SVD updating for nonstationary data

In this paper, we consider the tracking properties of the updating SVD algorithm based on Jacobi rotations proposed recently by Moonen, et al. (1992). The original algorithm is characterized by a fixed forgetting factor and fixed computational and throughput rates. Although these parameters can be satisfactorily selected for a given rate of data variability, they should ideally be adjusted to adapt to the changing data characteristics. We propose two schemes which can be used to improve the tracking performance, by dynamically varying the forgetting factor or the computational rate. In the "variable rotational rate" scheme, the number of Jacobi rotations per update is determined so that the computed singular matrices are close to convergence at all times. In the "variable forgetting" scheme, the effective observation window aperture adjusts to the data nonstationarity. Behavior and performance of both schemes are discussed and compared.