Initialize parameters for a PLN-PCA with missing data

Provides a quick, SVD‑based initialization of model and variational parameters from a (possibly sparse) count matrix Y and a design matrix X. The routine fits a (log‑transformed) linear model to obtain regression coefficients and uses the SVD of residuals to initialize the latent structure (loadings and variational means).

Usage

Init(Y, X, q)

Arguments

Y

Numeric n x p count matrix (may contain NA).

X

Numeric design matrix of covariates. Either n x d (rowwise design) or (n*p) x d (vectorized design matching MatrixToVector(Y)).

q

Integer, target latent dimension (rank) for the factor structure.

Value

A list with elements:

B

Matrix of regression coefficients (dimensions follow the chosen design; typically (1 x d) in the rowwise case).

C

Loadings matrix (p x q) for the latent factors.

M

Variational means of the latent factors (n x q).

S

Variational standard deviations (initialized to a small constant; n x q).

Details

Missing values in Y are handled via na.exclude in the linear model; residuals at missing entries are then set to zero before the SVD.

See also

MatrixToVector, VectorToMatrix

Examples

set.seed(1)
n <- 30; p <- 8; d <- 2; q <- 2
Y <- matrix(rpois(n * p, 2), n, p)
X <- cbind(1, rnorm(n))          # rowwise design
init <- Init(Y, X, q)
str(init)
#> List of 4
#>  $ B: num [1:2, 1:8] 0.9436 -0.105 1.0159 0.0321 1.024 ...
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:2] "X1" "X2"
#>   .. ..$ : NULL
#>  $ C: num [1:8, 1:2] 0.00246 0.20926 0.01447 0.4303 0.09398 ...
#>  $ M: num [1:30, 1:2] -0.4534 0.1827 -0.1048 0.0622 -0.1113 ...
#>  $ S: num [1:30, 1:2] 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 ...