A CG-type method for computing the dominant subspace of a symmetric matrix

Computing the subspace spanned by the eigenvectors corresponding to the r largest eigenvalues of a symmetric matrix is an important subtask in many signal processing applications and statistics. Here, from the application side, we focus on subspace based algorithms for sensor node localization in wireless sensor networks. A conjugate gradient method on the Grassmann manifold is proposed to compute the r-dimensional dominant subspace of an (n × n)-symmetric matrix. This leads to new subspace algorithms which avoid the time consuming eigendecomposition of the data matrix, but rather compute the signal and the noise space in O(n2r3) flops. Some convergence aspects are discussed and numerical simulations are presented to illustrate the performance of the proposed algorithm. When applied to the problem of sensor positions estimation with M sensors, the full-set subspace algorithm is reduced from order O(M6) to O(M4) without loosing accuracy.