A Decomposition Algorithm for the Sparse Generalized Eigenvalue Problem
It provides a more accurate solution for the sparse generalized eigenvalue problem, which is central to several statistical learning models.
The paper proposes a decomposition algorithm for the NP-hard sparse generalized eigenvalue problem, using random/swapping strategies to select a working set and solving quadratic fractional subproblems via bisection or coordinate descent. Experiments show significant and consistent accuracy improvements over existing methods.
The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis. However, this problem is difficult to solve since it is NP-hard. In this paper, we consider a new decomposition method to tackle this problem. Specifically, we use random or/and swapping strategies to find a working set and perform global combinatorial search over the small subset of variables. We consider a bisection search method and a coordinate descent method for solving the quadratic fractional programming subproblem. In addition, we provide some theoretical analysis for the proposed method. Our experiments have shown that the proposed method significantly and consistently outperforms existing solutions in term of accuracy.