Symplectic Nonlinear Component Analysis

Statistically independent features can be extracted by finding a factorial representationof a signal distribution. Principal Component Analysis (PCA) accomplishes this for linear correlated and Gaussian distributedsignals. Independent Component Analysis (ICA), formalized by Comon (1994), extracts features in the case of linear statisticaldependent but not necessarily Gaussian distributed signals. Nonlinear Component Analysis finally should find a factorial representationfor 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 statistics. 1 Introduction In previous papers Deco and Brauer (1994) and Parra, Deco, and Miesbach (1995) suggest volume conserving transformations and factorization as the key elements for a nonlinear version of Independent Component Analysis. As a general class of volume conserving transformations Parra et al. (1995) propose the symplectic transformation. It was defined by an implicit nonlinear equation, which leads to a complex relaxation procedure for the function recall. In this paper an explicit form of the symplectic map is proposed, overcoming thus the computational problems.