mfsc {fabia} | R Documentation

## Sparse Matrix Factorization for Bicluster Analysis (MFSC)

### Description

`mfsc`: R implementation of `mfsc`.

### Usage

    mfsc(X,p=5,cyc=100,sL=0.6,sZ=0.6,center=2,norm=1)

### Arguments

`X` | the data matrix.
`p` | number of hidden factors = number of biclusters; default = 5.
`cyc` | maximal number of iterations; default = 100.
`sL` | final sparseness loadings; default = 0.6.
`sZ` | final sparseness factors; default = 0.6.
`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.

### Details

Biclusters are found by sparse matrix factorization where both factors are sparse.

Essentially the model is the sum of outer products of vectors:

X = ∑_{i=1}^{p} λ_i z_i^T

where the number of summands p is the number of biclusters. The matrix factorization is

X = L Z

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 from R^{n \times l}.

No noise assumption: In contrast to factor analysis there is no noise assumption.

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 constraint optimization according to Hoyer, 2004. The Euclidean distance (the Frobenius norm) is minimized subject to sparseness constraints.

Model selection is done by gradient descent on the Euclidean objective and thereafter projection of single vectors of L and single vectors of Z to fulfill the sparseness constraints.

The projection minimize the Euclidean distance to the original vector given an l_1-norm and an l_2-norm.

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.

### 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)

### 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

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

### See Also

`fabia`, `fabias`, `fabiap`, `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 <- mfsc(X,3,30,0.6,0.6)

    ## 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

    #### MFSC

    resToy4 <- mfsc(X,13,100,0.6,0.6)

    extractPlot(resToy4,ti="MFSC",Y=Y)

    raToy4 <- extractBic(resToy4,thresZ=0.01,thresL=0.05)

    if ((raToy4$bic[[1]][1]>1) && (raToy4$bic[[1]][2])>1) {
        plotBicluster(raToy4,1)
    }
    if ((raToy4$bic[[2]][1]>1) && (raToy4$bic[[2]][2])>1) {
        plotBicluster(raToy4,2)
    }
    if ((raToy4$bic[[3]][1]>1) && (raToy4$bic[[3]][2])>1) {
        plotBicluster(raToy4,3)
    }
    if ((raToy4$bic[[4]][1]>1) && (raToy4$bic[[4]][2])>1) {
        plotBicluster(raToy4,4)
    }

    colnames(X(resToy4)) <- clab

    rownames(X(resToy4)) <- llab

    plot(resToy4,dim=c(1,2),label.tol=0.1,col.group = groups,lab.size=0.6)
    plot(resToy4,dim=c(1,3),label.tol=0.1,col.group = groups,lab.size=0.6)
    plot(resToy4,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)

    resBreast4 <- mfsc(X,5,100,0.6,0.6)

    extractPlot(resBreast4,ti="MFSC Breast cancer(Veer)")

    raBreast4 <- extractBic(resBreast4,thresZ=0.01,thresL=0.05)

    if ((raBreast4$bic[[1]][1]>1) && (raBreast4$bic[[1]][2])>1) {
        plotBicluster(raBreast4,1)
    }
    if ((raBreast4$bic[[2]][1]>1) && (raBreast4$bic[[2]][2])>1) {
        plotBicluster(raBreast4,2)
    }
    if ((raBreast4$bic[[3]][1]>1) && (raBreast4$bic[[3]][2])>1) {
        plotBicluster(raBreast4,3)
    }
    if ((raBreast4$bic[[4]][1]>1) && (raBreast4$bic[[4]][2])>1) {
        plotBicluster(raBreast4,4)
    }

    plot(resBreast4,dim=c(1,2),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,dim=c(1,3),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,dim=c(1,4),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,dim=c(1,5),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,dim=c(2,3),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,dim=c(2,4),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,dim=c(2,5),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,dim=c(3,4),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,dim=c(3,5),label.tol=0.03,col.group=CBreast,lab.size=0.6)
    plot(resBreast4,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)

    resMulti4 <- mfsc(X,5,100,0.6,0.6)

    extractPlot(resMulti4,ti="MFSC Multiple tissues(Su)")

    raMulti4 <- extractBic(resMulti4,thresZ=0.01,thresL=0.05)

    if ((raMulti4$bic[[1]][1]>1) && (raMulti4$bic[[1]][2])>1) {
        plotBicluster(raMulti4,1)
    }
    if ((raMulti4$bic[[2]][1]>1) && (raMulti4$bic[[2]][2])>1) {
        plotBicluster(raMulti4,2)
    }
    if ((raMulti4$bic[[3]][1]>1) && (raMulti4$bic[[3]][2])>1) {
        plotBicluster(raMulti4,3)
    }
    if ((raMulti4$bic[[4]][1]>1) && (raMulti4$bic[[4]][2])>1) {
        plotBicluster(raMulti4,4)
    }

    plot(resMulti4,dim=c(1,2),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,dim=c(1,3),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,dim=c(1,4),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,dim=c(1,5),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,dim=c(2,3),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,dim=c(2,4),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,dim=c(2,5),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,dim=c(3,4),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,dim=c(3,5),label.tol=0.01,col.group=CMulti,lab.size=0.6)
    plot(resMulti4,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)

    resDLBCL4 <- mfsc(X,5,100,0.6,0.6)

    extractPlot(resDLBCL4,ti="MFSC Lymphoma(Rosenwald)")

    raDLBCL4 <- extractBic(resDLBCL4,thresZ=0.01,thresL=0.05)

    if ((raDLBCL4$bic[[1]][1]>1) && (raDLBCL4$bic[[1]][2])>1) {
        plotBicluster(raDLBCL4,1)
    }
    if ((raDLBCL4$bic[[2]][1]>1) && (raDLBCL4$bic[[2]][2])>1) {
        plotBicluster(raDLBCL4,2)
    }
    if ((raDLBCL4$bic[[3]][1]>1) && (raDLBCL4$bic[[3]][2])>1) {
        plotBicluster(raDLBCL4,3)
    }
    if ((raDLBCL4$bic[[4]][1]>1) && (raDLBCL4$bic[[4]][2])>1) {
        plotBicluster(raDLBCL4,4)
    }

    plot(resDLBCL4,dim=c(1,2),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(1,3),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(1,4),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(1,5),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(2,3),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(2,4),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(2,5),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(3,4),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(3,5),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)
    plot(resDLBCL4,dim=c(4,5),label.tol=0.03,col.group=CDLBCL,lab.size=0.6)

    }

    ## End(Not run)

[Package fabia version 2.40.0 Index]