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In this paper, we describe a new algorithm to compute the extremeeigenvalue/eigenvector pairs of a symmetric matrix. The proposed algorithm canbe viewed as an extension of the Jacobi transformation method for symmetricmatrix diagonalization to the case where we want to compute just a feweigenvalues/eigenvectors. The method is also particularly well suited for thecomputation of sparse eigenspaces. We show the effectiveness of the method forsparse low-rank approximations and show applications to random symmetricmatrices, graph Fourier transforms, and with the sparse principal componentanalysis in image classification experiments.

An iterative Jacobi-like algorithm to compute a few sparse eigenvalue-eigenvector pairs