Method and system for reducing a number of eigenvectors. For example, a computer-implemented method for reducing a number of eigenvectors, the method comprising: obtaining a plurality of to-be-processed matrices； mapping the plurality of to-be-processed matrices to a space of symmetric positive definite matrices to form a Riemannian manifold corresponding to a Riemannian kernel function； obtaining a kernel-function matrix by using at least a principal component analysis to calculate one or more inner products of the mapped plurality of matrices based on at least the Riemannian kernel function； calculating a first group of eigenvectors of the kernel-function matrix, the first group of eigenvectors including a first number of eigenvectors； and selecting one or more eigenvectors from the first group of eigenvectors to obtain a second group of eigenvectors, the second group of eigenvectors including a second number of eigenvectors； wherein the second number is less than the first number.
