On adaptive extraction of minor subspace from high dimensional data stream

Minor subspace extraction is concerned with extracting multiple minor components from an autocorrelation matrix of an N-dimensional data stream. In this paper, a new adaptive algorithm for minor subspace extraction is established by approximating the well-known inverse-power iteration with Galerkin method. The proposed algorithm is of computational complexity O(N-2). The proposed algorithm is proved to have global convergence, and it has relatively fast convergence speed. Moreover, unlike the classical RLS-type algorithms that are lacking of long-term numerical stability, the proposed algorithm has mother attractive feature of good numerical stability due to no use of the well-known matrix inversion Lemma. Simulation results are included to demonstrate the effectiveness of the proposed algorithm.