# dsiNMF: Discretized Simultaneous Non-negative Matrix Factorization... In dcTensor: Discrete Matrix/Tensor Decomposition

 dsiNMF R Documentation

## Discretized Simultaneous Non-negative Matrix Factorization Algorithms (dsiNMF)

### Description

This function is the discretized version of nnTensor::siNMF. The input data objects are assumed to be a list containing multiple non-negative matrices (X_1, X_2, ..., X_K), and decomposed to multiple matrix products (W H_1', W H_2', ..., W H_K'), where W is common across all the data matrices but each H_k (k=1..K) is specific in each X_k. Unlike regular siNMF, in dsiNMF, W and H_k are estimated by adding binary regularization so that the values are 0 or 1 as much as possible. Likewise, W and H_k are estimated by adding ternary regularization so that the values are 0, 1, or 2 as much as possible.

### Usage

``````dsiNMF(X, M=NULL, pseudocount=.Machine\$double.eps,
initW=NULL, initH=NULL,
fixW=FALSE, fixH=FALSE,
Bin_W=1e-10, Bin_H=rep(1e-10, length=length(X)),
Ter_W=1e-10, Ter_H=rep(1e-10, length=length(X)),
L1_W=1e-10, L1_H=rep(1e-10, length=length(X)),
L2_W=1e-10, L2_H=rep(1e-10, length=length(X)),
J = 3, w=NULL, algorithm = c("Frobenius", "KL", "IS", "PLTF"), p=1,
thr = 1e-10, num.iter = 100,
viz = FALSE, figdir = NULL, verbose = FALSE)
``````

### Arguments

 `X` A list containing the input matrices (X_k, , k=1..K). `M` A list containing the mask matrices (X_k, , k=1..K). If the input matrix has missing values, specify the element as 0 (otherwise 1). `pseudocount` The pseudo count to avoid zero division, when the element is zero (Default: Machine Epsilon). `initW` The initial values of factor matrix W, which has N-rows and J-columns (Default: NULL). `initH` A list containing the initial values of multiple factor matrices (H_k, , k=1..K, Default: NULL). `fixW` Whether the factor matrix W is updated in each iteration step (Default: FALSE). `fixH` Whether the factor matrices Hk are updated in each iteration step (Default: FALSE). `Bin_W` Paramter for binary (0,1) regularitation (Default: 1e-10). `Bin_H` A K-length vector containing the paramters for binary (0,1) regularitation (Default: rep(1e-10, length=length(dim(X)))). `Ter_W` Paramter for terary (0,1,2) regularitation (Default: 1e-10). `Ter_H` A K-length vector containing the paramters for terary (0,1,2) regularitation (Default: rep(1e-10, length=length(dim(X)))). `L1_W` Paramter for L1 regularitation (Default: 1e-10). This also works as small positive constant to prevent division by zero, so should be set as 0. `L1_H` A K-length vector containing the paramters for L1 regularitation (Default: rep(1e-10, length=length(dim(X)))). This also works as small positive constant to prevent division by zero, so should be set as 0. `L2_W` Paramter for L2 regularitation (Default: 1e-10). `L2_H` A K-length vector containing the paramters for L2 regularitation (Default: rep(1e-10, length=length(dim(X)))). `J` Number of low-dimension (J < N, Mk). `w` Weight vector (Default: NULL) `algorithm` Divergence between X and X_bar. "Frobenius", "KL", and "IS" are available (Default: "KL"). `p` The parameter of Probabilistic Latent Tensor Factorization (p=0: Frobenius, p=1: KL, p=2: IS) `thr` When error change rate is lower than thr, the iteration is terminated (Default: 1E-10). `num.iter` The number of interation step (Default: 100). `viz` If viz == TRUE, internal reconstructed matrix can be visualized. `figdir` the directory for saving the figure, when viz == TRUE. `verbose` If verbose == TRUE, Error change rate is generated in console windos.

### Value

W : A matrix which has N-rows and J-columns (J < N, Mk). H : A list which has multiple elements containing Mk-rows and J-columns matrix (J < N, Mk). RecError : The reconstruction error between data matrix and reconstructed matrix from W and H. TrainRecError : The reconstruction error calculated by training set (observed values specified by M). TestRecError : The reconstruction error calculated by test set (missing values specified by M). RelChange : The relative change of the error.

Koki Tsuyuzaki

### References

Liviu Badea, (2008) Extracting Gene Expression Profiles Common to Colon and Pancreatic Adenocarcinoma using Simultaneous nonnegative matrix factorization. Pacific Symposium on Biocomputing 13:279-290

Shihua Zhang, et al. (2012) Discovery of multi-dimensional modules by integrative analysis of cancer genomic data. Nucleic Acids Research 40(19), 9379-9391

Zi Yang, et al. (2016) A non-negative matrix factorization method for detecting modules in heterogeneous omics multi-modal data, Bioinformatics 32(1), 1-8

Y. Kenan Yilmaz et al., (2010) Probabilistic Latent Tensor Factorization, International Conference on Latent Variable Analysis and Signal Separation 346-353

N. Fujita et al., (2018) Biomarker discovery by integrated joint non-negative matrix factorization and pathway signature analyses, Scientific Report

### Examples

``````matdata <- toyModel(model = "dsiNMF_Easy")
out <- dsiNMF(matdata, J=2, num.iter=2)
``````

dcTensor documentation built on June 22, 2024, 6:57 p.m.