EMBDSYMPLEC: MATLAB function to determine embedding dimension based on symplectic geometry
Determination of embedding dimension based on symplectic geometry. Let X be lag matrix of y, A=X'X, and A(n) is (n-1) times transformed form of A by Householder matrix. If descending sorted eigenvalues A(n) tend to be constant for dimension d+1 then d is the proper embedding dimension. let sigma be square of eigenvalues of A matrix, sigma1=(lambda^2)max,…,sigman=(lambda^2)min,where n is the dimension of X. If sigma1>sigma2>…>sigmad>sigma(d+1)>=...>=sigman, then d is the embedding dimension of the reconstruction system(Lei et al. 2002). The dimension before horizontal section of log(sigmai/tr(sigmai))plot is the proper dimension.
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