Preprint: Symplectic Nonlinear Component Analysis

[Lucas Parra]

Dear fellow connectionists,

a preprint of the following NIPS*95 paper is available at:


  ftp://archive.cis.ohio-state.edu/pub/neuroprose/parra.nips95.ps.Z


             Symplectic Nonlinear Component Analysis

                        Lucas C. Parra 
                   Siemens Corporate Research
                     lucas at scr.siemens.com 


Statistically independent features can be extracted by finding a
factorial representation of a signal distribution. Principal Component
Analysis (PCA) accomplishes this for linear correlated and Gaussian
distributed signals. Independent Component Analysis (ICA), formalized
by Comon (1994), extracts features in the case of linear
statistical dependent but not necessarily Gaussian distributed
signals. Nonlinear Component Analysis finally should find a factorial
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
statistics.