Quadratic independent component analysis
The transformation of a data set using a second-order polynomial mapping to find statistically independent components is considered (quadratic independent component analysis or ICA). Based on over-determined linear ICA, an algorithm together with separability conditions are given via linearization reduction. The linearization is achieved using a higher dimensional embedding defined by the linear parametrization of the monornials, which can also be applied for higher-order polynomials. The paper finishes with simulations for artificial data and natural images.
natural images nonlinear independent component analysis quadratic forms nonlinear blind source separation overdetermined blind source separation