spfabia: Factor Analysis for Bicluster Acquisition: SPARSE FABIA

Description

spfabia: C implementation of spfabia.

Usage

spfabia(X,p=13,alpha=0.01,cyc=500,spl=0,spz=0.5,non_negative=0,random=1.0,write_file=1,norm=1,scale=0.0,lap=1.0,nL=0,lL=0,bL=0,samples=0,initL=0,iter=1,quant=0.001,lowerB=0.0,upperB=1000.0,dorescale=FALSE,doini=FALSE,eps=1e-3,eps1=1e-10)

Arguments

the file name of the sparse matrix in sparse format.

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).

non_negative

Non-negative factors and loadings if non_negative > 0; default = 0.

random

>0: random initialization of loadings in [0,random],

write_file

>0: results are written to files (L in sparse format), default = 1.

norm

data normalization: >0 (var=1), 0 (no); default = 1.

scale

loading vectors are scaled in each iteration to the given variance. 0.0 indicates non scaling; default = 0.0.

lap

minimal value of the variational parameter; default = 1.0.

maximal number of biclusters at which a row element can participate; default = 0 (no limit).

maximal number of row elements per bicluster; default = 0 (no limit).

cycle at which the nL or lL maximum starts; default = 0 (start at the beginning).

samples

vector of samples which should be included into the analysis; default = 0 (all samples)

initL

vector of indices of the selected samples which are used to initialize L; default = 0 (random initialization).

iter

number of iterations; default = 1.

quant

qunatile of largest L values to remove in each iteration; default = 0.001.

lowerB

lower bound for filtering the inputs columns, the minimal column sum; default = 0.0.

upperB

upper bound for filtering the inputs columns, the maximal column sum; default = 1000.0.

dorescale

rescale factors Z to variance 1 and consequently also L; logical; default: FALSE.

doini

compute the information content of the biclusters and sort the biclusters according to their information content; logical, default: FALSE.

eps

lower bound for variational parameter lapla; default: 1e-3.

eps1

lower bound for divisions to avoid division by zero; default: 1e-10.

Value

object of the class Factorization. Containing L (loadings $L$), Z (factors $Z$), 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
non-negative matrix factorization
multivariate analysis
latent variables

Details

Version of fabia for a sparse data matrix. The data matrix is directly scanned by the C-code and must be in sparse matrix format.

Sparse matrix format: *first line: numer of rows (the samples). *second line: number of columns (the features). *following lines: for each sample (row) three lines with

I) number of nonzero row elements

II) indices of the nonzero row elements (ATTENTION: starts with 0!!)

III) values of the nonzero row elements (ATTENTION: floats with decimal point like 1.0 !!)

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.

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 C.

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.

Examples

Run this code

#---------------
# TEST
#---------------

samples <- 20
features <- 200
sparseness <- 0.9
write(samples, file = "sparseFabiaTest.txt",ncolumns = features,append = FALSE, sep = "")
write(features, file = "sparseFabiaTest.txt",ncolumns = features,append = TRUE, sep = "")
for (i in 1:samples)
{
  ind <- which(runif(features)>sparseness)-1
  num <- length(ind)
  val <- abs(rnorm(num))
  write(num, file = "sparseFabiaTest.txt",ncolumns = features,append = TRUE, sep = "")
  write(ind, file = "sparseFabiaTest.txt",ncolumns = features,append = TRUE, sep = "")
  write(val, file = "sparseFabiaTest.txt",ncolumns = features,append = TRUE, sep = "")
}

res <- spfabia("sparseFabiaTest",p=3,alpha=0.03,cyc=50,non_negative=1,write_file=0,norm=0)

unlink("sparseFabiaTest.txt")

plot(res,dim=c(1,2))
plot(res,dim=c(1,3))
plot(res,dim=c(2,3))

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