A Study of the Singular Spectrum Analysis with the Global Optimization Techniques

Singular spectral analysis has recently become an attractive tool in a broad range of applications. Its main mechanism of alternating between rank reduction and Hankel projection, however, deserves further mathematical justification. Exploiting a natural parametrization of a general Hankel matrix via its Vandermonde factorization, this paper recasts the numerical scheme for the singular spectral analysis as a semi-linear least squares problem over a compact feasible set. Such a formulation makes it possible to employ global optimization techniques to find the absolute best approximation which then is used to assess the quality of the approximation produced from the singular spectral analysis. What is the main conclusion at the end of this investigation?