This paper considers the sparse eigenvalue problem, which is to extract
dominant (largest) sparse eigenvectors with at most $k$ non-zero components. We
propose a simple yet effective solution called truncated power method that can
approximately solve the underlying nonconvex optimization problem. A strong
sparse recovery result is proved for the truncated power method, and this
theory is our key motivation for developing the new algorithm. The proposed
method is tested on applications such as sparse principal component analysis
and the densest $k$-subgraph problem.