An Inversefree Truncated RayleighRitz Method for Sparse Generalized Eigenvalue Problem
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:34603470, 2020.
Abstract
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 threestage algorithm named {\em inversefree truncated RayleighRitz method} ({\em IFTRR}) to efficiently solve SGEP. In each iteration of IFTRR, only a small number of matrixvector products is required. This makes IFTRR wellsuited 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.
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