Inspired by the recent developments in data sciences,we introduce an intrinsic sparse mode decomposition method for high dimensional random fields.This sparse representation of the random field allows us to break a high dimensional stochastic field into many spatially localized modes with low stochastic dimension.Such decomposition enables us to break the curse of dimensionality in our local solvers.We apply this technique to solve stochastic elliptic PDEs with high dimensional stochastic coefficients.