nmfsc {fabia} | R Documentation

## Non-negative Sparse Matrix Factorization

### Description

`nmfsc`: R implementation of `nmfsc`.

### Usage

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

### Arguments

`X` | the data matrix.
`p` | number of hidden factor = number of biclusters.
`sL` | sparseness loadings.
`sZ` | sparseness factors.
`cyc` | maximal number of iterations.

### 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.

X = L Z

X = sum_{i=1}^{p} L_i (Z_i )^T

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

`L` | Left matrix: L
`Z` | Right matrix: Z

### 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

`fabi`, `fabia`, `fabiap`, `fabias`, `fabiasp`, `mfsc`, `nmfdiv`, `nmfeu`, `nprojfunc`, `projfunc`, `make_fabi_data`, `make_fabi_data_blocks`, `make_fabi_data_pos`, `make_fabi_data_blocks_pos`, `extract_plot`, `extract_bic`, `myImagePlot`, `PlotBicluster`, `Breast_A`, `DLBCL_B`, `Multi_A`, `fabiaDemo`, `fabiaVersion`

### Examples

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

    dat <- make_fabi_data_blocks(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)
    XX <- tcrossprod(X)
    dXX <- 1/sqrt(diag(XX))
    X <- dXX*X

    resEx <- nmfsc(as.matrix(abs(X)),3,0.7,0.7)

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

    dat <- make_fabi_data_blocks(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)
    XX <- tcrossprod(X)
    dXX <- 1/sqrt(diag(XX))
    X <- dXX*X

    resToy <- nmfsc(as.matrix(abs(X)),8,0.7,0.7)

    rToy <- extract_plot(X,resToy$L,resToy$Z,ti="NMFSC",Y=Y)

    ## End(Not run)

[Package fabia version 0.1.1 Index]