Latent Block Model is used for performing co-clustering [@jacques17].
set.seed(1)
library(ordinalClust)
The package contains real datasets created from [@Anota17]. They relate to quality of life questionnaires for patients affected by breast cancer.
dataqol is a dataframe with 121 lines such that each line represents a patient and the columns contain information about the patient:
dataqol.classif is a dataframe with 40 lines such that a line represents a patient and the columns contain information about the patient:
To simulate a sample of ordinal data following the BOS distribution, the function pejSim is used.
This snippet of code creates a sample of ordinal data with 7 levels that follows a BOS distribution parameterized by mu=5 and pi=0.5:
m=7 nr=10000 mu=5 pi=0.5 probaBOS=rep(0,m) for (im in 1:m) probaBOS[im]=pejSim(im,m,mu,pi) M <- sample(1:m,nr,prob = probaBOS, replace=TRUE)
To plot the resulting distribution, the ggplot2 library can be used.
library(ggplot2) library(ordinalClust) m=7 nr=10000 probaBOS=rep(0,m) for (im in 1:m) probaBOS[im]=pejSim(im,m,5,0.5) M <- sample(1:m,nr,prob = probaBOS, replace=TRUE) M <- as.data.frame(M) cbPalette <- c("#560303", "#a30606", "#ceac18", "#e0e00d", "#f7f313", "#9bf713", "#0de037") plot1 <- ggplot(data = M, aes(x = M,fill=factor(M))) + geom_histogram() + ylim(0, nr) + ggtitle("ordinal data with m=7 \n mu=5 and pi=0.5") + theme(plot.title = element_text(vjust = -20,hjust = 0.5,size = 16)) + scale_x_continuous(breaks=1:7, labels=c(1:7), limits=c(0,8)) + scale_fill_manual(values=cbPalette) plot1
In this section, clustering is executed using the dataqol dataset. The purpose of performing clustering is to highlight the structure through the matrix rows.
set.seed(0) library(ordinalClust) data("dataqol") # loading the ordinal data M <- as.matrix(dataqol[,2:29]) m = 4 krow = 3 nbSEM=100 nbSEMburn=90 nbindmini=2 init = "randomBurnin" percentRandomB = c(30) object <- bosclust(x=M,kr=krow, m=m, nbSEM=nbSEM, nbSEMburn=nbSEMburn, nbindmini=nbindmini, percentRandomB=percentRandomB, init=init)
plot(object)
library(knitr) # For knitting document and include_graphics function include_graphics("figures/clust.png")
In this example, co-clustering is performed using the dataqol dataset. In this case, the interest in performing co-clustering is to detect an internal structure throughout the rows and columns of the data.
set.seed(0) library(ordinalClust) # loading the real dataset data("dataqol") # loading the ordinal data M <- as.matrix(dataqol[,2:29]) # defining different number of categories: m=4 # defining number of row and column clusters krow = 3 kcol = 3 # configuration for the inference nbSEM=100 nbSEMburn=90 nbindmini=2 init = "randomBurnin" percentRandomB = c(30, 30) # Co-clustering execution object <- boscoclust(x = M,kr = krow, kc = kcol, m = m, nbSEM = nbSEM, nbSEMburn = nbSEMburn, nbindmini = nbindmini, init = init, percentRandomB = percentRandomB)
This snippet of code shows how to visualize the resulting co-clustering, using the plot function:
plot(object)
library(knitr) # For knitting document and include_graphics function include_graphics("figures/coclust.png")
In this section, the dataset dataqol.classif is used. It contains the responses to a questionnaire by 40 patients affected by breast cancer. Furthermore, a column labeled death indicates whether the patient died from the disease (2) or not (1). The aim of this section is to predict the classes of a validation dataset from a training dataset.
The classification function bosclassif provides two classiﬁcation models. The ﬁrst model, (chosen by the option kc=0), is a multivariate BOS model with the assumption that, conditional to the class of the observations, the features are independent. The second model is a parsimonious version of the ﬁrst model. Parsimony is introduced by grouping the features into clusters (as in co-clustering) and assuming that the features of a cluster have a common distribution. The number L of clusters of features is defined with the option kc=L. In practice, L can be chosen by cross-validation, as shown in the following example:
set.seed(1) library(ordinalClust) # loading the real dataset data("dataqol.classif") # loading the ordinal data M <- as.matrix(dataqol.classif[,2:29]) # creating the classes values y <- as.vector(dataqol.classif$death) # sampling datasets for training and to predict nb.sample <- ceiling(nrow(M)*7/10) sample.train <- sample(1:nrow(M), nb.sample, replace=FALSE) M.train <- M[sample.train,] M.validation <- M[-sample.train,] nb.missing.validation <- length(which(M.validation==0)) y.train <- y[sample.train] y.validation <- y[-sample.train] # number of classes to predict kr <- 2 # configuration for SEM algorithm nbSEM=200 nbSEMburn=175 nbindmini=2 init="randomBurnin" percentRandomB = c(50, 50) # different kc to test with cross-validation kcol <- c(0,1,2,3) m <- 4 # matrix that contains the predictions for all different kc preds <- matrix(0,nrow=length(kcol),ncol=nrow(M.validation)) for(kc in 1:length(kcol)){ res <- bosclassif(x=M.train, y=y.train, kr=kr, kc=kcol[kc], m=m, nbSEM=nbSEM, nbSEMburn=nbSEMburn, nbindmini=nbindmini, init=init, percentRandomB=percentRandomB) new.prediction <- predict(res, M.validation) preds[kc,] <- new.prediction@zr_topredict } preds = as.data.frame(preds) row.names <- c() for(kc in kcol){ name= paste0("kc=",kc) row.names <- c(row.names,name) } rownames(preds)=row.names
library(caret) actual <- y.validation -1 specificities <- rep(0,length(kcol)) sensitivities <- rep(0,length(kcol)) for(i in 1:length(kcol)){ prediction <- unlist(as.vector(preds[i,])) -1 u <- union(prediction, actual) conf_matrix<-table(factor(prediction, u),factor(actual, u)) sensitivities[i] <- recall(conf_matrix) specificities[i] <- specificity(conf_matrix) } sensitivities specificities
The package can deal with ordinal data with different numbers of levels. In this section, we show how to introduce these kinds of datasets in a co-clustering context.
In this example, co-clustering is performed using the dataset dataqol, by including the questions with 4 levels, and questions with 7 levels. The function boscoclustMulti is executed, which might take a few minutes.
set.seed(0) library(ordinalClust) # loading the real dataset data("dataqol") # loading the ordinal data M <- as.matrix(dataqol[,2:31]) # defining different number of categories: m=c(4,7) # defining number of row and column clusters krow = 3 kcol = c(3,1) # configuration for the inference nbSEM=50 nbSEMburn=40 nbindmini=2 init='random' d.list <- c(1,29) # Co-clustering execution object <- boscoclust(x=M,kr=krow,kc=kcol,m=m, idx_list=d.list, nbSEM=nbSEM,nbSEMburn=nbSEMburn, nbindmini=nbindmini, init=init)
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