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

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

Description

NMF algorithms proposed by Kim and Park (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

...	extra argument not used.
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.

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, Park H (2007). “Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis.” _Bioinformatics (Oxford, England)_, *23*(12), 1495-502. ISSN 1460-2059, doi: 10.1093/bioinformatics/btm134 (URL: https://doi.org/10.1093/bioinformatics/btm134).

renozao/NMF documentation built on June 14, 2020, 9:35 p.m.