compHclust {compHclust}

Complementary Hierarchical Clustering

Description

Performs the complementary hierarchical clustering procedure and returns X' (the expected residual matrix) and a vector of the relative gene importances.

Usage

compHclust(x, xhc)

Arguments

x

A numeric matrix X, where interest lies in clustering its columns.

xhc

An object of class hclust, specifically, a hierarchical clustering of the columns of X.

Details

This function performs the complementary hierarchical clustering procedure, as described in Nowak and Tibshirani (2008). Although applicable to any numeric matrix X, we typically think of X as microarray data with the rows as genes and the columns as samples, with the number of genes much greater than the number of samples. The goal of the procedure is to uncover structures present in the data that arise from ‘weak’ genes.

Given X and a hierarchical clustering of the columns of X, the function returns X', which represents a modified version of X with the structural features arising from the strong genes removed. Using information present in the hierarchical clustering, we perform a series of linear regressions and set X' to be the expected value of the resulting residuals. Details are given in Nowak and Tibshirani (2008). The user can then apply a hierarchical clustering algorithm to cluster the columns of X' to discover any important structures arising from the weaker genes.

The function also returns a vector of length equal to the number of rows of X, where the ith element is equal to the relative gene importance of the ith gene. The relative gene importance lies between 0 and 1, with a value close to 1 indicating that a gene (row) was strongly influential in the hierarchical clustering of the columns of X.

Value

A list with components:

x.prime

The expected residual matrix X'.

gene.imp

A vector of the relative gene importances.

Author(s)

Gen Nowak [e-mail] and Robert Tibshirani

References

Nowak, G. and Tibshirani, R. (2008) Complementary hierarchical clustering. Biostatistics, 9(3), 467–483.

See Also

hclust

Examples

## Creating example microarray data with rows as genes and columns as
## samples.  Rows 1-20 represent the 'strong' genes which differentiate
## samples 1-4 from samples 5-8.  Rows 31-50 represent the 'weak' genes
## which differentiate the odd numbered samples from the even numbered
## samples.
set.seed(4872)
x <- matrix(0,nrow=50,ncol=8)
x[1:20,1:4] <- 8
x[1:20,5:8] <- -8
x[31:50,c(1,3,5,7)] <- 4
x[31:50,-c(1,3,5,7)] <- -4
x <- x + matrix(rnorm(50*8),ncol=8)

## Hierarchically cluster the columns of x.
x.hc <- hclust(as.dist(1-cor(x)))

## Run complementary hierarchical clustering.
x.chc <- compHclust(x,x.hc)
xp <- x.chc$x.prime
x.gi <- x.chc$gene.imp

## Hierarchically cluster the columns of x'.
xp.hc <- hclust(as.dist(1-cor(xp)))
xp.gi <- compHclust(xp,xp.hc)$gene.imp

## We use the function 'compHclust.heatmap' to display the
## initial and complementary clusterings.
## The initial clustering.
compHclust.heatmap(x,x.hc,x.gi,d.title="Initial Clustering")
## The complementary clustering.
compHclust.heatmap(xp,xp.hc,xp.gi,d.title="Complementary Clustering")