fabias {fabia} | R Documentation

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

### Description

`fabias`: C implementation of `fabias`.

### Usage

    fabias(X,p=13,alpha=0.6,cyc=500,spz=0.5,non_negative=0,random=1.0,center=2,norm=1,lap=1.0,nL=0,lL=0,bL=0)

### Arguments

`X` | the data matrix.
`p` | number of hidden factors = number of biclusters; default = 13.
`alpha` | sparseness loadings (0.1 - 1.0); default = 0.1.
`cyc` | number of iterations; default = 500.
`spz` | sparseness factors (0.5 - 2.0); default = 0.5 (Laplace).
`non_negative` | Non-negative factors and loadings if non_negative > 0; default = 0.
`random` | <=0: by SVD, >0: random initialization of loadings in [-random,random]; default = 1.0.
`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.
`nL` | maximal number of biclusters at which a row element can participate; default = 0 (no limit)
`lL` | maximal number of row elements per bicluster; default = 0 (no limit)
`bL` | cycle at which the nL or lL maximum starts; default = 0 (start at the beginning)

### 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 C.

### 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 <- fabias(X,3,0.6,50)

    ## Not run:
    #-----------------
    # DEMO1: Toy Data
    #-----------------

    n = 1000
    l= 100
    p = 10

    dat <- makeFabiaDataBlocks(n = n,l= l,p = p,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]]
    ZC <- dat[[3]]
    LC <- dat[[4]]

    gclab <- rep.int(0,l)
    gllab <- rep.int(0,n)
    clab <- as.character(1:l)
    llab <- as.character(1:n)
    for (i in 1:p){
     for (j in ZC[i]){
         clab[j] <- paste(as.character(i),"_",clab[j],sep="")
     }
     for (j in LC[i]){
         llab[j] <- paste(as.character(i),"_",llab[j],sep="")
     }
     gclab[unlist(ZC[i])] <- gclab[unlist(ZC[i])] + p^i
     gllab[unlist(LC[i])] <- gllab[unlist(LC[i])] + p^i
    }

    groups <- gclab

    #### FABIAS

    resToy2 <- fabias(X,13,0.6,400)

    extractPlot(resToy2,ti="FABIAS",Y=Y)

    raToy2 <- extractBic(resToy2)

    if ((raToy2$bic[[1]][1]>1) && (raToy2$bic[[1]][2])>1) {
        plotBicluster(raToy2,1)
    }
    if ((raToy2$bic[[2]][1]>1) && (raToy2$bic[[2]][2])>1) {
        plotBicluster(raToy2,2)
    }
    if ((raToy2$bic[[3]][1]>1) && (raToy2$bic[[3]][2])>1) {
        plotBicluster(raToy2,3)
    }
    if ((raToy2$bic[[4]][1]>1) && (raToy2$bic[[4]][2])>1) {
        plotBicluster(raToy2,4)
    }

    colnames(X(resToy2)) <- clab

    rownames(X(resToy2)) <- llab

    plot(resToy2,dim=c(1,2),label.tol=0.1,col.group = groups,lab.size=0.6)
    plot(resToy2,dim=c(1,3),label.tol=0.1,col.group = groups,lab.size=0.6)
    plot(resToy2,dim=c(2,3),label.tol=0.1,col.group = groups,lab.size=0.6)

    #------------------------------------------
    # DEMO2: Laura van't Veer's gene expression
    #        data set for breast cancer
    #------------------------------------------

    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)

    resBreast2 <- fabias(X,5,0.6,300)

    extractPlot(resBreast2,ti="FABIAS Breast cancer(Veer)")

    raBreast2 <- extractBic(resBreast2)

    if ((raBreast2$bic[[1]][1]>1) && (raBreast2$bic[[1]][2])>1) {
        plotBicluster(raBreast2,1)
    }
    if ((raBreast2$bic[[2]][1]>1) && (raBreast2$bic[[2]][2])>1) {
        plotBicluster(raBreast2,2)
    }
    if ((raBreast2$bic[[3]][1]>1) && (raBreast2$bic[[3]][2])>1) {
        plotBicluster(raBreast2,3)
    }
    if ((raBreast2$bic[[4]][1]>1) && (raBreast2$bic[[4]][2])>1) {
        plotBicluster(raBreast2,4)
    }

    plot(resBreast2,dim=c(1,2),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(1,3),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(1,4),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(1,5),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(2,3),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(2,4),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(2,5),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(3,4),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(3,5),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast2,dim=c(4,5),label.tol=0.03,col.group=CBreast,lab.size=0.6)

    }

    #-----------------------------------
    # DEMO3: Su's multiple tissue types
    #        gene expression data set
    #-----------------------------------

    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)

    resMulti2 <- fabias(X,5,0.6,300)

    extractPlot(resMulti2,ti="FABIAS Multiple tissues(Su)")

    raMulti2 <- extractBic(resMulti2)

    if ((raMulti2$bic[[1]][1]>1) && (raMulti2$bic[[1]][2])>1) {
        plotBicluster(raMulti2,1)
    }
    if ((raMulti2$bic[[2]][1]>1) && (raMulti2$bic[[2]][2])>1) {
        plotBicluster(raMulti2,2)
    }
    if ((raMulti2$bic[[3]][1]>1) && (raMulti2$bic[[3]][2])>1) {
        plotBicluster(raMulti2,3)
    }
    if ((raMulti2$bic[[4]][1]>1) && (raMulti2$bic[[4]][2])>1) {
        plotBicluster(raMulti2,4)
    }

    plot(resMulti2,dim=c(1,2),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(1,3),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(1,4),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(1,5),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(2,3),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(2,4),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(2,5),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(3,4),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(3,5),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti2,dim=c(4,5),label.tol=0.01,col.group=CMulti,lab.size=0.6)

    }

    #-----------------------------------------
    # DEMO4: Rosenwald's diffuse large-B-cell
    #        lymphoma gene expression data set
    #-----------------------------------------

    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)

    resDLBCL2 <- fabias(X,5,0.6,300)

    extractPlot(resDLBCL2,ti="FABIAS Lymphoma(Rosenwald)")

    raDLBCL2 <- extractBic(resDLBCL2)

    if ((raDLBCL2$bic[[1]][1]>1) && (raDLBCL2$bic[[1]][2])>1) {
        plotBicluster(raDLBCL2,1)
    }
    if ((raDLBCL2$bic[[2]][1]>1) && (raDLBCL2$bic[[2]][2])>1) {
        plotBicluster(raDLBCL2,2)
    }
    if ((raDLBCL2$bic[[3]][1]>1) && (raDLBCL2$bic[[3]][2])>1) {
        plotBicluster(raDLBCL2,3)
    }
    if ((raDLBCL2$bic[[4]][1]>1) && (raDLBCL2$bic[[4]][2])>1) {
        plotBicluster(raDLBCL2,4)
    }

    plot(resDLBCL2,dim=c(1,2),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(1,3),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(1,4),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(1,5),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(2,3),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(2,4),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(2,5),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(3,4),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(3,5),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL2,dim=c(4,5),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)

    }

    ## End(Not run)

[Package fabia version 2.32.0 Index]