4 papers
Proximity Operator of the over Function
Lixin Shen, Guohui Song
We study the complete, possibly set-valued proximity operator of the nonconvex, scale-invariant ratio \(h(\vx)=\|\vx\|_{1}/\|\vx\|_{2}\). A polar decomposition of the nonzero branc…
A Successive Two-stage Method for Sparse Generalized Eigenvalue Problems
Qia Li, Jianmin Liao, Lixin Shen +1
The Sparse Generalized Eigenvalue Problem (sGEP), a pervasive challenge in statistical learning methods including sparse principal component analysis, sparse Fisher's discriminant…
Principal Component Projection with Low-Degree Polynomials
Stephen D. Farnham, Lixin Shen, Bruce W. Suter
In this paper, we consider approximations of principal component projection (PCP) without explicitly computing principal components. This problem has been studied in several recent…
A Simple Convergence Analysis of Bregman Proximal Gradient Algorithm
Yi Zhou, Yingbin Liang, Lixin Shen
In this paper, we provide a simple convergence analysis of proximal gradient algorithm with Bregman distance, which provides a tighter bound than existing result. In particular, fo…