# SNMF-nmf: NMF Algorithm - Sparse NMF via Alternating NNLS In NMF: Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

 nmfAlgorithm.SNMF_R R Documentation

## NMF Algorithm - Sparse NMF via Alternating NNLS

### 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, <URL: http://dx.doi.org/10.1093/bioinformatics/btm134>, <URL: http://www.ncbi.nlm.nih.gov/pubmed/17483501>.

NMF documentation built on March 30, 2022, 1:05 a.m.