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’).
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)
maximum number of iterations.
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.
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.
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.
threshold for the KKT convergence test.
extra argument not used.
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.
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>.