extract_bic {fabia} | R Documentation

## Extraction of Biclusters

### Description

`extract_bic`: R implementation of `extract_bic`.

### Usage

    extract_bic(L,Z,thresZ=0.5,thresL=NULL,lapla=NULL,Psi=NULL)

### Arguments

`L` | loading, left matrix.
`Z` | factor, right matrix.
`thresZ` | threshold for sample belonging to bicluster (default 0.5).
`thresL` | threshold for loading belonging to bicluster (if not given it is estimated).
`lapla` | inverse variance of the variational approximation for each sample and each factor.
`Psi` | noise variance vector for observations where independent noise is asumed.

### Details

Essentially the model is the sum of outer products of vectors. The number of summands p is the number of biclusters.

X = L Z + U

X = sum_{i=1}^{p} L_i (Z_i )^T + U

The hidden dimension p is used for kmeans clustering of L_i and Z_i .

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 L_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 L_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 cluster to the biclusters are give. 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 indexes of `bic` with components: `numng` = `bix` and `numnp` = `biypn`.

`numn` gives the indexes 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.
`avini` | average over j of the variance Z_i given x_j.
`ini` | for each j the variance Z_i given x_j.

### Author(s)

Sepp Hochreiter

### See Also

`fabi`, `fabia`, `fabiap`, `fabias`, `fabiasp`, `mfsc`, `nmfdiv`, `nmfeu`, `nmfsc`, `nprojfunc`, `projfunc`, `make_fabi_data`, `make_fabi_data_blocks`, `make_fabi_data_pos`, `make_fabi_data_blocks_pos`, `extract_plot`, `myImagePlot`, `PlotBicluster`, `Breast_A`, `DLBCL_B`, `Multi_A`, `fabiaDemo`, `fabiaVersion`

### Examples

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

    dat <- make_fabi_data_blocks(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,20,0.1,1.0,1.0,3)

    rEx <- extract_bic(resEx$L,resEx$Z,lapla=resEx$lapla,Psi=resEx$Psi)

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

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

    dat <- make_fabi_data_blocks(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,200,0.4,1.0,1.0,13)

    rToy <- extract_bic(resToy$L,resToy$Z,lapla=resToy$lapla,Psi=resToy$Psi)

    rToy$avini

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

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

    data(Breast_A)

    X <- as.matrix(XBreast)

    resBreast <- fabia(X,200,0.1,1.0,1.0,5)

    rBreast <- extract_bic(resBreast$L,resBreast$Z,lapla=resBreast$lapla,Psi=resBreast$Psi)

    rBreast$avini

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

    ## End(Not run)

[Package fabia version 0.1.1 Index]