Symplectic nonlinear component analysis

Statistically independent features can be extracted by finding a fac-torial representation of a signal distribution. Principal Component Analysis (PCA) accomplishes this for linear correlated and Gaus-sian distributed signals. Independent Component Analysis (ICA), formalized by Comon (1994), extracts features in the case of lin-ear statistical dependent but not necessarily Gaussian distributed signals. Nonlinear Component Analysis finally should find a facto-rial representation for nonlinear statistical dependent distributed signals. This paper proposes for this task a novel feed-forward, information conserving, nonlinear map- the explicit symplectic transformations. It also solves the problem of non-Gaussian output distributions by considering single coordinate higher order statis-tics