I am familiar with the Principal Component Analysis method of covariance and dimensionality reduction. I am considering using its multivariate time series brother, Multivariate Singular Spectrum Analysis as a dimensionality reduction technique for a dataset of highly covariant time series.
Yet, if my understanding of the matter is correct, then nonlinear covariance between two dimensions in a real vector space ( let us say, quadratic or cubic covariance) would not be adequately captured and reduced by this method of analysis. Some covariance would surely be captured in one of the principal component vectors, but it wouldn’t be a perfect one, as nonlinear behavior cannot, by definition, be adequately represented by vectors in a real space as they are, well, linear.
If I suspect that some of my variables may be covariant in a nonlinear fashion, how may I go about reducing dimensionality in a way that doesn’t needlessly lose information about the original variables due to nonlinear covariance? Please forgive me if I am misguided, but this would be impossible under M-SSA, correct?