  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.
