Symplectic Nonlinear Component Analysis

Part of Advances in Neural Information Processing Systems 8 (NIPS 1995)

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Lucas Parra


Statistically independent features can be extracted by finding a fac(cid:173) torial representation of a signal distribution. Principal Component Analysis (PCA) accomplishes this for linear correlated and Gaus(cid:173) sian distributed signals. Independent Component Analysis (ICA), formalized by Comon (1994), extracts features in the case of lin(cid:173) ear statistical dependent but not necessarily Gaussian distributed signals. Nonlinear Component Analysis finally should find a facto(cid:173) 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(cid:173) tics.