# fabi: Factor Analysis for Bicluster Acquisition: Laplace Prior... In fabia: FABIA: Factor Analysis for Bicluster Acquisition

## Description

fabi: R implementation of fabia, therefore it is slow.

## Usage

 1 fabi(X,p=13,alpha=0.01,cyc=500,spl=0,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 (0-1.0); default = 0.01. cyc number of iterations; default = 500. spl sparseness prior loadings (0 - 2.0); default = 0 (Laplace). 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.

We recommend to normalize the components to variance one in order to make the signal and noise comparable across components.

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).

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).

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.

fabia, fabias, fabiap, spfabia, fabi, fabiasp, mfsc, nmfdiv, nmfeu, nmfsc, extractPlot, extractBic, plotBicluster, Factorization, projFuncPos, projFunc, estimateMode, makeFabiaData, makeFabiaDataBlocks, makeFabiaDataPos, makeFabiaDataBlocksPos, matrixImagePlot, fabiaDemo, fabiaVersion
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 #--------------- # 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 <- fabi(X,3,0.01,20) ## 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 <- fabi(X,13,0.01,200) extractPlot(resToy,ti="FABI",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 <- fabi(X,5,0.1,200) extractPlot(resBreast,ti="FABI 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 <- fabi(X,5,0.1,200) extractPlot(resMulti,ti="FABI 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 <- fabi(X,5,0.1,200) extractPlot(resDLBCL,ti="FABI Lymphoma(Rosenwald)") #sorting of predefined labels CDLBCL } ## End(Not run)