symmPMD {snQTL} | R Documentation |
Symmetric Penalized Matrix Decomposition.
Description
This function solves for the Sparse Principal Component Analysis given a positive definite matrix A:
max_{v} v^T A v
subject to
||v||_2 \leq 1, ||v||_1 \leq s
The solution v is the sparse leading eigenvector, and the corresponding objective
v^T A v
is the sparse leading engenvalue.
The algorithm uses an iterative procedure similar to the R Package "PMA", but speeds up the computation using the extra constraint that the decomposition is symmetric.
Usage
symmPMD(x, sumabs = 0.3, niter = 50, v = NULL, trace = TRUE)
Arguments
x |
p-by-p matrix, symmetric and positive definite |
sumabs |
sumabs* |
niter |
number of iterations to perform the iterative optimizations |
v |
the starting value of the algorithm, either a pre-calculated first singular vector of x, or NULL. |
trace |
whether to print tracing info during optimization |
Value
A list containing the following components:
v |
the sparse leading eigenvector v |
d |
the sparse leading eigenvalue |
sumabs |
sumabs* |
References
Zhu, Lingxue, et al. "Testing high-dimensional covariance matrices, with application to detecting schizophrenia risk genes." The annals of applied statistics 11.3 (2017): 1810.
Witten, Tibshirani and Hastie (2009), "A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis", Biostatistics 10(3):515-534.