makeFabiaDataBlocksPos {fabia} | R Documentation

## Generation of Bicluster Data with Bicluster Blocks

### Description

`makeFabiaDataBlocksPos`: R implementation of `makeFabiaDataBlocksPos`.

### Usage

    makeFabiaDataBlocksPos(n,l,p,f1,f2,of1,of2,sd_noise,sd_z_noise,
                  mean_z,sd_z,sd_l_noise,mean_l,sd_l)

### Arguments

`n` | number of observations.
`l` | number of samples.
`p` | number of biclusters.
`f1` | nn/f1 max. additional samples are active in a bicluster.
`f2` | n/f2 max. additional observations that form a pattern in a bicluster.
`of1` | minimal active samples in a bicluster.
`of2` | minimal observations that form a pattern in a bicluster.
`sd_noise` | Gaussian zero mean noise std on data matrix.
`sd_z_noise` | Gaussian zero mean noise std for deactivated hidden factors.
`mean_z` | Gaussian mean for activated factors.
`sd_z` | Gaussian std for activated factors.
`sd_l_noise` | Gaussian zero mean noise std if no observation patterns are present.
`mean_l` | Gaussian mean for observation patterns.
`sd_l` | Gaussian std for observation patterns.

### Details

Bicluster data is generated for visualization because the biclusters are now in block format. That means observations and samples that belong to a bicluster are consecutive. This allows visual inspection because the use can identify blocks and whether they have been found or reconstructed.

Essentially the data generation model is the sum of outer products of sparse 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

and noise free

Y = L Z

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, Y from R^{n \times l}.

Sequentially L_i are generated using `n`, `f2`, `of2`, `sd_l_noise`, `mean_l`, `sd_l`. `of2` gives the minimal observations participating in a bicluster to which between 0 and n/f2 observations are added, where the number is uniformly chosen. `sd_l_noise` gives the noise of observations not participating in the bicluster. `mean_l` and `sd_l` determines the Gaussian from which the values are drawn for the observations that participate in the bicluster. "POS": The sign of the mean is fixed.

Sequentially Z_i are generated using `l`, `f1`, `of1`, `sd_z_noise`, `mean_z`, `sd_z`. `of1` gives the minimal samples participating in a bicluster to which between 0 and l/f1 samples are added, where the number is uniformly chosen. `sd_z_noise` gives the noise of samples not participating in the bicluster. `mean_z` and `sd_z` determines the Gaussian from which the values are drawn for the samples that participate in the bicluster.

U is the overall Gaussian zero mean noise generated by `sd_noise`.

Implementation in R.

### Value

`Y` | the noise data from R^{n \times l}.
`X` | the noise free data from R^{n \times l}.
`ZC` | list where i-th element gives samples belonging to i-th bicluster.
`LC` | list where i-th element gives observations belonging to i-th bicluster.

### 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 <- makeFabiaDataBlocksPos(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]]

    matrixImagePlot(Y)
    dev.new()
    matrixImagePlot(X)

    ## Not run:
    #---------------
    # DEMO
    #---------------

    dat <- makeFabiaDataBlocksPos(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)

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

    matrixImagePlot(Y)
    dev.new()
    matrixImagePlot(X)

    ## End(Not run)

[Package fabia version 2.33.3 Index]