A clustering system generates an original Laplacian matrix representing objects and their relationships. The clustering system initially applies an eigenvalue decomposition solver to the original Laplacian matrix for a number of iterations. The clustering system then identifies the elements of the resultant eigenvector that are stable. The clustering system then aggregates the elements of the original Laplacian matrix corresponding to the identified stable elements and forms a new Laplacian matrix that is a compressed form of the original Laplacian matrix. The clustering system repeats the applying of the eigenvalue decomposition solver and the generating of new compressed Laplacian matrices until the new Laplacian matrix is small enough so that a final solution can be generated in a reasonable amount of time.