Principal and Minor Subspace Tracking: Algorithms & Stability Analysis

We consider the problem of tracking the minor or principal subspace of a positive Hermitian covariance matrix. We first propose a fast and numerically robust implementation of Oja algorithm (FOOja: fast orthogonal Oja). The latter is said fast in the sense that its computational cost is of order O(np) flops per iteration where n is the size of the observation vector and p < n is the number of minor or principal eigenvectors we need to estimate. FOOja guarantees the orthogonality of the weight matrix at each iteration. Moreover, this algorithm is analyzed and compared with two other fast algorithms (OOjaH and FDPM) with respect to their numerical stability. Simulation results highlights the relatively good stability behavior of FOOja