Design of Regularized Taper Window With Alternating Optimization for Reducing Component Mixing in Generalized Singular Spectrum Analysis

The singular spectrum analysis (SSA) is considered a filter bank that can identify a signal’s principal components. Due to the default rectangular window in SSA, the reconstructed principal components exhibit energy dispersion in frequency bands, leading to components mixing with each other. To address this issue, we present a comprehensive study of the generalized SSA (GSSA) model, which incorporates a taper window. To design an adaptive taper window for GSSA such that it can decompose various nonstationary signals, we reformulate the decomposition process of GSSA as an energy maximization model and introduce an $L_{1}$ -norm regularization term as a measure of energy concentration in the taper window. A novel optimization problem that simultaneously focuses on energy maximization and energy concentration is formulated. To find an approximated optimal taper window, the projected gradient descent-based alternating optimization (PGD-AO) algorithm is utilized. Experiments were conducted with synthetic signals, an electroencephalogram (EEG) signal, and an ankle joint motion signal. The results show that compared to benchmark strategies, the proposed method significantly reduces component mixing, extracts energy-concentrated principal components, and contributes to better signal reconstruction. Specifically, GSSA achieves an $L_{2}$ -norm error reduction of 85% compared with conventional SSA in strength-identical sinusoid reconstruction.