solvePMD: Solving symmetric Penalized Matrix Decomposition

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

Description

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

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, controling 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=t(v)*A*v
v.init	the initial value of v

See Also

symmPMD().

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