Adaptive estimation of eigensubspace

Abstract

In a recent work we recast the problem of estimating the minimum eigenvector (eigenvector corresponding to the minimum eigenvalue) of a symmetric positive definite matrix into a neural network framework. We now extend this work using an inflation technique to estimate all or some of the orthogonal eigenvectors of the given matrix. Based on these results, we form a cost function for the finite data case and derive a Newton-based adaptive algorithm. The inflation technique leads to a highly modular and parallel structure for implementation. The computational requirement of the algorithm is O(N²), N being the size of the covariance matrix. We also present a rigorous convergence analysis of this adaptive algorithm. The algorithm is locally convergent and the undesired stationary points are unstable. Computer simulation results are provided to compare its performance with that of two adaptive subspace estimation methods proposed by Yang and Kaveh (1988) and an improved version of one of them, for stationary and nonstationary signal scenarios. The results show that the proposed approach performs identically to one of them and is significantly superior to the remaining two.