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

In this paper, we describe a new algorithm to compute the extreme eigenvalue/eigenvector pairs of a symmetric matrix. The proposed algorithm can be viewed as an extension of the Jacobi transformation method for symmetric matrix diagonalization to the case where we want to compute just a few eigenvalues/eigenvectors. The method is also particularly well suited for the computation of sparse eigenspaces. We show the effectiveness of the method for sparse low-rank approximations and show applications to random symmetric matrices, graph Fourier transforms, and with the sparse principal component analysis in image classification experiments.