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The problem of estimating sparse eigenvectors of a symmetric matrix has attracted a lot of attention in many applications, especially those with a high dimensional dataset. While classical eigenvectors can be obtained as the solution of a maximization problem, existing approaches formulate this problem by adding a penalty term into the objective function that encourages a sparse solution. However, the vast majority of the resulting methods achieve sparsity at the expense of sacrificing the orthogonality property. In this paper, we develop a new method to estimate dominant sparse eigenvectors without trading off their orthogonality. The problem is highly nonconvex and hard to handle. We apply the minorization–maximization framework, wherein we iteratively maximize a tight lower bound (surrogate function) of the objective function over the Stiefel manifold. The inner maximization problem turns out to be a …