Description Usage Arguments Value References Examples
This function solves the optimization problem
min -tr(SX) + λ * p(X),
s.t. O ≼ X ≼ I, X ≥ 0, and tr(X) = 1,
where O ≼ X ≼ I means all eigenvalues of X are between 0 and 1, X ≥ 0 means all elements of X are nonnegative, and p(X) is a penalty function defined in the article (see the References section).
1 2 3 4 5 6 7 8 9 10 | pca_pen(
S,
gr,
lambda,
w = 1.5,
alpha = 0.01,
maxit = 1000,
eps = 1e-04,
verbose = 0
)
|
S |
The sample correlation matrix of gene expression. |
gr |
Indices of genes that are treated as markers in the prior information. |
lambda |
Tuning parameter to control the sparsity of eigenvectors. |
w |
Tuning parameter to control the weight on prior information. Larger w means genes not in the prior list are less likely to be selected as markers. |
alpha |
Step size of the optimization algorithm. |
maxit |
Maximum number of iterations. |
eps |
Tolerance parameter for convergence. |
verbose |
Level of verbosity. |
A list containing the following components:
The estimated projection matrix.
The estimated eigenvectors.
Number of iterations used in the optimization process.
The optimization error in each iteration.
Qiu, Y., Wang, J., Lei, J., & Roeder, K. (2020). Identification of cell-type-specific marker genes from co-expression patterns in tissue samples.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | set.seed(123)
n = 200 # Sample size
p = 500 # Number of genes
s = 50 # Number of true signals
# The first s genes are true markers, and others are noise
Sigma = matrix(0, p, p)
Sigma[1:s, 1:s] = 0.9
diag(Sigma) = 1
# Simulate data from the covariance matrix
x = matrix(rnorm(n * p), n) %*% chol(Sigma)
# Sample correlation matrix
S = cor(x)
# Indices of prior marker genes
# Note that we have omitted 10 true markers, and included 10 false markers
gr = c(1:(s - 10), (s + 11):(s + 20))
# Run the algorithm
res = pca_pen(S, gr, lambda = 0.1, verbose = 1)
# See if we can recover the true correlation structure
image(res$projection, asp = 1)
|
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