robustness {isa2}R Documentation

Robustness of ISA biclusters

Description

Robustness of ISA biclusters. The more robust biclusters are more significant in the sense that it is less likely to see them in random data.

Usage

## S4 method for signature 'list':
robustness(normed.data, ...)
## S4 method for signature 'matrix':
isa.filter.robust(data, ...)

Arguments

normed.data The normalized input data, usually calculated with isa.normalize.
data The original, not normalized input data.
... Additional arguments, see details below.

Details

robustness can be called as

    robustness(normed.data, row.scores, col.scores)
and isa.filter.robust can be called as
    isa.filter.robust(data, normed.data, isares,
                      perms = 1, row.seeds, col.seeds)
These arguments are:
normed.data
The normalized input data, usually calculated with isa.normalize.
row.scores
The scores of the row components of the biclusters. Usually the rows member of the result list, as returned by isa, or isa.iterate or some other ISA function.
col.scores
The scores of the columns of the biclusters, usually the columns member of the result list from isa.
data
The original, not normalized input data.
isares
The result of ISA, coming from isa or isa.iterate or any other function that return the same format.
perms
The number of permutations to perform on the input data.
row.seeds
Optionally the row seeds for the ISA run on the scrambled data. If this and col.seeds are both omitted the same number of random seeds are used as for isaresult.
col.seeds
Optionally the column seed to use for the ISA on the scrambled input matrix. If both this and row.seeds are omitted, then the same number of random (row) seeds will be used as for isares.

Even if you generate a matrix with uniform random noise in it, if you calculate ISA on it, you will get some biclusters, except maybe if you use very strict threshold parameters. These biclusters contain rows and columns that are correlated just by chance.

To circumvent this, you can use the so-called robustness measure of the biclusters. The robustness of a bicluster is the function of its rows, columns and the input data, and it is a real number, usually positive. It is roughly equivalent to the principal singular value of the submatrix (of the reordered input matrix) defined by the bicluster.

robustness calculates the robustness score of a set of biclusters, usually coming from one or more ISA iterations.

isa.filter.robust provides filtering based on the robustness measure. It reshuffles the input matrix and calculates ISA on it, with the parameters that were used to find the biclusters under evaluation. It then calculates the robustness for the modules that were found in the scrambled matrix (if there is any) and removes any modules from the data set that have a lower robustness score than at least one module in the scrambled data.

You can think of isa.filter.robust as a permutation test, but the input data is shuffled only once, because of the relatively high computational demands of the ISA.

Value

robustness returns a numeric vector, the robustness score of each bicluster.
isa.filter.robust returns a named list, the filtered isares, see the return value of isa.iterate for the structure of the list.

Author(s)

Gabor Csardi Gabor.Csardi@unil.ch

References

Bergmann S, Ihmels J, Barkai N: Iterative signature algorithm for the analysis of large-scale gene expression data Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Mar;67(3 Pt 1):031902. Epub 2003 Mar 11.

Ihmels J, Friedlander G, Bergmann S, Sarig O, Ziv Y, Barkai N: Revealing modular organization in the yeast transcriptional network Nat Genet. 2002 Aug;31(4):370-7. Epub 2002 Jul 22

Ihmels J, Bergmann S, Barkai N: Defining transcription modules using large-scale gene expression data Bioinformatics 2004 Sep 1;20(13):1993-2003. Epub 2004 Mar 25.

See Also

isa2-package for a short introduction on the Iterative Signature Algorithm. See isa for an easy way of running ISA.

Examples

## A basic ISA work flow for a single threshold combination
## In-silico data
set.seed(1)
insili <- isa.in.silico()

## Random seeds
seeds <- generate.seeds(length=nrow(insili[[1]]), count=100)

## Normalize input matrix
nm <- isa.normalize(insili[[1]])

## Do ISA
isares <- isa.iterate(nm, row.seeds=seeds, thr.row=2, thr.col=1)

## Eliminate duplicates
isares <- isa.unique(nm, isares)

## Calculate robustness
rob <- robustness(nm, isares$rows, isares$columns)
rob

## There are three robust ones and a lot of less robust ones
## Plot the three robust ones and three others
if (interactive()) {
  toplot1 <- rev(order(rob))[1:3]
  toplot2 <- sample(seq_along(rob)[-toplot1], 3)
  layout( rbind(1:3,4:6) )
  for (i in c(toplot1, toplot2)) {
    image(outer(isares$rows[,i], isares$column[,i]),
          main=round(rob[i],2))
  }
}

## Filter out not robust ones
isares2 <- isa.filter.robust(insili[[1]], nm, isares)

## Probably there are only three of them left
ncol(isares2$rows)

[Package isa2 version 0.1 Index]