Analysis of a class of continuous-time algorithms for principal component analysis and subspace tracking

We give a new analysis of a class of continuous-time subspace tracking algorithms, related to a number of discrete-time algorithms, such as stochastic gradient algorithms, spherical subspace trackers, and a new discrete-time algorithm based on one of the continuous-time algorithms. Using formulas for tracking the singular value decomposition (SVD) of a time-varying matrix, we show attraction to orthogonality of the matrix representing the subspace estimate, and we analyze the evolution of the canonical angles between the subspace estimate and the subspace to be estimated.