fabia {fabia} | R Documentation

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

### Description

`fabia`: C implementation of `fabia`.

### Usage

    fabia(X,cyc,alpha,spl,spz,p,random=NULL,scale=0.0,norm=1,lap=1.0)

### 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.
`random` | random initialization of loadings in [-random,random] (if not given: half of the square root of variance of component).
`scale` | loading vectors are scaled in each iteration to the given variance. zero (default) indicates that non scaling.
`norm` | should the data be standardized, default = 1 (yes, using mean), 2 (yes, using median).
`lap` | minimal value of the variational parameter, default = 1.

### 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.

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 C using the Rcpp package.

### 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

`fabi`, `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 <- fabia(X,50,0.3,1.0,1.0,3)

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

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

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

    data(Breast_A)

    X <- as.matrix(XBreast)
    resBreast <- fabia(X,200,0.1,1.0,1.0,5)

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

    #sorting of predefined labels
    CBreast

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

    data(Multi_A)

    X <- as.matrix(XMulti)

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

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

    #sorting of predefined labels
    CMulti

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

    data(DLBCL_B)

    X <- as.matrix(XDLBCL)

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

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

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

[Package fabia version 0.1.1 Index]