# fabias: Factor Analysis for Bicluster Acquisition: Sparseness... In Bioconductor-mirror/fabia: FABIA: Factor Analysis for Bicluster Acquisition

## Description

fabias: C implementation of fabias.

## Usage

 1 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).

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.

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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 #--------------- # 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)