  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.
