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.
solvePMD(x, sumabsv, v, niter = 50, trace = TRUE)A list containing the following components:
the sparse leading eigenvector v
the sparse leading eigenvalue \(d=v^T A v\)
the initial value of v
p-by-p matrix, symmetric and positive definite
the upperbound of the L_1 norm of \(v\), controlling the sparsity of solution. Must be between 1 and \(sqrt(p)\).
the starting value of the algorithm.
number of iterations to perform the iterative optimizations
whether to print tracing info during optimization
symmPMD().