fabiasp {fabia} | R Documentation

## Factor Analysis for Bicluster Acquisition: Sparseness Projection (FABIASP)

### Description

`fabiasp`: R implementation of `fabias`, therefore it is slow.

### Usage

    fabiasp(X,p=13,alpha=0.6,cyc=500,spz=0.5,center=2,norm=1,lap=1.0)

### Arguments

`X` | the data matrix.
`p` | number of hidden factors = number of biclusters; default = 13.
`alpha` | sparseness loadings (0.1 - 1.0); default = 0.6.
`cyc` | number of iterations; default = 500.
`spz` | sparseness factors (0.5 - 2.0); default = 0.5 (Laplace).
`center` | data centering: 1 (mean), 2 (median), > 2 (mode), 0 (no); default = 2.
`norm` | data normalization: 1 (0.75-0.25 quantile), >1 (var=1), 0 (no); default = 1.
`lap` | minimal value of the variational parameter; default = 1.0.

### 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 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

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 from R^{n \times l}.

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.

The prior has finite support, therefore after each update of the loadings they are projected to the finite support. The projection is done according to Hoyer, 2004: given an l_1-norm and an l_2-norm minimize the Euclidean distance to the original vector (currently the l_2-norm is fixed to 1). The projection is a convex quadratic problem which is solved iteratively where at each iteration at least one component is set to zero. Instead of the l_1-norm a sparseness measurement is used which relates the l_1-norm to the l_2-norm.

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

### Value

`` | object of the class `Factorization`. Containing `LZ` (estimated noise free data L Z), `L` (loadings L), `Z` (factors Z), `U` (noise X-LZ), `center` (centering vector), `scaleData` (scaling vector), `X` (centered and scaled data X), `Psi` (noise variance σ), `lapla` (variational parameter), `avini` (the information which the factor z_{ij} contains about x_j averaged over j) `xavini` (the information which the factor z_{j} contains about x_j) `ini` (for each j the information which the factor z_{ij} contains about x_j).

### Author(s)

Sepp Hochreiter

### References

S. Hochreiter et al., ‘FABIA: Factor Analysis for Bicluster Acquisition’, Bioinformatics 26(12):1520-1527, 2010. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btq227

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.

Patrik O. Hoyer, ‘Non-negative Matrix Factorization with Sparseness Constraints’, Journal of Machine Learning Research 5:1457-1469, 2004.

### See Also

`fabia`, `fabias`, `fabiap`, `spfabia`, `fabi`, `fabiasp`, `mfsc`, `nmfdiv`, `nmfeu`, `nmfsc`, `extractPlot`, `extractBic`, `plotBicluster`, `Factorization`, `projFuncPos`, `projFunc`, `estimateMode`, `makeFabiaData`, `makeFabiaDataBlocks`, `makeFabiaDataPos`, `makeFabiaDataBlocksPos`, `matrixImagePlot`, `fabiaDemo`, `fabiaVersion`

### Examples

    #---------------
    # TEST
    #---------------

    dat <- makeFabiaDataBlocks(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 <- fabiasp(X,3,0.6,50)

    ## Not run:
    #---------------
    # DEMO1
    #---------------

    dat <- makeFabiaDataBlocks(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 <- fabiasp(X,13,0.6,200)

    extractPlot(resToy,"ti=FABIASP",Y=Y)

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

    avail <- require(fabiaData)

    if (!avail) {
        message("")
        message("")
        message("#####################################################")
        message("Package 'fabiaData' is not available: please install.")
        message("#####################################################")
    } else {

    data(Breast_A)

    X <- as.matrix(XBreast)

    resBreast <- fabiasp(X,5,0.6,200)

    extractPlot(resBreast,ti="FABIASP Breast cancer(Veer)")

    #sorting of predefined labels
    CBreast

    }

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

    avail <- require(fabiaData)

    if (!avail) {
        message("")
        message("")
        message("#####################################################")
        message("Package 'fabiaData' is not available: please install.")
        message("#####################################################")
    } else {

    data(Multi_A)

    X <- as.matrix(XMulti)

    resMulti <- fabiasp(X,5,0.6,200)

    extractPlot(resMulti,"ti=FABIASP Multiple tissues(Su)")

    #sorting of predefined labels
    CMulti

    }

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

    avail <- require(fabiaData)

    if (!avail) {
        message("")
        message("")
        message("#####################################################")
        message("Package 'fabiaData' is not available: please install.")
        message("#####################################################")
    } else {

    data(DLBCL_B)

    X <- as.matrix(XDLBCL)

    resDLBCL <- fabiasp(X,5,0.6,200)

    extractPlot(resDLBCL,ti="FABIASP Lymphoma(Rosenwald)")

    #sorting of predefined labels
    CDLBCL
    }

    ## End(Not run)

[Package fabia version 2.33.3 Index]