siNMF {nnTensor}

Simultaneous Non-negative Matrix Factorization Algorithms (siNMF)

Description

The input data objects are assumed to be non-negative matrices. siNMF decompose the matrices to two low-dimensional factor matices simultaneously.

Usage

siNMF(X, M=NULL, pseudocount=.Machine$double.eps, initW=NULL, initH=NULL,
  fixW=FALSE, fixH=FALSE,
  L1_W=1e-10, L1_H=1e-10, L2_W=1e-10, L2_H=1e-10, 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, <N*Mk>, k=1..K).

M

A list containing the mask matrices (X_k, <N*Mk>, 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, <Mk*J>, 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).

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

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.

L2_W

Paramter for L2 regularitation (Default: 1e-10).

L2_H

Paramter for L2 regularitation (Default: 1e-10).

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.

Author(s)

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 = "siNMF_Easy")
out <- siNMF(matdata, J=2, num.iter=2)