projFunc: Projection of a Vector to a Sparse Vector
In fabia: FABIA: Factor Analysis for Bicluster Acquisition

Description Usage Arguments Details Value Author(s) References See Also Examples

projFunc: R implementation of projFunc.

1	projFunc(s, k1, k2)

`s`	data vector.
`k1`	sparseness, l1 norm constraint.
`k2`	l2 norm constraint.

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. The projection is a convex quadratic problem which is solved iteratively where at each iteration at least one component is set to zero.

In the applications, instead of the l_1-norm a sparseness measurement is used which relates the l_1-norm to the l_2-norm.

Implementation in R.

`v`	sparse projected vector.

Sepp Hochreiter

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

fabia, fabias, fabiap, fabi, fabiasp, mfsc, nmfdiv, nmfeu, nmfsc, extractPlot, extractBic, plotBicluster, Factorization, projFuncPos, projFunc, estimateMode, makeFabiaData, makeFabiaDataBlocks, makeFabiaDataPos, makeFabiaDataBlocksPos, matrixImagePlot, fabiaDemo, fabiaVersion

#---------------
# DEMO
#---------------

size <- 30
sparseness <- 0.7

s <- as.vector(rnorm(size))
sp <- sqrt(1.0*size)-(sqrt(1.0*size)-1.0)*sparseness

ss <- projFunc(s,k1=sp,k2=1)

s
ss