`makeFabiaDataBlocksPos`

: **R** implementation of `makeFabiaDataBlocksPos`

.

1 2 | ```
makeFabiaDataBlocksPos(n,l,p,f1,f2,of1,of2,sd_noise,sd_z_noise,
mean_z,sd_z,sd_l_noise,mean_l,sd_l)
``` |

`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. |

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**.

`Y` |
the noise data from |

`X` |
the noise free data from |

`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. |

Sepp Hochreiter

`fabia`

,
`fabias`

,
`fabiap`

,
`fabi`

,
`fabiasp`

,
`mfsc`

,
`nmfdiv`

,
`nmfeu`

,
`nmfsc`

,
`extractPlot`

,
`extractBic`

,
`plotBicluster`

,
`Factorization`

,
`projFuncPos`

,
`projFunc`

,
`estimateMode`

,
`makeFabiaData`

,
`makeFabiaDataBlocks`

,
`makeFabiaDataPos`

,
`makeFabiaDataBlocksPos`

,
`matrixImagePlot`

,
`fabiaDemo`

,
`fabiaVersion`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | ```
#---------------
# 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)
``` |

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