An asymptotic analysis of spherical subspace updating

We perform an asymptotic perturbation analysis of spherical subspace (SS) updating. Using eigen-based perturbation theory, we develop an asymptotic proof of convergence for two eigenlevel SS updating. We also show that SS convergence is dependent on the eigenvalue spread with the stronger/weaker eigenvectors in the sphericalized subspace converging more quickly/slowly than the corresponding components in an eigen update. By contrast, in rank-one eigen updating the rate of subspace convergence is uniform for all eigenvectors and the rate is independent of eigenvalue spread. We also show that a four level SS update can be combined with MDL to yield asymptotically consistent detection