An efficient algorithm for rank-1 sparse PCA

Sparse principal component analysis (PCA) imposes extra constraints or penalty terms to the original PCA to achieve sparsity. In this paper, we introduce an efficient algorithm to find a single sparse principal component with a specified cardinality. The algorithm consists of two stages. In the first stage, it identifies an active index set with desired cardinality corresponding to the nonzero entries of the principal component. In the second one, it finds the best direction with respect to the active index set, using the power iteration method. Experiments on both randomly generated data and real-world data sets show that our algorithm is very fast, especially on large and sparse data sets, while the numerical quality of the solution is comparable to other methods.