On convergence of fast subspace tracking based on novel information criterion

The averaging differential equation associated with a family of fast subspace tracking algorithms based on a novel information criterion (NIC) is known as the NIC flow. This paper investigates global exponential convergence of the NIC flow. It is shown that at a characterized exponential speed the NIC flow globally converges to the principal subspace spanned by the eigenvectors corresponding to the principal eigenvalues of the covariance matrix of a high dimensional data stream. The given exponential convergence rate may be a very tight estimate. It is also demonstrated that the convergence speed of the NIC flow is typically faster than that of the well-known Oja´s flow. Numerical results are presented to support the theoretical analysis.