scTenifoldNet (version 1.3)

tensorDecomposition: Performs CANDECOMP/PARAFAC (CP) Tensor Decomposition.

Description

Generate weight-averaged denoised gene regulatory networks using CANDECOMP/PARAFAC (CP) Tensor Decomposition. The tensorDecomposition function takes one or two lists of gene regulatory matrices, if two list are provided, the shared genes are selected and the CP tensor decomposition is performed independently for each list (3d-tensor). The tensor decomposed matrices are then averaged to generate weight-averaged denoised networks.

Usage

tensorDecomposition(
  xList,
  yList = NULL,
  nDecimal = 1,
  K = 5,
  maxError = 1e-05,
  maxIter = 1000
)

Arguments

xList

A list of gene regulatory networks.

yList

Optional. A list of gene regulatory networks.

nDecimal

An integer value indicating the number of decimal places to be used.

K

The number of rank-one tensors used to approximate the data using CANDECOMP/PARAFAC (CP) Tensor Decomposition,

maxError

A decimal value between 0 and 1. Defines the relative Frobenius norm error tolerance

maxIter

An integer value. Defines the maximum number of iterations if error stay above maxError.

Value

A list of weight-averaged denoised gene regulatory networks.

Details

CANDECOMP/PARAFRAC (CP) tensor decomposition approximate a K-Tensor using a sum of K rank-1 K-Tensors. A rank-1 K-Tensor can be written as an outer product of K vectors. This is an iterative algorithm, with two possible stopping conditions: either relative error in Frobenius norm has gotten below maxError, or the maxIter number of iterations has been reached. For more details on CP decomposition, consult Kolda and Bader (2009) and Morup (2011).

References

• Li, J., Bien, J., & Wells, M. T. (2018). rTensor: An R Package for Multidimensional Array (Tensor) Unfolding, Multiplication, and Decomposition. Journal of Statistical Software, 87(10), 1-31.

• Kolda, Tamara G., and Brett W. Bader. "Tensor decompositions and applications." SIAM review 51.3 (2009): 455-500.

• Morup, Morten. "Applications of tensor (multiway array) factorizations and decompositions in data mining." Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 1.1 (2011): 24-40.

Examples

# NOT RUN {
library(scTenifoldNet)

# Simulating of a dataset following a negative binomial distribution with high sparcity (~67%)
nCells = 2000
nGenes = 100
set.seed(1)
X <- rnbinom(n = nGenes * nCells, size = 20, prob = 0.98)
X <- round(X)
X <- matrix(X, ncol = nCells)
rownames(X) <- c(paste0('ng', 1:90), paste0('mt-', 1:10))

# Performing Single cell quality control
qcOutput <- scQC(
  X = X,
  minLibSize = 30,
  removeOutlierCells = TRUE,
  minPCT = 0.05,
  maxMTratio = 0.1
)

# Computing 3 single-cell gene regulatory networks each one from a subsample of 500 cells
mnOutput <- makeNetworks(X = X,
                         nNet = 3, 
                         nCells = 500, 
                         nComp = 3, 
                         scaleScores = TRUE, 
                         symmetric = FALSE, 
                         q = 0.95
                         )

# Computing a K = 3 CANDECOMP/PARAFAC (CP) Tensor Decomposition
tdOutput <- tensorDecomposition(mnOutput, K = 3, maxError = 1e5, maxIter = 1e3)

# Verifying the number of networks
length(tdOutput)

# Veryfying the dimention of the networks
lapply(tdOutput,dim)

# Weight-averaged denoised single-cell gene regulatory networks
tdOutput[[1]][1:10,1:10]
# }