**varclust** is a package that enables dimension reduction via variables clustering.
We assume that each group of variables can be summarized with few latent variables.

It also provides a function to determine number of principal components in PCA.

This tutorial will gently introduce you to usage of package **varclust** and
familiarize with its options.

You can install **varclust** from github (current development version).

install_github("psobczyk/varclust")

or from CRAN

install.package("varclust")

library(varclust) library(mclust)

Let us consider some real genomic data. We're going to use FactoMineR package data. As they are no longer available online we added them to this package This data consists of two types of variables. First group are gene expression data. The second is RNA data. Please note that it may take few minutes to run the following code:

comp_file_name <- system.file("extdata", "gene.csv", package = "varclust") comp <- read.table(comp_file_name, sep=";", header=T, row.names=1) benchmarkClustering <- c(rep(1, 68), rep(2, 356)) comp <- as.matrix(comp[,-ncol(comp)]) set.seed(2) mlcc.fit <- mlcc.bic(comp, numb.clusters = 1:10, numb.runs = 10, max.dim = 8, greedy = TRUE, estimate.dimensions = TRUE, numb.cores = 1, verbose = FALSE) print(mlcc.fit) plot(mlcc.fit) mclust::adjustedRandIndex(mlcc.fit$segmentation, benchmarkClustering) misclassification(mlcc.fit$segmentation, benchmarkClustering, max(table(benchmarkClustering)), 2) integration(mlcc.fit$segmentation, benchmarkClustering)

Please note that although we use *benchmarkClustering* as a reference, it is not
an oracle. Some variables from expression data can be highly correlated and act together with RNA data.

The algorithm aims to reduce dimensionality of data by clustering variables. It is assumed that variables lie in few low-rank subspaces. Our iterative algorithm recovers their partition as well as estimates number of clusters and dimensions of subspaces. This kind of problem is called Subspace Clustering. For a reference comparing multiple approaches see here.

You should also use **mlcc.reps** function if you have some apriori knowledge regarding true segmentation.
You can enforce starting point

mlcc.fit3 <- mlcc.reps(comp, numb.clusters = 2, numb.runs = 0, max.dim = 8, initial.segmentations = list(benchmarkClustering), numb.cores = 1) print(mlcc.fit3) mclust::adjustedRandIndex(mlcc.fit3$segmentation, benchmarkClustering) misclassification(mlcc.fit3$segmentation, benchmarkClustering, max(table(benchmarkClustering)), 2) integration(mlcc.fit3$segmentation, benchmarkClustering)

Execution time of **mlcc.bic** depends mainly on:

- Number of clusters (
*numb.clusters*) - Number of variables
- Number of runs of k-means algorithm (
*numb.runs*)

For a dataset of 1000 variables and 10 clusters computation takes about 8 minutes on Intel(R) Core(TM) i7-4770 CPU @ 3.40GHz.

- If possible one should use multiple cores for computation. By default all
but one cores are used. User can override this with
**numb.cores**parameter - For more precise segmentation one should increase
**numb.runs**. Default value is 20 - Parameter
**max.dim**should reflect how large we expect subspaces to be. Default value is 4 - If parameter
**greedy**is TRUE (value set by default) the number of clusters is estimated in a greedy way. So program stops after getting first BIC local maximum - If
**estimate.dimensions**is TRUE subspaces dimensions are estimated. Otherwise all subspaces are assumed to be of dimension*max.dim*

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