fabia (version 2.18.0)

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

Description

fabiasp: Rimplementation 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.

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 $\sigma$), 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 $x_j$).

concept

• biclustering
• factor analysis
• sparse coding
• Laplace distribution
• EM algorithm
• nonnegative matrix factorization
• multivariate analysis
• latent variables

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: $$X = \sum_{i=1}^{p} \lambda_i z_i^T + U$$ where the number of summands $p$ is the number of biclusters. The matrix factorization is $$X = L Z + U$$

Here $\lambda_i$ 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.

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)


#---------------
# 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}