Recent methods for the analysis of molecular kinetics from massive molecular dynamics (MD) data rely on the solution of very large eigenvalue problems. Here we build upon recent results from the field of compressed sensing and develop the spectral oASIS method, a highly efficient approach to approximate the leading eigenvalues and eigenvectors of large generalized eigenvalue problems without ever having to evaluate the full matrices. The approach is demonstrated to reduce the dimensionality of the problem by 1 or 2 orders of magnitude, directly leading to corresponding savings in the computation and storage of the necessary matrices and a speedup of 2 to 4 orders of magnitude in solving the eigenvalue problem. We demonstrate the method on extensive data sets of protein conformational changes and protein-ligand binding using the variational approach to conformation dynamics (VAC) and time-lagged independent component analysis (TICA). Our approach can also be applied to kernel formulations of VAC, TICA, and extended dynamic mode decomposition (EDMD).