makeFabiaDataPos {fabia} | R Documentation

## Generation of Bicluster Data

### Description

`makeFabiaDataPos`: R implementation of `makeFabiaDataPos`.

### Usage

    makeFabiaDataPos(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

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

`X` | the noise data from R^{n \times l}.
`Y` | 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 <- makeFabiaDataPos(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 <- makeFabiaDataPos(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]]

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

    ## End(Not run)

[Package fabia version 2.26.0 Index]