solvePMD {snQTL}R Documentation

Solving symmetric Penalized Matrix Decomposition

Description

An iterative algorithm that solves the Sparse Principal Component Analysis problem: 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 eigenvalue.

Usage

solvePMD(x, sumabsv, v, niter = 50, trace = TRUE)

Arguments

x

p-by-p matrix, symmetric and positive definite

sumabsv

the upperbound of the L_1 norm of v, controlling the sparsity of solution. Must be between 1 and sqrt(p).

v

the starting value of the algorithm.

niter

number of iterations to perform the iterative optimizations

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=v^T A v

v.init

the initial value of v

See Also

symmPMD().


[Package snQTL version 0.2 Index]