diffuseMat {roots} | R Documentation |
Generic diffusion function
Description
Generic diffusion function using automated individualised sigma calculation
Usage
diffuseMat(data, ndims = 20, nsig = 5, removeFirst = TRUE,
useARPACK = TRUE, distfun = NULL, sigmas = NULL, sqdistmat = NULL)
Arguments
data |
Matrix of data with genes in rows and cells in columns. |
ndims |
Number of dimensions to return |
nsig |
For automatic sigma calculation |
removeFirst |
Default TRUE. Removes the first eigenvector |
useARPACK |
Default TRUE. Uses Arnoldi algorithm for eignvector calculations |
distfun |
A different distance function that returns the squared distance |
sigmas |
Manually provide sigma |
sqdistmat |
Squared distance matrix. Give your own squared distance matrix. |
Details
Generic diffusion function using automated individualised sigma calculation.
A Gaussian kernel is applied to the chosen distance metric producing
an n \times n
square unnormalised symmetric transition matrix, A
.
Let D
be an n \times n
diagonal matrix with row(column) sums of
A
as entries. The density corrected transition matrix will now
be:
D^{-1} A D^{-1}
and can be normalised:
B^{-1} D^{-1} A D^{-1}
where B
is an n \times n
diagonal matrix with row sums of
the density corrected transition matrix as entries. The eigen decomposition of
this matrix can be simplified by solving the symmetric system:
B^{-\frac{1}{2}} D^{-1} A D^{-1} B^{-\frac{1}{2}} R^\prime = %
R^\prime \lambda^\prime
where R^\prime
is a matrix of the right eigenvectors that solve
the system and \lambda^\prime
is the corresponding eigenvalue
diagonal matrix. Now the solution of:
B^{-1} D^{-1} A D^{-1} R = R \lambda
in terms of R^\prime
and B^{-\frac{1}{2}}
is:
B^{-1} D^{-1} A D^{-1} B^{-\frac{1}{2}} R^\prime = %
B^{-\frac{1}{2}} R^\prime \lambda^\prime
and
R = B^{-\frac{1}{2}} R^\prime
This R
without the first eigen vector is returned as the diffusion map.
Value
List output containing:
values | Eigenvalues, excluding the first eigenvalue, which should always be 1. |
vectors | Matrix of eigen vectors in columns, first eigen vector removed. |
nconv | Number of eigen vectors/values that converged. |
niter | Iterations taken for Arnoldi algorithm to converge. |
nops | Number of operations. |
val0 | 1st eigen value - should be 1. If not be suspicious! |
vec0 | 1st eigen vector - should be n^{-\frac{1}{2}} ,
where n is the number of cells/samples. |
usedARPACK | Predicates use of ARPACK for spectral decomposition. |
distfun | Function used to calculate the squared distance. |
nn | Number of nearest neighbours used for calculating sigmas . |
d2 | Matrix of squared distances, returned from distfun . |
sigmas | Vector of sigmas. Same length as number of cells if individual |
sigmas were calculated, otherwise a scalar if was supplied. | |
gaussian | Unnormalised transition matrix after applying Gaussian. |
markov | Normalised gaussian matrix. |
densityCorrected | Matrix after applying density correction to
markov . |
Author(s)
Wajid Jawaid
References
Haghverdi, L., Buettner, F., Theis, F.J., 2015. Diffusion maps for high-dimensional single-cell analysis of differentiation data. Bioinformatics 31, 2989–2998.
Haghverdi, L., Büttner, M., Wolf, F.A., Buettner, F., Theis, F.J., 2016. Diffusion pseudotime robustly reconstructs lineage branching. Nat Meth 13, 845–848.
Angerer, P., Haghverdi, L., Büttner, M., Theis, F.J., Marr, C., Buettner, F., 2016. destiny: diffusion maps for large-scale single-cell data in R. Bioinformatics 32, 1241–1243.
Examples
## Not run:
xx <- diffuseMat(x)
## End(Not run)