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The sparse generalized eigenvalue problem arises in a number of standard andmodern statistical learning models, including sparse principal componentanalysis, sparse Fisher discriminant analysis, and sparse canonical correlationanalysis. However, this problem is difficult to solve since it is NP-hard. Inthis paper, we consider a new decomposition method to tackle this problem.Specifically, we use random or/and swapping strategies to find a working setand perform global combinatorial search over the small subset of variables. Weconsider a bisection search method and a coordinate descent method for solvingthe quadratic fractional programming subproblem. In addition, we provide sometheoretical analysis for the proposed method. Our experiments have shown thatthe proposed method significantly and consistently outperforms existingsolutions in term of accuracy.

A Decomposition Algorithm for the Sparse Generalized Eigenvalue Problem