manifoldAlignment {scTenifoldNet}

Performs non-linear manifold alignment of two gene regulatory networks.

Description

Build comparable low-dimensional features for two weight-averaged denoised single-cell gene regulatory networks. Using a non-linear network embedding method manifoldAlignment aligns two gene regulatory networks and finds the structural similarities between them. This function is a wrapper of the Python code provided by Vu et al., (2012) at https://github.com/all-umass/ManifoldWarping.

Usage

manifoldAlignment(X, Y, d = 30, nCores = parallel::detectCores())

Arguments

X

A gene regulatory network.

Y

A gene regulatory network.

d

The dimension of the low-dimensional feature space.

nCores

An integer value. Defines the number of cores to be used.

Details

Manifold alignment builds connections between two or more disparate data sets by aligning their underlying manifolds and provides knowledge transfer across the data sets. For further information please see: Wang et al., (2009)

Value

A low-dimensional projection for two the two gene regulatory networks used as input. The output is a labeled matrix with two times the number of shared genes as rows ( X_ genes followed by Y_ genes in the same order) and d number of columns.

References

• Vu, Hoa Trong, Clifton Carey, and Sridhar Mahadevan. "Manifold warping: Manifold alignment over time." Twenty-Sixth AAAI Conference on Artificial Intelligence. 2012.

• Wang, Chang, and Sridhar Mahadevan. "A general framework for manifold alignment." 2009 AAAI Fall Symposium Series. 2009.

Examples

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
xNetworks <- 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(xNetworks, K = 3, maxError = 1e5, maxIter = 1e3)

## Not run: 
# Computing the alignment
# For this example, we are using the same input, the match should be perfect. 
maOutput <- manifoldAlignment(tdOutput$X, tdOutput$X)

# Separating the coordinates for each gene
X <- maOutput[grepl('X_', rownames(maOutput)),]
Y <- maOutput[grepl('Y_', rownames(maOutput)),]

# Plotting
# X Points
plot(X, pch = 16)

# Y Points
points(Y, col = 'red')

# Legend
legend('topright', legend = c('X', 'Y'), 
       col = c('black', 'red'), bty = 'n', 
       pch = c(16,1), cex = 0.7)

## End(Not run)