SNMF-nmf: NMF Algorithm - Sparse NMF via Alternating NNLS

In NMF: Algorithms and Framework for Nonnegative Matrix Factorization (NMF)

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 \times p:

\begin{array}{ll} & \min_{W,H} \frac{1}{2} \left(|| A - WH ||_F^2 + \eta ||W||_F^2 + \beta (\sum_{j=1}^p ||H_{.j}||_1^2)\right)\\ s.t. & W\geq 0, H\geq 0 \end{array}

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 Sept. 11, 2024, 8:34 p.m.