论文标题
无逆截短的雷利 - 里兹方法，用于稀疏广义特征值问题
An Inverse-free Truncated Rayleigh-Ritz Method for Sparse Generalized Eigenvalue Problem
论文作者
论文摘要
本文考虑了稀疏的广义特征值问题（SGEP），该问题旨在找到最多$ k $ nonZero条目的领先特征向量。 SGEP自然在机器学习，统计和科学计算中的许多应用中都出现，例如，稀疏的主成分分析（SPCA），稀疏的判别分析（SDA）和稀疏的规范相关分析（SCCA）。在本文中，我们关注的是一种名为{\ em无反截断的雷利 - 里兹方法}的三阶段算法}（{\ em iftrr}），以有效地求解SGEP。在IFTRR的每次迭代中，仅需要少量矩阵矢量产物。这使IFTRR非常适合大规模问题。特别是提出了一种新的截断策略，该策略能够有效地找到领先的特征向量的支持集。开发理论结果是为了解释为什么IFTRR效果很好。数值模拟证明了IFTRR的优点。
This paper considers the sparse generalized eigenvalue problem (SGEP), which aims to find the leading eigenvector with at most $k$ nonzero entries. SGEP naturally arises in many applications in machine learning, statistics, and scientific computing, for example, the sparse principal component analysis (SPCA), the sparse discriminant analysis (SDA), and the sparse canonical correlation analysis (SCCA). In this paper, we focus on the development of a three-stage algorithm named {\em inverse-free truncated Rayleigh-Ritz method} ({\em IFTRR}) to efficiently solve SGEP. In each iteration of IFTRR, only a small number of matrix-vector products is required. This makes IFTRR well-suited for large scale problems. Particularly, a new truncation strategy is proposed, which is able to find the support set of the leading eigenvector effectively. Theoretical results are developed to explain why IFTRR works well. Numerical simulations demonstrate the merits of IFTRR.
