nmfsc {fabia} | R Documentation

## Non-negative Sparse Matrix Factorization

### Description

`nmfsc`: R implementation of `nmfsc`.

### Usage

    nmfsc(X,p=5,cyc=100,sL=0.6,sZ=0.6)

### Arguments

`X` | the data matrix.
`p` | number of hidden factors = number of biclusters; default = 5.
`cyc` | maximal number of iterations; default = 100.
`sL` | sparseness loadings; default = 0.6.
`sZ` | sparseness factors; default = 0.6.

### Details

Non-negative Matrix Factorization represents positive matrix X by positive matrices L and Z that are sparse.

Objective for reconstruction is Euclidean distance and sparseness constraints.

Essentially the model is the sum of outer products of vectors:

X = ∑_{i=1}^{p} λ_i z_i^T

where the number of summands p is the number of biclusters. The matrix factorization is

X = L Z

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 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 constraint optimization according to Hoyer, 2004. The Euclidean distance (the Frobenius norm) is minimized subject to sparseness and non-negativity constraints.

Model selection is done by gradient descent on the Euclidean objective and thereafter projection of single vectors of L and single vectors of Z to fulfill the sparseness and non-negativity constraints.

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. 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 R.

### Value

`` | object of the class `Factorization`. Containing `LZ` (estimated noise free data L Z), `L` (loadings L), `Z` (factors Z), `U` (noise X-LZ), `X` (data X).

### Author(s)

Sepp Hochreiter

### References

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

D. D. Lee and H. S. Seung, ‘Algorithms for non-negative matrix factorization’, In Advances in Neural Information Processing Systems 13, 556-562, 2001.

### 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

    #---------------
    # 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]]
    X <- abs(X)

    resEx <- nmfsc(X,3,30,0.6,0.6)

    ## Not run:
    #---------------
    # DEMO
    #---------------

    dat <- makeFabiaDataBlocks(n = 1000,l= 100,p = 10,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]]
    X <- abs(X)

    resToy <- nmfsc(X,13,100,0.6,0.6)

    extractPlot(resToy,ti="NMFSC",Y=Y)

    ## End(Not run)

[Package fabia version 2.40.0 Index]