nmfsc {fabia} | R Documentation |
nmfsc
: R implementation of nmfsc
.
nmfsc(X,p,sL,sZ,cyc=100)
X |
the data matrix. |
p |
number of hidden factor = number of biclusters. |
sL |
sparseness loadings. |
sZ |
sparseness factors. |
cyc |
maximal number of iterations. |
Non-negative Matrix Factorization represents positive matrix X by positive matrices L and Z that are sparse.
Objective for reconstruction is Euclidean distance and sparseness constraints.
X = L Z
X = sum_{i=1}^{p} L_i (Z_i )^T
If the nonzero components of the sparse vectors are grouped together then the outer product results in a matrix with a nonzero block and zeros elsewhere.
The model selection is performed by a constraint optimization according to Hoyer, 2004. The Euclidean distance (the Frobenius norm) is minimized subject to sparseness and non-negativity constraints.
Model selection is done by gradient descent on the Euclidean objective and thereafter projection of single vectors of L and single vectors of Z to fulfill the sparseness and non-negativity constraints.
The projection minimize the Euclidean distance to the original vector given an l_1-norm and an l_2-norm and enforcing non-negativity.
The projection is a convex quadratic problem which is solved iteratively where at each iteration at least one component is set to zero. Instead of the l_1-norm a sparseness measurement is used which relates the l_1-norm to the l_2-norm.
The code is implemented in R.
L |
Left matrix: L |
Z |
Right matrix: Z |
Sepp Hochreiter
Patrik O. Hoyer, ‘Non-negative Matrix Factorization with Sparseness Constraints’, Journal of Machine Learning Research 5:1457-1469, 2004.
D. D. Lee and H. S. Seung, ‘Algorithms for non-negative matrix factorization’, In Advances in Neural Information Processing Systems 13, 556-562, 2001.
fabi
,
fabia
,
fabiap
,
fabias
,
fabiasp
,
mfsc
,
nmfdiv
,
nmfeu
,
nprojfunc
,
projfunc
,
make_fabi_data
,
make_fabi_data_blocks
,
make_fabi_data_pos
,
make_fabi_data_blocks_pos
,
extract_plot
,
extract_bic
,
myImagePlot
,
PlotBicluster
,
Breast_A
,
DLBCL_B
,
Multi_A
,
fabiaDemo
,
fabiaVersion
#--------------- # TEST #--------------- dat <- make_fabi_data_blocks(n = 100,l= 50,p = 3,f1 = 5,f2 = 5, of1 = 5,of2 = 10,sd_noise = 3.0,sd_z_noise = 0.2,mean_z = 2.0, sd_z = 1.0,sd_l_noise = 0.2,mean_l = 3.0,sd_l = 1.0) X <- dat[[1]] Y <- dat[[2]] X <- abs(X) XX <- tcrossprod(X) dXX <- 1/sqrt(diag(XX)) X <- dXX*X resEx <- nmfsc(as.matrix(abs(X)),3,0.7,0.7) ## Not run: #--------------- # DEMO #--------------- dat <- make_fabi_data_blocks(n = 1000,l= 100,p = 10,f1 = 5,f2 = 5, of1 = 5,of2 = 10,sd_noise = 3.0,sd_z_noise = 0.2,mean_z = 2.0, sd_z = 1.0,sd_l_noise = 0.2,mean_l = 3.0,sd_l = 1.0) X <- dat[[1]] Y <- dat[[2]] X <- abs(X) XX <- tcrossprod(X) dXX <- 1/sqrt(diag(XX)) X <- dXX*X resToy <- nmfsc(as.matrix(abs(X)),8,0.7,0.7) rToy <- extract_plot(X,resToy$L,resToy$Z,ti="NMFSC",Y=Y) ## End(Not run)