Estimate the largest sparse generalized eigenvector using truncated rayleigh flow method. The details are given in Tan et al. (2018).
rifle(A, B, init, k, eta = 0.01, convergence = 0.001, maxiter = 5000)Input the matrix A for sparse generalized eigenvalue problem.
Input the matrix B for sparse generalized eigenvalue problem.
Input an initial vector for the largest generalized eigenvector. This value can be obtained by taking the largest eigenvector of the results from initial.convex function.
A positive integer tuning parameter that controls the number of non-zero elements in the estimated leading generalized eigenvector.
A tuning parameter that controls the convergence of the algorithm. Default value is 0.01. Theoretical results suggest that this value should be set such that eta*(largest eigenvalues of B) < 1.
Threshold for convergence. Default value is 0.001.
Maximum number of iterations. Default is 5000 iterations.
xprime is the estimated largest generalized eigenvector.
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.