Design of regularized taper window with alternating optimization for reducing component mixing in generalized singular spectrum analysis

Singular spectrum analysis (SSA) is considered as 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 component mixing with each other. To address this issue, we present a comprehensive study of the generalized singular spectrum analysis (GSSA) model, which incorporates a taper window. To design an adaptive taper window for GSSA such that it can decompose various non-stationary signals, we reformulate the decomposition process of GSSA as an energy maximization model and introduce an L₁-norm regularization term as a measure of energy concentration in the taper window. A novel optimization problem which 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 L2-norm error reduction of 85% compared with conventional SSA in strength-identical sinusoids reconstruction. Copyright © 2025 IEEE.