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

## Description

`projFunc`: R implementation of `projFunc`.

## Usage

 `1` ```projFunc(s, k1, k2) ```

## Arguments

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

## Details

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.

## Value

 `v` sparse projected vector.

Sepp Hochreiter

## References

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`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```#--------------- # 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 ```