A self-stabilizing MSA algorithm in high-dimension data stream

Minor subspace analysis (MSA) is a statistical method for extracting the subspace spanned by all the eigenvectors associated with the minor eigenvalues of the autocorrelation matrix of a high-dimension vector sequence. In this paper, we propose a self-stabilizing neural network learning algorithm for tracking minor subspace in high-dimension data stream. Dynamics of the proposed algorithm are analyzed via a corresponding deterministic continuous time (DCT) system and stochastic discrete time (SDT) system methods. The proposed algorithm provides an efficient online learning for tracking the MS and can track an orthonormal basis of the MS. Computer simulations are carried out to confirm the theoretical results.