symmPMD: Symmetric Penalized Matrix Decomposition.

In lingxuez/sLED: A Sparse Leading Eigenvalue Driven (sLED) Test for High-dimensional Matrices

Description

This function solves for the Sparse Principal Component Analysis given a positive definite matrix A:

max_{v} t(v)*A*v

subject to

||v||_2 <= 1, ||v||_1 <= s

The solution v is the sparse leading eigenvector, and the corresponding objective t(v)*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*sqrt(p) is the upperbound of the L_1 norm of v, controling the sparsity of solution. Must be between 1/sqrt(p) and 1.
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 d=t(v)*A*v
sumabs	sumabs*sqrt(p) is the upperbound of the L_1 norm of v

References

Zhu, Lei, Devlin and Roeder (2016), "Testing High Dimensional Covariance Matrices, with Application to Detecting Schizophrenia Risk Genes", arXiv:1606.00252.

Witten, Tibshirani and Hastie (2009), "A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis", Biostatistics 10(3):515-534.

lingxuez/sLED documentation built on May 7, 2019, 2:55 a.m.