## Description

NMF algorithms proposed by Kim et al. (2007) that
enforces sparsity constraint on the basis matrix
(algorithm ‘SNMF/L’) or the mixture coefficient
matrix (algorithm ‘SNMF/R’).

## Usage

nmfAlgorithm.SNMF_R(..., maxIter = 20000L, eta = -1, beta = 0.01, bi_conv = c(0,
10), eps_conv = 1e-04)
nmfAlgorithm.SNMF_L(..., maxIter = 20000L, eta = -1, beta = 0.01, bi_conv = c(0,
10), eps_conv = 1e-04)

## Arguments

- maxIter
- maximum number of iterations.
- eta
- parameter to suppress/bound the L2-norm of
`W`

and in `H`

in ‘SNMF/R’ and
‘SNMF/L’ respectively.
If `eta < 0`

, then it is set to the maximum value in
the target matrix is used.
- beta
- regularisation parameter for sparsity
control, which balances the trade-off between the
accuracy of the approximation and the sparseness of
`H`

and `W`

in ‘SNMF/R’ and
‘SNMF/L’ respectively.
Larger beta generates higher sparseness on `H`

(resp. `W`

). Too large beta is not recommended.
- bi_conv
- parameter of the biclustering convergence
test. It must be a size 2 numeric vector
`bi_conv=c(wminchange, iconv)`

, with:
`wminchange`

:the minimal allowance of change
in row-clusters.
`iconv`

: decide
convergence if row-clusters (within the allowance of
`wminchange`

) and column-clusters have not changed
for `iconv`

convergence checks.

Convergence checks are performed every 5 iterations.
- eps_conv
- threshold for the KKT convergence test.
- ...
- extra argument not used.

## Details

The algorithm ‘SNMF/R’ solves the following NMF
optimization problem on a given target matrix `A`

of
dimension `n x p`

:

min_{W,H} 1/2 (|| A - WH ||_F^2 + eta
||W||_F^2 + beta (sum_j ||H[,j]||_1^2))
s.t. W>=0, H>=0

The algorithm ‘SNMF/L’ solves a similar problem on
the transposed target matrix `A`

, where `H`

and
`W`

swap roles, i.e. with sparsity constraints
applied to `W`

.

## References

Kim H and Park H (2007). "Sparse non-negative matrix
factorizations via alternating non-negativity-constrained
least squares for microarray data analysis."
_Bioinformatics (Oxford, England)_, *23*(12), pp.
1495-502. ISSN 1460-2059, , .