Estimate the K-dimensional subspace spanned by the largest K generalized eigenvector by solving a convex relaxation. The details are given in Tan et al. (2018).
initial.convex(A, B, lambda, K, nu = 1, epsilon = 0.005, maxiter = 1000, trace = FALSE)Input the matrix A for sparse generalized eigenvalue problem.
Input the matrix B for sparse generalized eigenvalue problem.
A positive tuning parameter that constraints the solution to be sparse
A positive integer tuning parameter that constraints the solution to be low rank.
An ADMM tuning parameter that controls the convergence of the ADMM algorithm.
Threshold for convergence. Default value is 0.005.
Maximum number of iterations. Default is 1000 iterations.
Default value of trace=FALSE. If trace=TRUE, each iteration of the ADMM algorithm is printed.
Estimated subspace Pi
Sparse Generalized Eigenvalue Problewm: Optimal Statistical Rates via Truncated Rayleigh Flow", by Tan et al. (2018). To appear in Journal of the Royal Statistical Society: Series B. https://arxiv.org/pdf/1604.08697.pdf.