A method of embedding dimension estimation based on symplectic geometry

Nonlinear Analysis of Surface EMG Signals

“…These eigenvalues , reflect the noise level in the data [49,55]. The corresponding matrix Q denotes symplectic eigenvectors of A.…”

“…Palus and Dvorak [37] explain why singular-value decomposition(SVD), the heart of the singular system analysis and by nature a linear method, may become misleading technique when it is used in nonlinear dynamics studies that reconstruction parameters are time-delay, embedding dimension (or embedding windows). For this, we propose a novel nonlinear analysis method based symplectic geometry, called symplectic principal component analysis(SPCA) [49].…”

“…However, from the view of data analysis, few literatures have employed symplectic geometry theory to explore the dynamics of the system. Our previous works have proposed the estimation of the embedding dimension based on symplectic geometry from a time series [49,[54][55][56]. Subsequently, Niu et al have used our method to evaluate sprinter's surface EMG signals [57].…”

Symplectic geometry spectrum analysis of nonlinear time series

“…Symplectic geometry originated from and is widely used in the study of Hamiltonian dynamic systems [26][27][28][29][30]. It has been rapidly expanded to describe singular differential equations, partial differential equations and other dynamic systems [31].…”

“…Several studies have shown that symplectic geometry-based methods are superior to SVDbased techniques in the detection of chaos [26,27], estimation of the embedding dimension of a nonlinear dynamic system [29] and de-noising nonlinear systems [30]. In this paper, we present a method, termed symplectic geometry spectrum analysis (SGSA), which is parallel to wavelets, EMD, ICA and SSA, to decompose a time series into the sum of a small number of independent and interpretable components.…”