Abstract:

High-dimensional time-series data are increasingly collected for the purpose of classifying the underlying process into one of a few known processes. As the linear dynamical information of a stationary vector process can be succinctly summarized by its spectral density matrix, it is natural to adopt spectral classifiers, which is, however, infeasible with high-dimensional time-series data, because the spectral density matrix is of dimensions p × p where p is the time-series dimension. To overcome the aforementioned curse of dimensionality, we develop new reduced-rank spectral classifiers. The efficacy of the proposed methods will be demonstrated by both simulations and real applications. Some theoretical properties of the proposed approach will be discussed. The talk is based on joint work with Fuli Zhang.