rifle: Rifle - Truncated Rayleigh Flow Method

In rifle: Sparse Generalized Eigenvalue Problem

Description

Estimate the largest sparse generalized eigenvector using truncated rayleigh flow method. The details are given in Tan et al. (2018).

Usage

rifle(A, B, init, k, eta = 0.01, convergence = 0.001, maxiter = 5000)

Arguments

A	Input the matrix A for sparse generalized eigenvalue problem.
B	Input the matrix B for sparse generalized eigenvalue problem.
init	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.
k	A positive integer tuning parameter that controls the number of non-zero elements in the estimated leading generalized eigenvector.
eta	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.
convergence	Threshold for convergence. Default value is 0.001.
maxiter	Maximum number of iterations. Default is 5000 iterations.

Value

xprime

xprime is the estimated largest generalized eigenvector.

Author(s)

Kean Ming Tan

References

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.

rifle documentation built on May 2, 2019, 2:51 p.m.