  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.
