extractBic {fabia} | R Documentation

## Extraction of Biclusters

### Description

`extractBic`: R implementation of `extractBic`.

### Usage

    extractBic(fact,thresZ=0.5,thresL=NULL)

### Arguments

`fact` | object of the class `Factorization`.
`thresZ` | threshold for sample belonging to bicluster; default 0.5.
`thresL` | threshold for loading belonging to bicluster (if not given it is estimated).

### Details

Essentially the model is the sum of outer products of vectors:

X = ∑_{i=1}^{p} λ_i z_i^T + U

where the number of summands p is the number of biclusters. The matrix factorization is

X = L Z + U

Here λ_i are from R^n, z_i from R^l, L from R^{n \times p}, Z from R^{p \times l}, and X, U from R^{n \times l}.

U is the Gaussian noise with a diagonal covariance matrix which entries are given by `Psi`.

The Z is locally approximated by a Gaussian with inverse variance given by `lapla`.

Using these values we can computer for each j the variance z_i given x_j. Here

x_j = L z_j + u_j

This variance can be used to determine the information content of a bicluster.

The λ_i and z_i are used to extract the bicluster i, where a threshold determines which observations and which samples belong the the bicluster.

In `bic` the biclusters are extracted according to the largest absolute values of the component i, i.e. the largest values of λ_i and the largest values of z_i . The factors z_i are normalized to variance 1.

The components of `bic` are `binp`, `bixv`, `bixn`, `biypv`, and `biypn`.

`binp` give the size of the bicluster: number observations and number samples. `bixv` gives the values of the extracted observations that have absolute values above a threshold. They are sorted. `bixn` gives the extracted observation names (e.g. gene names). `biypv` gives the values of the extracted samples that have absolute values above a threshold. They are sorted. `biypn` gives the names of the extracted samples (e.g. sample names).

In `bicopp` the opposite clusters to the biclusters are given. Opposite means that the negative pattern is present.

The components of opposite clusters `bicopp` are `binn`, `bixv`, `bixn`, `biypnv`, and `biynn`.

`binp` give the size of the opposite bicluster: number observations and number samples. `bixv` gives the values of the extracted observations that have absolute values above a threshold. They are sorted. `bixn` gives the extracted observation names (e.g. gene names). `biynv` gives the values of the opposite extracted samples that have absolute values above a threshold. They are sorted. `biynn` gives the names of the opposite extracted samples (e.g. sample names).

That means the samples are divided into two groups where one group shows large positive values and the other group has negative values with large absolute values. That means a observation pattern can be switched on or switched off relative to the average value.

`numn` gives the indices of `bic` with components: `numng` = `bix` and `numnp` = `biypn`.

`numn` gives the indices of `bicopp` with components: `numng` = `bix` and `numnn` = `biynn`.

Implementation in R.

### Value

`bic` | extracted biclusters.
`numn` | indexes for the extracted biclusters.
`bicopp` | extracted opposite biclusters.
`numnopp` | indexes for the extracted opposite biclusters.
`X` | scaled and centered data matrix.
`np` | number of biclusters.

### Author(s)

Sepp Hochreiter

### See Also

`fabia`, `fabias`, `fabiap`, `fabi`, `fabiasp`, `mfsc`, `nmfdiv`, `nmfeu`, `nmfsc`, `extractPlot`, `extractBic`, `plotBicluster`, `Factorization`, `projFuncPos`, `projFunc`, `estimateMode`, `makeFabiaData`, `makeFabiaDataBlocks`, `makeFabiaDataPos`, `makeFabiaDataBlocksPos`, `matrixImagePlot`, `fabiaDemo`, `fabiaVersion`

### Examples

    #---------------
    # TEST
    #---------------

    dat <- makeFabiaDataBlocks(n = 100,l= 50,p = 3,f1 = 5,f2 = 5,
      of1 = 5,of2 = 10,sd_noise = 3.0,sd_z_noise = 0.2,mean_z = 2.0,
      sd_z = 1.0,sd_l_noise = 0.2,mean_l = 3.0,sd_l = 1.0)

    X <- dat[[1]]
    Y <- dat[[2]]

    resEx <- fabia(X,3,0.01,20)

    rEx <- extractBic(resEx)

    rEx$bic[1,]
    rEx$bic[2,]
    rEx$bic[3,]

    ## Not run:
    #---------------
    # DEMO1
    #---------------

    dat <- makeFabiaDataBlocks(n = 1000,l= 100,p = 10,f1 = 5,f2 = 5,
      of1 = 5,of2 = 10,sd_noise = 3.0,sd_z_noise = 0.2,mean_z = 2.0,
      sd_z = 1.0,sd_l_noise = 0.2,mean_l = 3.0,sd_l = 1.0)

    X <- dat[[1]]
    Y <- dat[[2]]

    resToy <- fabia(X,13,0.01,200)

    rToy <- extractBic(resToy)

    avini(resToy)

    rToy$bic[1,]
    rToy$bic[2,]
    rToy$bic[3,]

    #---------------
    # DEMO2
    #---------------

    avail <- require(fabiaData)

    if (!avail) {
        message("")
        message("")
        message("#####################################################")
        message("Package 'fabiaData' is not available: please install.")
        message("#####################################################")
    } else {

    data(Breast_A)

    X <- as.matrix(XBreast)

    resBreast <- fabia(X,5,0.1,200)

    rBreast <- extractBic(resBreast)

    avini(resBreast)

    rBreast$bic[1,]
    rBreast$bic[2,]
    rBreast$bic[3,]
    }

    ## End(Not run)

[Package fabia version 2.32.0 Index]