fabiap {fabia} | R Documentation

## Factor Analysis for Bicluster Acquisition: Post-Projection (FABIAP)

### Description

`fabiap`: C implementation of `fabiap`.

### Usage

    fabiap(X,cyc,alpha,spl,spz,p,sL,sZ,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.
`sL` | final sparseness loadings.
`sZ` | final sparseness factors.
`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. Post-processing by projecting the final results to a given sparseness criterion.

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).

Post-processing: The final results of the loadings and the factors are projected to a sparse vector 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 C using the Rcpp package. The projection is implemented in R.

### 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.

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

### See Also

`fabi`, `fabia`, `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 <- fabiap(X,50,0.3,1.0,1.0,3,0.7,0.7)

    ## 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 <- fabiap(X,200,0.4,1.0,1.0,13,0.7,0.7)

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

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

    data(Breast_A)

    X <- as.matrix(XBreast)

    resBreast <- fabiap(X,200,0.1,1.0,1.0,5,0.5,0.3)

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

    #sorting of predefined labels
    CBreast

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

    data(Multi_A)

    X <- as.matrix(XMulti)

    resMulti <- fabiap(X,200,0.1,1.0,1.0,5,0.5,0.3)

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

    #sorting of predefined labels
    CMulti

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

    data(DLBCL_B)

    X <- as.matrix(XDLBCL)

    resDLBCL <- fabiap(X,200,0.1,1.0,1.0,5,0.5,0.3)

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

    #sorting of predefined labels
    CDLBCL

    ## End(Not run)

[Package fabia version 0.1.1 Index]