projFuncPos {fabia} | R Documentation

## Projection of a Vector to a Non-negative Sparse Vector

### Description

`projFuncPos`: R implementation of `projFuncPos`.

### Usage

    projFuncPos(s, k1, k2)

### Arguments

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

### Details

The projection minimize the Euclidean distance to the original vector given an l_1-norm and an l_2-norm and enforcing non-negativity.

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` | non-negative sparse projected vector.

### Author(s)

Sepp Hochreiter

### References

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

### See Also

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

### Examples

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

    size <- 30
    sparseness <- 0.7

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

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

    s
    ss

[Package fabia version 2.40.0 Index]