fabi {fabia} | R Documentation

## Factor Analysis for Bicluster Acquisition: Laplace Prior (FABI)

### Description

`fabi`: R implementation of `fabia`, therefore it is slow.

### Usage

    fabi(X,cyc,alpha,spl,spz,p,norm=1)

### Arguments

`X` | the data matrix.
`cyc` | number of cycles to run.
`alpha` | sparseness loadings (0.1-1.0).
`spl` | sparseness prior loadings (0.5 - 4.0).
`spz` | sparseness factors (0.5-4.0).
`p` | number of hidden factors = number of biclusters.
`norm` | should the data be standardized, default = 1 (yes, using mean), 2 (yes, using median).

### Details

Biclusters are found by sparse factor analysis where both the factors and the loadings are sparse.

Essentially the model is the sum of outer products of sparse 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

If the nonzero components of the sparse vectors are grouped together then the outer product results in a matrix with a nonzero block and zeros elsewhere.

We recommend to normalize the components to variance one in order to make the signal and noise comparable across components.

The model selection is performed by a variational approach according to Girolami 2001 and Palmer et al. 2006.

We included a prior on the parameters and minimize a lower bound on the posterior of the parameters given the data. The update of the loadings includes an additive term which pushes the loadings toward zero (Gaussian prior leads to an multiplicative factor).

The code is implemented in R, therefore it is slow.

### Value

`LZ` | Estimated Noise Free Data: L Z
`L` | Loadings: L
`Z` | Factors: Z
`Psi` | Noise variance: σ
`lapla` | Variational parameter

### Author(s)

Sepp Hochreiter

### References

Mark Girolami, ‘A Variational Method for Learning Sparse and Overcomplete Representations’, Neural Computation 13(11): 2517-2532, 2001.

J. Palmer, D. Wipf, K. Kreutz-Delgado, B. Rao, ‘Variational EM algorithms for non-Gaussian latent variable models’, Advances in Neural Information Processing Systems 18, pp. 1059-1066, 2006.

### See Also

`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`, `extract_bic`, `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 <- fabi(X,10,0.3,1.0,1.0,3)

    ## 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 <- fabi(X,200,0.4,1.0,1.0,13)

    rToy <- extract_plot(X,resToy$L,resToy$Z,ti="FABI",Y=Y)

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

    data(Breast_A)

    X <- as.matrix(XBreast)

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

    rBreast <- extract_plot(X,resBreast$L,resBreast$Z,ti="FABI Breast cancer(Veer)")

    #sorting of predefined labels
    CBreast

    #---------------
    # DEMO3
    #---------------

    data(Multi_A)

    X <- as.matrix(XMulti)

    resMulti <- fabi(X,200,0.1,1.0,1.0,5)

    rMulti <- extract_plot(X,resMulti$L,resMulti$Z,ti="FABI Multiple tissues(Su)")

    #sorting of predefined labels
    CMulti

    #---------------
    # DEMO4
    #---------------

    data(DLBCL_B)

    X <- as.matrix(XDLBCL)

    resDLBCL <- fabi(X,200,0.1,1.0,1.0,5)

    rDLBCL <- extract_plot(X,resDLBCL$L,resDLBCL$Z,ti="FABI Lymphoma(Rosenwald)")

    #sorting of predefined labels
    CDLBCL
    ## End(Not run)

[Package fabia version 0.1.1 Index]